From: guyeux Date: Thu, 24 May 2012 14:50:55 +0000 (+0200) Subject: Import initial X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/review_prng.git/commitdiff_plain/2a4c35a90cbd9b41b4a730aafa519c8e28ea04ab?ds=sidebyside Import initial --- diff --git a/mabase.bib b/mabase.bib new file mode 100644 index 0000000..0033443 --- /dev/null +++ b/mabase.bib @@ -0,0 +1,4479 @@ +% This file was created with JabRef 2.7.2. +% Encoding: UTF8 + +@INPROCEEDINGS{AdelsbachKS06, + author = {Andr{\'e} Adelsbach and Stefan Katzenbeisser and Ahmad-Reza Sadeghi}, + title = {A Computational Model for Watermark Robustness}, + booktitle = {Information Hiding}, + year = {2006}, + pages = {145-160}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/ih/2006}, + ee = {http://dx.doi.org/10.1007/978-3-540-74124-4_10}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@INPROCEEDINGS{BattiatoCGG99, + author = {Sebastiano Battiato and Dario Catalano and Giovanni Gallo and Rosario + Gennaro}, + title = {Robust Watermarking for Images Based on Color Manipulation}, + booktitle = {Information Hiding}, + year = {1999}, + pages = {302-317}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/ih/1999}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@INPROCEEDINGS{ComesanaPP05, + author = {Pedro Comesa{\~n}a and Luis P{\'e}rez-Freire and Fernando P{\'e}rez-Gonz{\'a}lez}, + title = {The Return of the Sensitivity Attack}, + booktitle = {IWDW}, + year = {2005}, + pages = {260-274}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/iwdw/2005}, + ee = {http://dx.doi.org/10.1007/11551492_20}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@INPROCEEDINGS{ComesanaPP05bis, + author = {Pedro Comesa{\~n}a and Luis P{\'e}rez-Freire and Fernando P{\'e}rez-Gonz{\'a}lez}, + title = {Fundamentals of Data Hiding Security and Their Application to Spread-Spectrum + Analysis}, + booktitle = {IH'05: Information Hiding Workshop}, + year = {2005}, + pages = {146-160}, + publisher = {Lectures Notes in Computer Science, Springer-Verlag}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/ih/2005}, + ee = {http://dx.doi.org/10.1007/11558859_12}, + owner = {guyeux}, + timestamp = {2009.06.30} +} + +@INPROCEEDINGS{CongJQZ06, + author = {Jin Cong and Yan Jiang and Zhiguo Qu and Zhongmei Zhang}, + title = {A Wavelet Packets Watermarking Algorithm Based on Chaos Encryption}, + booktitle = {ICCSA (1)}, + year = {2006}, + pages = {921-928}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/iccsa/2006-1}, + ee = {http://dx.doi.org/10.1007/11751540_100} +} + +@INPROCEEDINGS{DBLP:conf/focs/DziembowskiP08, + author = {Stefan Dziembowski and Krzysztof Pietrzak}, + title = {Leakage-Resilient Cryptography}, + booktitle = {FOCS}, + year = {2008}, + pages = {293-302}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/focs/2008}, + ee = {http://dx.doi.org/10.1109/FOCS.2008.56} +} + +@INCOLLECTION{Filiol10, + author = {Eric Filiol}, + title = {Viruses and Malware}, + booktitle = {Handbook of Information and Communication Security}, + year = {2010}, + pages = {747-769}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:reference/icsec/2010}, + ee = {http://dx.doi.org/10.1007/978-3-642-04117-4_34} +} + +@INPROCEEDINGS{Filiol00, + author = {Eric Filiol}, + title = {Decimation Attack of Stream Ciphers}, + booktitle = {INDOCRYPT}, + year = {2000}, + pages = {31-42}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/indocrypt/2000}, + ee = {http://link.springer.de/link/service/series/0558/bibs/1977/19770031.htm} +} + +@INPROCEEDINGS{Furon05, + author = {Teddy Furon}, + title = {A Survey of Watermarking Security}, + booktitle = {IWDW}, + year = {2005}, + pages = {201-215}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/iwdw/2005}, + ee = {http://dx.doi.org/10.1007/11551492_16}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@INPROCEEDINGS{DBLP:conf/cec/HiggsSHS10, + author = {Trent Higgs and Bela Stantic and Tamjidul Hoque and Abdul Sattar}, + title = {Genetic algorithm feature-based resampling for protein structure + prediction}, + booktitle = {IEEE Congress on Evolutionary Computation}, + year = {2010}, + pages = {1-8}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/cec/2010}, + ee = {http://dx.doi.org/10.1109/CEC.2010.5586149} +} + +@INPROCEEDINGS{Higgs2010, + author = {Trent Higgs and Bela Stantic and Tamjidul Hoque and Abdul Sattar}, + title = {Genetic algorithm feature-based resampling for protein structure + prediction}, + booktitle = {IEEE Congress on Evolutionary Computation}, + year = {2010}, + pages = {1-8}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/cec/2010}, + ee = {http://dx.doi.org/10.1109/CEC.2010.5586149} +} + +@INPROCEEDINGS{DBLP:conf/cec/HorvathC10, + author = {Dragos Horvath and Camelia Chira}, + title = {Simplified chain folding models as metaheuristic benchmark for tuning + real protein folding algorithms?}, + booktitle = {IEEE Congress on Evolutionary Computation}, + year = {2010}, + pages = {1-8}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/cec/2010}, + ee = {http://dx.doi.org/10.1109/CEC.2010.5585932} +} + +@INPROCEEDINGS{DBLP:conf/cec/IslamC10, + author = {Md. Kamrul Islam and Madhu Chetty}, + title = {Clustered memetic algorithm for protein structure prediction}, + booktitle = {IEEE Congress on Evolutionary Computation}, + year = {2010}, + pages = {1-8}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/cec/2010}, + ee = {http://dx.doi.org/10.1109/CEC.2010.5586187} +} + +@INPROCEEDINGS{Ker06, + author = {Andrew D. Ker}, + title = {Batch Steganography and Pooled Steganalysis}, + booktitle = {Information Hiding}, + year = {2006}, + pages = {265-281}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/ih/2006}, + ee = {http://dx.doi.org/10.1007/978-3-540-74124-4_18}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@INPROCEEDINGS{Lin2009, + author = {H.-Y. Lin and T.-C. Chiang}, + title = {Cooperative Secure Data Aggregation in Sensor Networks Using Elliptic + Curve Based Cryptosystems}, + booktitle = {CDVE}, + year = {2009}, + pages = {384-387}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/cdve/2009}, + ee = {http://dx.doi.org/10.1007/978-3-642-04265-2_58} +} + +@INPROCEEDINGS{DBLP:conf/cse/MaimourPH09, + author = {Moufida Maimour and CongDuc Pham and Doan B. Hoang}, + title = {A Congestion Control Framework for Handling Video Surveillance Traffics + on WSN}, + booktitle = {CSE (2)}, + year = {2009}, + pages = {943-948}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/cse/2009}, + ee = {http://dx.doi.org/10.1109/CSE.2009.200} +} + +@INPROCEEDINGS{DBLP:conf/icumt/MakhoulSP09, + author = {Abdallah Makhoul and Rachid Saadi and CongDuc Pham}, + title = {Coverage and adaptive scheduling algorithms for criticality management + on video wireless sensor networks}, + booktitle = {ICUMT}, + year = {2009}, + pages = {1-8}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/icumt/2009}, + ee = {http://dx.doi.org/10.1109/ICUMT.2009.5345630} +} + +@INPROCEEDINGS{Mittelholzer99, + author = {Thomas Mittelholzer}, + title = {An Information-Theoretic Approach to Steganography and Watermarking}, + booktitle = {Information Hiding}, + year = {1999}, + pages = {1-16}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/ih/1999}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@INPROCEEDINGS{PellegriniBA10, + author = {Andrea Pellegrini and Valeria Bertacco and Todd M. Austin}, + title = {Fault-based attack of RSA authentication}, + booktitle = {DATE}, + year = {2010}, + pages = {855-860}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/date/2010}, + ee = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5456933} +} + +@INPROCEEDINGS{DBLP:conf/cec/Perez-HernandezRG10, + author = {Luis Germ{\'a}n P{\'e}rez-Hern{\'a}ndez and Katya Rodr\'{\i}guez-V{\'a}zquez + and Ram{\'o}n Gardu{\~n}o-Ju{\'a}rez}, + title = {Estimation of 3D Protein Structure by means of parallel Particle + Swarm Optimization}, + booktitle = {IEEE Congress on Evolutionary Computation}, + year = {2010}, + pages = {1-8}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/cec/2010}, + ee = {http://dx.doi.org/10.1109/CEC.2010.5586549} +} + +@INPROCEEDINGS{WangNHZH07, + author = {Chuntao Wang and Jiangqun Ni and Jiwu Huang and Rongyue Zhang and + Meiying Huang}, + title = {Robust and High Capacity Image Watermarking Based on Jointly Coding + and Embedding Optimization}, + booktitle = {Information Hiding}, + year = {2007}, + pages = {65-79}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/ih/2007}, + ee = {http://dx.doi.org/10.1007/978-3-540-77370-2_5}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@INPROCEEDINGS{Zhao04, + author = {Jian Zhao and Mingquan Zhou and Hongmei Xie and Jinye Peng and Xin + Zhou}, + title = {A Novel Wavelet Image Watermarking Scheme Combined with Chaos Sequence + and Neural Network}, + booktitle = {ISNN (2)}, + year = {2004}, + pages = {663-668}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + crossref = {DBLP:conf/isnn/2004-2}, + ee = {http://springerlink.metapress.com/openurl.asp?genre=article{\&}issn=0302-9743{\&}volume=3174{\&}spage=663} +} + +@INPROCEEDINGS{Acharya05securecomparison, + author = {Acharya, Mithun and Girao, Joao and Westhoff, Dirk}, + title = {Secure Comparison of Encrypted Data in Wireless Sensor Networks}, + booktitle = {WIOPT '05: Proceedings of the Third International Symposium on Modeling + and Optimization in Mobile, Ad Hoc, and Wireless Networks}, + year = {2005}, + pages = {47--53}, + address = {Washington, DC, USA}, + publisher = {IEEE Computer Society}, + doi = {http://dx.doi.org/10.1109/WIOPT.2005.44}, + isbn = {0-7695-2267-X} +} + +@INPROCEEDINGS{Acimez07onthe, + author = {Onur Acıi\c{c}mez and \c{C}etin Kaya Ko\c{c} and Jean-Pierre Seifert}, + title = {On the power of simple branch prediction analysis }, + booktitle = {2007 ACM Symposium on Information, Computer and Communications Security + (ASIACCS'07)}, + year = {2007}, + pages = {312--320}, + publisher = {ACM Press} +} + +@ARTICLE{Adler65, + author = {R. L. Adler and A. G. Konheim and M. H. McAndrew}, + title = {Topological entropy}, + journal = {Trans. Amer. Math. Soc.}, + year = {1965}, + volume = {114}, + pages = {309-319}, + owner = {guyeux}, + timestamp = {2008.05.29} +} + +@INPROCEEDINGS{Agrawal04, + author = {Agrawal, Rakesh and Kiernan, Jerry and Srikant, Ramakrishnan and + Xu, Yirong}, + title = {Order preserving encryption for numeric data}, + booktitle = {SIGMOD '04: Proceedings of the 2004 ACM SIGMOD international conference + on Management of data}, + year = {2004}, + pages = {563--574}, + address = {New York, NY, USA}, + publisher = {ACM}, + doi = {http://doi.acm.org/10.1145/1007568.1007632}, + isbn = {1-58113-859-8}, + location = {Paris, France} +} + +@ARTICLE{Anfinsen20071973, + author = {Anfinsen, Christian B.}, + title = {Principles that Govern the Folding of Protein Chains}, + journal = {Science}, + year = {1973}, + volume = {181}, + pages = {223-230}, + number = {4096}, + doi = {10.1126/science.181.4096.223}, + eprint = {http://www.sciencemag.org/content/181/4096/223.full.pdf}, + url = {http://www.sciencemag.org/content/181/4096/223.short} +} + +@ARTICLE{Arques1998, + author = {D. G. Arqu\`{e}s and J. P. Fallot and C. J. Michel}, + title = {An evolutionary analytical model of a complementary circular code + simulating the protein coding genes, the 5' and 3' regions.}, + journal = {Bull Math Biol}, + year = {1998}, + volume = {60}, + pages = {163--194}, + number = {1}, + month = {Jan}, + abstract = {The self-complementary subset T0 = X0 [symbol: see text] ¿AAA, TTT¿ + with X0 = ¿AAC, AAT, ACC, ATC, ATT, CAG, CTC, CTG, GAA, GAC, GAG, + GAT, GCC, GGC, GGT, GTA, GTC, GTT, TAC, TTC¿ of 22 trinucleotides + has a preferential occurrence in the frame 0 (reading frame established + by the ATG start trinucleotide) of protein (coding) genes of both + prokaryotes and eukaryotes. The subsets T1 = X1 [symbol: see text] + ¿CCC¿ and T2 = X2 [symbol: see text] ¿GGG¿ of 21 trinucleotides have + a preferential occurrence in the shifted frames 1 and 2 respectively + (frame 0 shifted by one and two nucleotides respectively in the 5'-3' + direction). T1 and T2 are complementary to each other. The subset + T0 contains the subset X0 which has the rarity property (6 x 10(-8) + to be a complementary maximal circular code with two permutated maximal + circular codes X1 and X2 in the frames 1 and 2 respectively. X0 is + called a C3 code. A quantitative study of these three subsets T0, + T1, T2 in the three frames 0, 1, 2 of protein genes, and the 5' and + 3' regions of eukaryotes, shows that their occurrence frequencies + are constant functions of the trinucleotide positions in the sequences. + The frequencies of T0, T1, T2 in the frame 0 of protein genes are + 49, 28.5 and 22.5\% respectively. In contrast, the frequencies of + T0, T1, T2 in the 5' and 3' regions of eukaryotes, are independent + of the frame. Indeed, the frequency of T0 in the three frames of + 5' (respectively 3') regions is equal to 35.5\% (respectively 38\%) + and is greater than the frequencies T1 and T2, both equal to 32.25\% + (respectively 31\%) in the three frames. Several frequency asymmetries + unexpectedly observed (e.g. the frequency difference between T1 and + T2 in the frame 0), are related to a new property of the subset T0 + involving substitutions. An evolutionary analytical model at three + parameters (p, q, t) based on an independent mixing of the 22 codons + (trinucleotides in frame 0) of T0 with equiprobability (1/22) followed + by t approximately 4 substitutions per codon according to the proportions + p approximately 0.1, q approximately 0.1 and r = 1 - p - q approximately + 0.8 in the three codon sites respectively, retrieves the frequencies + of T0, T1, T2 observed in the three frames of protein genes and explains + these asymmetries. Furthermore, the same model (0.1, 0.1, t) after + t approximately 22 substitutions per codon, retrieves the statistical + properties observed in the three frames of the 5' and 3' regions. + The complex behaviour of these analytical curves is totally unexpected + and a priori difficult to imagine.}, + doi = {10.1006/bulm.1997.0033}, + institution = {Equipe de Biologie Théorique, Université de Marne la Vallée, Institut + Gaspard Monge, Noisy Le Grand, France. Arqu\`{e}s@univ-mlv.fr}, + keywords = {Animals; Biological Evolution; Codon, genetics; Genetic Code; Humans; + Mammals; Models, Genetic; Probability; Proteins, genetics; Rodentia; + Vertebrates}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pii = {S0092-8240(97)90033-1}, + pmid = {9530018}, + timestamp = {2011.05.05}, + url = {http://dx.doi.org/10.1006/bulm.1997.0033} +} + +@ARTICLE{Arques1994, + author = {D. G. Arqu\`{e}s and C. J. Michel}, + title = {Analytical expression of the purine/pyrimidine autocorrelation function + after and before random mutations.}, + journal = {Math Biosci}, + year = {1994}, + volume = {123}, + pages = {103--125}, + number = {1}, + month = {Sep}, + abstract = {The mutation process is a classical evolutionary genetic process. + The type of mutations studied here is the random substitutions of + a purine base R (adenine or guanine) by a pyrimidine base Y (cytosine + or thymine) and reciprocally (transversions). The analytical expressions + derived allow us to analyze in genes the occurrence probabilities + of motifs and d-motifs (two motifs separated by any d bases) on the + R/Y alphabet under transversions. These motif probabilities can be + obtained after transversions (in the evolutionary sense; from the + past to the present) and, unexpectedly, also before transversions + (after back transversions, in the inverse evolutionary sense, from + the present to the past). This theoretical part in Section 2 is a + first generalization of a particular formula recently derived. The + application in Section 3 is based on the analytical expression giving + the autocorrelation function (the d-motif probabilities) before transversions. + It allows us to study primitive genes from actual genes. This approach + solves a biological problem. The protein coding genes of chloroplasts + and mitochondria have a preferential occurrence of the 6-motif YRY(N)6YRY + (maximum of the autocorrelation function for d = 6, N = R or Y) with + a periodicity modulo 3. The YRY(N)6YRY preferential occurrence without + the periodicity modulo 3 is also observed in the RNA coding genes + (ribosomal, transfer, and small nuclear RNA genes) and in the noncoding + genes (introns and 5' regions of eukaryotic nuclei). However, there + are two exceptions to this YRY(N)6YRY rule: the protein coding genes + of eukaryotic nuclei, and prokaryotes, where YRY(N)6YRY has the second + highest value after YRY(N)0YRY (YRYYRY) with a periodicity modulo + 3. When we go backward in time with the analytical expression, the + protein coding genes of both eukaryotic nuclei and prokaryotes retrieve + the YRY(N)6YRY preferential occurrence with a periodicity modulo + 3 after 0.2 back transversions per base. In other words, the actual + protein coding genes of chloroplasts and mitochondria are similar + to the primitive protein coding genes of eukaryotic nuclei and prokaryotes. + On the other hand, this application represents the first result concerning + the mutation process in the model of DNA sequence evolution we recently + proposed. According to this model, the actual genes on the R/Y alphabet + derive from two successive evolutionary genetic processes: an independent + mixing of a few nonrandom types of oligonucleotides leading to genes + called primitive followed by a mutation process in these primitive + genes.(ABSTRACT TRUNCATED AT 400 WORDS)}, + institution = {Université de Franche-Comté, Laboratoire d'Informatique de Besançon, + France.}, + keywords = {Base Sequence; Biological Evolution; DNA, genetics; Mathematics; Models, + Genetic; Mutation; Probability; Proteins, genetics; Purines; Pyrimidines}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pii = {0025-5564(94)90020-5}, + pmid = {7949744}, + timestamp = {2011.05.05} +} + +@ARTICLE{Arques1993, + author = {D. G. Arqu\`{e}s and C. J. Michel}, + title = {Analytical expression of the purine/pyrimidine codon probability + after and before random mutations.}, + journal = {Bull Math Biol}, + year = {1993}, + volume = {55}, + pages = {1025--1038}, + number = {6}, + month = {Nov}, + abstract = {Recently, we proposed a new model of DNA sequence evolution (Arqu\`{e}s + and Michel. 1990b. Bull. math. Biol. 52, 741-772) according to which + actual genes on the purine/pyrimidine (R/Y) alphabet (R = purine + = adenine or guanine, Y = pyrimidine = cytosine or thymine) are the + result of two successive evolutionary genetic processes: (i) a mixing + (independent) process of non-random oligonucleotides (words of base + length less than 10: YRY(N)6, YRYRYR and YRYYRY are so far identified; + N = R or Y) leading to primitive genes (words of several hundreds + of base length) and followed by (ii) a random mutation process, i.e., + transformations of a base R (respectively Y) into the base Y (respectively + R) at random sites in these primitive genes. Following this model + the problem investigated here is the study of the variation of the + 8 R/Y codon probabilities RRR, ..., YYY under random mutations. Two + analytical expressions solved here allow analysis of this variation + in the classical evolutionary sense (from the past to the present, + i.e., after random mutations), but also in the inverted evolutionary + sense (from the present to the past, i.e., before random mutations). + Different properties are also derived from these formulae. Finally, + a few applications of these formulae are presented. They prove the + proposition in Arqu\`{e}s and Michel (1990b. Bull. math. Biol. 52, + 741-772), Section 3.3.2, with the existence of a maximal mean number + of random mutations per base of the order 0.3 in the protein coding + genes. They also confirm the mixing process of oligonucleotides by + excluding the purine/pyrimidine contiguous and alternating tracts + from the formation process of primitive genes.}, + institution = {Université de Franche-Comté, Besançon, France.}, + keywords = {Base Sequence; Codon; DNA, chemistry/genetics; Mathematics; Models, + Genetic; Mutation; Probability; Purines; Pyrimidines}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pmid = {8281128}, + timestamp = {2011.05.05} +} + +@ARTICLE{Arques1993b, + author = {D. G. Arqu\`{e}s and C. J. Michel}, + title = {Identification and simulation of new non-random statistical properties + common to different eukaryotic gene subpopulations.}, + journal = {Biochimie}, + year = {1993}, + volume = {75}, + pages = {399--407}, + number = {5}, + abstract = {The nucleotide distribution in protein coding genes, introns and transfer + RNA genes of eukaryotic subpopulations (primates, rodent and mammals) + is studied by autocorrelation functions. The autocorrelation function + analysing the occurrence probability of the i-motif YRY(N)iYRY (YRY-function) + in protein coding genes and transfer RNA genes of these three eukaryotic + subpopulations retrieves the preferential occurrence of YRY(N)6YRY + (R = purine = adenine or guanine, Y = pyrimidine = cytosine or thymine, + N = R or Y). The autocorrelation functions analysing the occurrence + probability of the i-motifs RRR(N)iRRR (RRR-function) and YYY(N)iYYY + (YYY-function) identify new non-random genetic statistical properties + in these three eukaryotic subpopulations, mainly: i) in their protein + coding genes: local maxima for i identical to 6 [12] (peaks for i + = 6, 18, 30, 42) with the RRR-function and local maxima for i identical + to 8 [10] (peaks for i = 8, 18, 28) with the YYY-function; and ii) + in their introns: local maxima for i identical to 3 [6] (peaks for + i = 3, 9, 15) and a short linear decrease followed by a large exponential + decrease both with the RRR- and YYY-functions. The non-random properties + identified in eukaryotic intron subpopulations are modelised with + a process of random insertions and deletions of nucleotides simulating + the RNA editing.}, + institution = {Equipe de Biologie Théorique, Université de Franche-Comté, Laboratoire + d'Informatique de Besançon, France.}, + keywords = {Animals; Base Sequence; Data Interpretation, Statistical; Genes; Introns; + Mammals; Models, Genetic; Primates; Probability; Proteins, genetics; + RNA Editing; RNA, Transfer, genetics; Rodentia; Sequence Analysis, + DNA}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pii = {0300-9084(93)90173-P}, + pmid = {8347726}, + timestamp = {2011.05.05} +} + +@ARTICLE{Arques1992, + author = {D. G. Arqu\`{e}s and C. J. Michel}, + title = {A simulation of the genetic periodicities modulo 2 and 3 with processes + of nucleotide insertions and deletions.}, + journal = {J Theor Biol}, + year = {1992}, + volume = {156}, + pages = {113--127}, + number = {1}, + month = {May}, + abstract = {Recently, a new genetic process termed RNA editing has been identified + showing insertions and deletions of nucleotides in particular RNA + molecules. On the other hand, there are a few non-random statistical + properties in genes: in particular, the periodicity modulo 3 (P3) + associated with an open reading frame, the periodicity modulo 2 (P2) + associated with alternating purine/pyrimidine stretches, the YRY(N)6YRY + preferential occurrence (R = purine = adenine or guanine, Y = pyrimidine + = cytosine or thymine, N = R or Y) representing a "code" of the DNA + helix pitch, etc. The problem investigated here is whether a process + of the type RNA editing can lead to the non-random statistical properties + commonly observed in genes. This paper will show in particular that: + The process of insertions and deletions of mononucleotides in the + initial sequence [YRY(N)3]* [series of YRY(N)3] can lead to the periodicity + modulo 2 (P2). The process of insertions and deletions of trinucleotides + in the initial sequence [YRY(N)6]* [series of YRY(N)6] can lead to + the periodicity modulo 3 (P3) and the YRY(N)6YRY preferential occurrence. + Furthermore, these two processes lead to a strong correlation with + the reality, namely the mononucleotide insertion/deletion process, + with the 5' eukaryotic regions and the trinucleotide insertion/deletion + process, with the eukaryotic protein coding genes.}, + institution = {Université de Franche-Comté, Laboratoire d'Informatique de Besançon, + Unité Associée CNRS No 822, France.}, + keywords = {Chromosome Deletion; Computer Simulation; Humans; Models, Genetic; + Mutagenesis, genetics; RNA, genetics}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pmid = {1379311}, + timestamp = {2011.05.05} +} + +@ARTICLE{Arques1990, + author = {D. G. Arqu\`{e}s and C. J. Michel}, + title = {Periodicities in coding and noncoding regions of the genes.}, + journal = {J Theor Biol}, + year = {1990}, + volume = {143}, + pages = {307--318}, + number = {3}, + month = {Apr}, + abstract = {Gene population statistical studies of protein coding genes and introns + have identified two types of periodicities on the purine/pyrimidine + alphabet: (i) the modulo 3 periodicity or coding periodicity (periodicity + P3) in protein coding genes of eukaryotes, prokaryotes, viruses, + chloroplasts, mitochondria, plasmids and in introns of viruses and + mitochondria, and (ii) the modulo 2 periodicity (periodicity P2) + in the eukaryotic introns. The periodicity study is herein extended + to the 5' and 3' regions of eukaryotes, prokaryotes and viruses and + shows: (i) the periodicity P3 in the 5' and 3' regions of eukaryotes. + Therefore, these observations suggest a unitary and dynamic concept + for the genes as for a given genome, the 5' and 3' regions have the + genetic information for protein coding genes and for introns: (1) + In the eukaryotic genome, the 5' (P2 and P3) and 3' (P2 and P3) regions + have the information for protein coding genes (P3) and for introns + (P2). The intensity of P3 is high in 5' regions and weak in 3' regions, + while the intensity of P2 is weak in 5' regions and high in 3' regions. + (2) In the prokaryotic genome, the 5' (P3) and 3' (P3) regions have + the information for protein coding genes (P3). (3) In the viral genome, + the 5' (P3) and 3' (P3) regions have the information for protein + coding genes (P3) and for introns (P3). The absence of P2 in viral + introns (in opposition to eukaryotic introns) may be related to the + absence of P2 in 5' and 3' regions of viruses.}, + institution = {Université de Franche-Comté, Unité Associée CNRS No. 822, Besançon, + France.}, + keywords = {Animals; Base Sequence; Eukaryotic Cells; Genes; Introns; Prokaryotic + Cells; Purine Nucleotides; Pyrimidine Nucleotides; Repetitive Sequences, + Nucleic Acid; Viruses, genetics}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pmid = {2385108}, + timestamp = {2011.05.05} +} + +@ARTICLE{Arques1990a, + author = {D. G. Arqu\`{e}s and C. J. Michel}, + title = {A model of DNA sequence evolution.}, + journal = {Bull Math Biol}, + year = {1990}, + volume = {52}, + pages = {741--772}, + number = {6}, + abstract = {Statistical studies of gene populations on the purine/pyrimidine alphabet + have shown that the mean occurrence probability of the i-motif YRY(N)iYRY + (R = purine, Y = pyrimidine, N = R or Y) is not uniform by varying + i in the range, but presents a maximum at i = 6 in the following + populations: protein coding genes of eukaryotes, prokaryotes, chloroplasts + and mitochondria, and also viral introns, ribosomal RNA genes and + transfer RNA genes (Arqu\`{e}s and Michel, 1987b, J. theor. Biol. + 128, 457-461). From the "universality" of this observation, we suggested + that the oligonucleotide YRY(N)6 is a primitive one and that it has + a central function in DNA sequence evolution (Arqu\`{e}s and Michel, + 1987b, J. theor. Biol. 128, 457-461). Following this idea, we introduce + a concept of a model of DNA sequence evolution which will be validated + according to a schema presented in three parts. In the first part, + using the last version of the gene database, the YRY(N)6YRY preferential + occurrence (maximum at i = 6) is confirmed for the populations mentioned + above and is extended to some newly analysed populations: chloroplast + introns, chloroplast 5' regions, mitochondrial 5' regions and small + nuclear RNA genes. On the other hand, the YRY(N)6YRY preferential + occurrence and periodicities are used in order to classify 18 gene + populations. In the second part, we will demonstrate that several + statistical features characterizing different gene populations (in + particular the YRY(N)6YRY preferential occurrence and the periodicities) + can be retrieved from a simple Markov model based on the mixing of + the two oligonucleotides YRY(N)6 and YRY(N)3 and based on the percentages + of RYR and YRY in the unspecified trinucleotides (N)3 of YRY(N)6 + and YRY(N)3. Several properties are identified and prove in particular + that the oligonucleotide mixing is an independent process and that + several different features are functions of a unique parameter. In + the third part, the return of the model to the reality shows a strong + correlation between reality and simulation concerning the presence + of a large alternating purine/pyrimidine stretches and of periodicities. + It also contributes to a greater understanding of biological reality, + e.g. the presence or the absence of large alternating purine/pyrimidine + stretches can be explained as being a simple consequence of the mixing + of two particular oligonucleotides. Finally, we believe that such + an approach is the first step toward a unified model of DNA sequence + evolution allowing the molecular understanding of both the origin + of life and the actual biological reality.}, + institution = {Université de Franche-Comté, Laboratoire d'Informatique de Besançon, + Unité Associée CNRS No 822, France.}, + keywords = {Base Sequence; Biological Evolution; DNA, genetics; Genetics, Population; + Models, Genetic}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pmid = {2279193}, + timestamp = {2011.05.05} +} + +@ARTICLE{Arques1993a, + author = {D. G. Arqu\`{e}s and C. J. Michel and K. Orieux}, + title = {Identification and simulation of new non-random statistical properties + common to different populations of eukaryotic non-coding genes.}, + journal = {J Theor Biol}, + year = {1993}, + volume = {161}, + pages = {329--342}, + number = {3}, + month = {Apr}, + abstract = {The autocorrelation function analysing the occurrence probability + of the i-motif YRY(N)iYRY in genes allows the identification of mainly + two periodicities modulo 2, 3 and the preferential occurrence of + the motif YRY(N)6YRY (R = purine = adenine or guanine, Y = pyrimidine + = cytosine or thymine, N = R or Y). These non-random genetic statistical + properties can be simulated by an independent mixing of the three + oligonucleotides YRYRYR, YRYYRY and YRY(N)6 (Arqu\`{e}s & Michel, + 1990b). The problem investigated in this study is whether new properties + can be identified in genes with other autocorrelation functions and + also simulated with an oligonucleotide mixing model. The two autocorrelation + functions analysing the occurrence probability of the i-motifs RRR(N)iRRR + and YYY(N)iYYY simultaneously identify three new non-random genetic + statistical properties: a short linear decrease, local maxima for + i identical to 3[6] (i = 3, 9, etc) and a large exponential decrease. + Furthermore, these properties are common to three different populations + of eukaryotic non-coding genes: 5' regions, introns and 3' regions + (see section 2). These three non-random properties can also be simulated + by an independent mixing of the four oligonucleotides R8, Y8, RRRYRYRRR, + YYYRYRYYY and large alternating R/Y series. The short linear decrease + is a result of R8 and Y8, the local maxima for i identical to 3[6], + of RRRYRYRRR and YYYRYRYYY, and the large exponential decrease, of + large alternating R/Y series (section 3). The biological meaning + of these results and their relation to the previous oligonucleotide + mixing model are presented in the Discussion.}, + doi = {10.1006/jtbi.1993.1059}, + institution = {Equipe de Biologie Théorique, Université de Franche-Comté, Laboratoire + d'Informatique de Besançon, France.}, + keywords = {Animals; Biological Evolution; Genes, genetics; Models, Genetic; Models, + Statistical; Mutation, genetics; Oligonucleotides, genetics; Probability}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pii = {S0022-5193(83)71059-3}, + pmid = {8331957}, + timestamp = {2011.05.05}, + url = {http://dx.doi.org/10.1006/jtbi.1993.1059} +} + +@ARTICLE{Arroyo08, + author = {David Arroyo and Gonzalo Alvarez and Veronica Fernandez}, + title = {On the inadequacy of the logistic map for cryptographic applications}, + journal = {X Reunión Española sobre Criptología y Seguridad de la Información + (X RECSI)}, + year = {2008}, + volume = {1}, + pages = {77-82}, + owner = {christophe}, + timestamp = {2010.03.01} +} + +@MISC{Backofen99algorithmicapproach, + author = {R. Backofen and S. Will and P. Clote}, + title = {Algorithmic Approach To Quantifying The Hydrophobic Force Contribution + In Protein Folding}, + year = {1999} +} + +@INPROCEEDINGS{bgc11:ip, + author = {Bahi, Jacques and C\^ot\'e, Nathalie and Guyeux, Christophe}, + title = {Chaos of Protein Folding}, + booktitle = {IJCNN 2011, Int. Joint Conf. on Neural Networks}, + year = {2011}, + pages = {1948--1954}, + address = {San Jose, California, United States}, + month = jul, + classement = {ACTI}, + doi = {10.1109/IJCNN.2011.6033463}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no}, + url = {http://dx.doi.org/10.1109/IJCNN.2011.6033463} +} + +@ARTICLE{bgcs11:ij, + author = {Bahi, Jacques and C\^ot\'e, Nathalie and Guyeux, Christophe and Salomon, + Michel}, + title = {Protein Folding in the {2D} Hydrophobic-Hydrophilic {(HP)} Square + Lattice Model is Chaotic}, + journal = {Cognitive Computation}, + year = {2011}, + pages = {1--17}, + note = {Published online. Paper version to appear}, + classement = {ACLI}, + doi = {10.1007/s12559-011-9118-z}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + impact-factor = {#}, + inhal = {no}, + isi-acro = {#}, + publisher = {Springer}, + url = {http://dx.doi.org/10.1007/s12559-011-9118-z} +} + +@INPROCEEDINGS{bcgr11:ip, + author = {Bahi, Jacques and Couchot, Jean-Fran\c{c}ois and Guyeux, Christophe + and Richard, Adrien}, + title = {On the Link Between Strongly Connected Iteration Graphs and Chaotic + Boolean Discrete-Time Dynamical Systems}, + booktitle = {FCT'11, 18th Int. Symp. on Fundamentals of Computation Theory}, + year = {2011}, + volume = {*}, + series = {LNCS}, + pages = {***--***}, + address = {Oslo, Norway}, + month = aug, + note = {To appear}, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@ARTICLE{bg10:ij, + author = {Bahi, Jacques and Guyeux, Christophe}, + title = {Hash Functions Using Chaotic Iterations}, + journal = {Journal of Algorithms \& Computational Technology}, + year = {2010}, + volume = {4}, + pages = {167--181}, + number = {2}, + classement = {ACLI}, + doi = {10.1260/1748-3018.4.2.167}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + impact-factor = {#}, + inhal = {no}, + isi-acro = {#}, + url = {http://dx.doi.org/10.1260/1748-3018.4.2.167} +} + +@INPROCEEDINGS{guyeux10ter, + author = {Bahi, Jacques and Guyeux, Christophe}, + title = {A new chaos-based watermarking algorithm}, + booktitle = {SECRYPT'10, Int. conf. on security and cryptography}, + year = {2010}, + pages = {455--458}, + address = {Athens, Greece}, + month = jul, + publisher = {SciTePress}, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@ARTICLE{bgm11:ij, + author = {Bahi, Jacques and Guyeux, Christophe and Makhoul, Abdallah}, + title = {Two Security Layers for Hierarchical Data Aggregation in Sensor Networks}, + journal = {IJAACS, International Journal of Autonomous and Adaptive Communications + Systems}, + year = {2011}, + volume = {*}, + pages = {***--***}, + number = {*}, + note = {Accepted manuscript. To appear}, + classement = {ACLI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + impact-factor = {#}, + inhal = {no}, + isi-acro = {#} +} + +@INPROCEEDINGS{guyeux10bis, + author = {Bahi, Jacques and Guyeux, Christophe and Makhoul, Abdallah}, + title = {Efficient and Robust Secure Aggregation of Encrypted Data in Sensor + Networks}, + booktitle = {SENSORCOMM'10, 4-th Int. Conf. on Sensor Technologies and Applications}, + year = {2010}, + pages = {472--477}, + address = {Venice-Mestre, Italy}, + month = jul, + classement = {ACTI}, + doi = {10.1109/SENSORCOMM.2010.76}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no}, + url = {http://dx.doi.org/10.1109/SENSORCOMM.2010.76} +} + +@INPROCEEDINGS{guyeuxVictoria, + author = {Bahi, Jacques and Guyeux, Christophe and Makhoul, Abdallah}, + title = {Secure Data Aggregation in Wireless Sensor Networks. Homomorphism + versus Watermarking Approach}, + booktitle = {ADHOCNETS 2010, 2nd Int. Conf. on Ad Hoc Networks}, + year = {2010}, + volume = {49}, + series = {Lecture Notes in ICST}, + pages = {344--358}, + address = {Victoria, Canada}, + month = aug, + classement = {ACTI}, + doi = {10.1007/978-3-642-17994-5_23}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no}, + url = {http://dx.doi.org/10.1007/978-3-642-17994-5_23} +} + +@INPROCEEDINGS{bgmp11:ip, + author = {Bahi, Jacques and Guyeux, Christophe and Makhoul, Abdallah and Pham, + Congduc}, + title = {Secure scheduling of wireless video sensor nodes for surveillance + applications}, + booktitle = {ADHOCNETS 11, 3rd Int. ICST Conference on Ad Hoc Networks}, + year = {2011}, + volume = {0089}, + series = {LNICST}, + pages = {***--***}, + address = {Paris, France}, + month = sep, + publisher = {Springer}, + note = {To appear}, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@INPROCEEDINGS{bgs11:ip, + author = {Bahi, Jacques and Guyeux, Christophe and Salomon, Michel}, + title = {Building a Chaotic Proven Neural Network}, + booktitle = {ICCANS 2011, IEEE Int. Conf. on Computer Applications and Network + Security}, + year = {2011}, + pages = {***--***}, + address = {Maldives, Maldives}, + month = may, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@INPROCEEDINGS{bgw10:ip, + author = {Bahi, Jacques and Guyeux, Christophe and Wang, Qianxue}, + title = {A Pseudo Random Numbers Generator Based on Chaotic Iterations. Application + to Watermarking}, + booktitle = {WISM 2010, Int. Conf. on Web Information Systems and Mining}, + year = {2010}, + volume = {6318}, + series = {LNCS}, + pages = {202--211}, + address = {Sanya, China}, + month = oct, + classement = {ACTI}, + doi = {10.1007/978-3-642-16515-3_26}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no}, + url = {http://dx.doi.org/10.1007/978-3-642-16515-3_26} +} + +@INPROCEEDINGS{bgw09:ip, + author = {Bahi, Jacques and Guyeux, Christophe and Wang, Qianxue}, + title = {A novel pseudo-random generator based on discrete chaotic iterations}, + booktitle = {INTERNET'09, 1-st Int. Conf. on Evolving Internet}, + year = {2009}, + pages = {71--76}, + address = {Cannes, France}, + month = aug, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@INPROCEEDINGS{bmg10:onp, + author = {Bahi, Jacques and Makhoul, Abdallah and Guyeux, Christophe}, + title = {Efficient and Robust Secure Aggregation of Encrypted Data in Sensor + Networks for critical applications}, + booktitle = {RESSACS, Journ\'ee th\'ematique PHC/ResCom sur RESeaux de capteurS + et Applications Critiques de Surveillance}, + year = {2010}, + address = {Bayonne, France}, + month = jun, + note = {Communication orale}, + classement = {COM}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@INPROCEEDINGS{guyeuxBayonne, + author = {Bahi, Jacques and Makhoul, Abdallah and Guyeux, Christophe}, + title = {Efficient and Robust Secure Aggregation of Encrypted Data in Sensor + Networks for critical applications}, + booktitle = {RESSACS, Journ\'ee th\'ematique PHC/ResCom sur RESeaux de capteurS + et Applications Critiques de Surveillance}, + year = {2010}, + address = {Bayonne, France}, + month = jun, + note = {Communication orale}, + classement = {COM}, + equipe = {and}, + inhal = {no} +} + +@ARTICLE{bs10:ij, + author = {Bahi, Jacques and Salomon, Michel}, + title = {A Decentralized Energy-based Diffusion Algorithm to Increase the + Lifetime of {MANETs}}, + journal = {Computer Networks Journal}, + year = {2010}, + pages = {***--***}, + note = {Accepted manuscript. To appear}, + classement = {ACLI}, + equipe = {and}, + impact-factor = {1.201}, + inhal = {no}, + isi-acro = {#}, + publisher = {Elsevier} +} + +@ARTICLE{Bahi2000, + author = {J. M. Bahi}, + title = {Boolean totally asynchronous iterations}, + journal = {Int. Journal of Mathematical Algorithms}, + year = {2000}, + volume = {1}, + pages = {331--346}, + owner = {guyeux}, + timestamp = {17/02/2008} +} + +@ARTICLE{Bahi2000bis, + author = {Jacques M. Bahi}, + title = {Asynchronous iterative algorithms for nonexpansive linear systems}, + journal = {Journal of Parallel and Distributed Computing}, + year = {2000}, + volume = {60}, + pages = {92--112}, + owner = {guyeux}, + timestamp = {2009.01.10} +} + +@ARTICLE{Bahi1999, + author = {J. M. Bahi}, + title = {Parallel synchronous chaotic iterations for singular linear systems}, + journal = {Parallel Algorithms and Applications}, + year = {1999}, + volume = {14}, + pages = {19--35}, + owner = {guyeux}, + timestamp = {17/02/2008} +} + +@ARTICLE{Bahi1998, + author = {Jacques M. Bahi}, + title = {Algorithmes paralleles asynchrones pour les systemes singuliers}, + journal = {Comptes Rendus de l'Academie des Sciences}, + year = {1998}, + volume = {t. 326, serie 1}, + pages = {1421--1425}, + owner = {guyeux}, + timestamp = {2009.01.18} +} + +@PHDTHESIS{bahi98, + author = {Jacques M. Bahi}, + title = {Méthodes itératives dans des espaces produits. Application au calcul + parall\`{e}le}, + school = {Université de Franche-Comté}, + year = {1998}, + type = {Habilitation à diriger des recherches}, + owner = {christophe}, + timestamp = {2010.08.24} +} + +@PHDTHESIS{bahi91, + author = {Jacques M. Bahi}, + title = {Algorithmes asynchrones pour des syst\`{e}mes différentiels-algébriques. + Simulation numérique sur des exemples de circuits électriques}, + school = {Université de Franche-Comté}, + year = {1991}, + owner = {christophe}, + timestamp = {2010.08.24} +} + +@ARTICLE{bcv06:ij, + author = {Jacques M. Bahi and Sylvain Contassot-Vivier}, + title = {Basins of attraction in fully asynchronous discrete-time discrete-state + dynamic networks}, + journal = {IEEE Transactions on Neural Networks}, + year = {2006}, + volume = {17}, + pages = {397--408}, + number = {2}, + inhal = {no}, + owner = {guyeux}, + timestamp = {2009.12.04} +} + +@ARTICLE{Bahi2002, + author = {J.~M. Bahi and S. Contassot-Vivier}, + title = {Stability of fully asynchronous discrete-time discrete state dynamic + networks}, + journal = {IEEE Transactions on Neural Networks}, + year = {2002}, + volume = {13(6)}, + pages = {1353-1363}, + owner = {guyeux}, + timestamp = {2009.02.14} +} + +@TECHREPORT{bcgg10:ir, + author = {Bahi, J. M. and Couchot, J.-F. and Grasset, O. and Guyeux, C.}, + title = {{D}iscrete {D}ynamical {S}ystems: {N}ecessary {D}ivergence {C}onditions + for {S}ynchronous {I}terations}, + institution = {LIFC - Laboratoire d'{I}nformatique de l'{U}niversit\'{e} de {F}ranche + {C}omt\'{e}}, + year = {2010}, + type = {Research Report}, + number = {RR2010-04}, + month = sep, + pdf = {/~publis/papers/pub/2010/RR2010-04.pdf} +} + +@ARTICLE{guyeux09, + author = {Bahi, Jacques M. and Guyeux, Christophe}, + title = {Hash Functions Using Chaotic Iterations}, + journal = {Journal of Algorithms \& Computational Technology}, + year = {2010}, + volume = {4}, + pages = {167--181}, + number = {2}, + classement = {ACLNI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + impact-factor = {#}, + inhal = {no}, + isi-acro = {#} +} + +@INPROCEEDINGS{guyeux10, + author = {Bahi, Jacques M. and Guyeux, Christophe}, + title = {Topological chaos and chaotic iterations, application to Hash functions}, + booktitle = {WCCI'10, IEEE World Congress on Computational Intelligence}, + year = {2010}, + pages = {1--7}, + address = {Barcelona, Spain}, + month = jul, + note = {Best paper award}, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@MISC{ih10, + author = {Jacques M. Bahi and Christophe Guyeux}, + title = {A chaos-based approach for information hiding security.}, + howpublished = {arXiv}, + month = {April}, + year = {2010}, + institution = {Computer Science Laboratory LIFC, University of Franche-Comte, France} +} + +@ARTICLE{arxiv, + author = {Jacques M. Bahi and Christophe Guyeux}, + title = {A watermarking algorithm satisfying topological chaos properties}, + journal = {CoRR}, + year = {2008}, + volume = {abs/0810.4713}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + ee = {http://arxiv.org/abs/0810.4713} +} + +@ARTICLE{Bahi2008, + author = {Jacques M. Bahi and Christophe Guyeux}, + title = {Chaotic iterations and topological chaos}, + year = {2008}, + abstract = {Chaotic iterations have been introduced on the one hand by Chazan, + Miranker [5] and Miellou [9] in a numerical analysis context, and + on the other hand by Robert [11] and Pellegrin [10] in the discrete + dynamical systems framework. In both cases, the objective was to + derive conditions of convergence of such iterations to a fixed state. + In this paper, a new point of view is presented, the goal here is + to derive conditions under which chaotic iterations admit a chaotic + behaviour in a rigorous mathematical sense. Contrary to what has + been studied in the literature, convergence is not desired. More + precisely, we establish in this paper a link between the concept + of chaotic iterations on a finite set and the notion of topological + chaos [8], [6], [7]. We are motivated by concrete applications of + our approach, such as the use of chaotic boolean iterations in the + computer security field. Indeed, the concept of chaos is used in + many areas of data security without real rigorous theoretical foundations, + and without using the fundamental properties that allow chaos. The + wish of this paper is to bring a bit more mathematical rigour in + this field.}, + citeseerurl = {\href{http://arxiv.org/abs/0810.3154v1}{arXiv:0810.3154}}, + comment = {arXiv}, + comments = {6 pages}, + eprint = {\href{http://arxiv.org/abs/0810.3154v1}{arXiv:0810.3154}}, + oai2identifier = {0810.3154}, + owner = {guyeux}, + timestamp = {2008.10.23}, + url = {\href{http://arxiv.org/abs/0810.3154v1}{arXiv:0810.3154}} +} + +@ARTICLE{arxivRNNchaos, + author = {Jacques M. Bahi and Christophe Guyeux and Michel Salomon}, + title = {Building a Chaotic Proved Neural Network}, + journal = {CoRR}, + year = {2011}, + volume = {abs/1101.4351}, + ee = {http://arxiv.org/abs/1101.4351} +} + +@INPROCEEDINGS{guyeuxTaiwan10, + author = {Bahi, Jacques M. and Guyeux, Christophe and Wang, Qianxue}, + title = {Improving random number generators by chaotic iterations. Application + in data hiding}, + booktitle = {ICCASM 2010, Int. Conf. on Computer Application and System Modeling}, + year = {2010}, + pages = {V13-643--V13-647}, + address = {Taiyuan, China}, + month = oct, + classement = {ACTI}, + doi = {10.1109/ICCASM.2010.5622199}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no}, + url = {http://dx.doi.org/10.1109/ICCASM.2010.5622199} +} + +@ARTICLE{Bahi2009, + author = {Jacques M Bahi and Christian J Michel}, + title = {A stochastic model of gene evolution with time dependent pseudochaotic + mutations.}, + journal = {Bull Math Biol}, + year = {2009}, + volume = {71}, + pages = {681--700}, + number = {3}, + month = {Apr}, + abstract = {We develop here a new class of stochastic models of gene evolution + in which a random subset of the 64 possible trinucleotides mutates + at each evolutionary time t according to some time dependent substitution + probabilities. Therefore, at each time t, the numbers and the types + of mutable trinucleotides are unknown. Thus, the mutation matrix + changes at each time t. This pseudochaotic model developed generalizes + the standard model in which all the trinucleotides mutate at each + time t. It determines the occurrence probabilities at time t of trinucleotides + which pseudochaotically mutate according to 3 time dependent substitution + parameters associated with the 3 trinucleotide sites. The main result + proves that under suitable assumptions, this pseudochaotic model + converges to a uniform probability vector identical to that of the + standard model. Furthermore, an application of this pseudochaotic + model allows an evolutionary study of the 3 circular codes identified + in both eukaryotic and prokaryotic genes. A circular code is a particular + set of trinucleotides whose main property is the retrieval of the + frames in genes locally, i.e., anywhere in genes and particularly + without start codons, and automatically with a window of a few nucleotides. + After a certain evolutionary time and with particular time dependent + functions for the 3 substitution parameters, precisely an exponential + decrease in the 1st and 2nd trinucleotide sites and an exponential + increase in the 3rd one, this pseudochaotic model retrieves the main + statistical properties of the 3 circular codes observed in genes. + Furthermore, it leads to a circular code asymmetry stronger than + the standard model (nonpseudochaotic) and, therefore, to a better + correlation with the genes.}, + doi = {10.1007/s11538-008-9376-4}, + institution = {LIFC-EA 4157, Université de Franche-Comté, IUT de Belfort, BP 527, + 90016, Belfort Cedex, France. jacques.bahi@univ-fcomte.fr}, + keywords = {Evolution, Molecular; Genes; Models, Genetic; Mutation; Stochastic + Processes}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pmid = {19198957}, + timestamp = {2011.05.05}, + url = {http://dx.doi.org/10.1007/s11538-008-9376-4} +} + +@ARTICLE{Bahi2008a, + author = {Jacques M Bahi and Christian J Michel}, + title = {A stochastic model of gene evolution with chaotic mutations.}, + journal = {J Theor Biol}, + year = {2008}, + volume = {255}, + pages = {53--63}, + number = {1}, + month = {Nov}, + abstract = {We develop here a new class of stochastic models of gene evolution + in which the mutations are chaotic, i.e. a random subset of the 64 + possible trinucleotides mutates at each evolutionary time t according + to some substitution probabilities. Therefore, at each time t, the + numbers and the types of mutable trinucleotides are unknown. Thus, + the mutation matrix changes at each time t. The chaotic model developed + generalizes the standard model in which all the trinucleotides mutate + at each time t. It determines the occurrence probabilities at time + t of trinucleotides which chaotically mutate according to three substitution + parameters associated with the three trinucleotide sites. Two theorems + prove that this chaotic model has a probability vector at each time + t and that it converges to a uniform probability vector identical + to that of the standard model. Furthermore, four applications of + this chaotic model (with a uniform random strategy for the 64 trinucleotides + and with a particular strategy for the three stop codons) allow an + evolutionary study of the three circular codes identified in both + eukaryotic and prokaryotic genes. A circular code is a particular + set of trinucleotides whose main property is the retrieval of the + frames in genes locally, i.e. anywhere in genes and particularly + without start codons, and automatically with a window of a few nucleotides. + After a certain evolutionary time and with particular values for + the three substitution parameters, the chaotic models retrieve the + main statistical properties of the three circular codes observed + in genes. These applications also allow an evolutionary comparison + between the standard and chaotic models.}, + doi = {10.1016/j.jtbi.2008.07.028}, + institution = {LIFC-EA 4157, Université de Franche-Comté, IUT de Belfort, BP 527, + 90016 Belfort Cedex, France. jacques.bahi@univ-fcomte.fr}, + keywords = {Animals; Computer Simulation; DNA, Circular, genetics; Evolution, + Molecular; Genetic Code; Models, Genetic; Mutation; Nonlinear Dynamics; + Stochastic Processes; Time}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pii = {S0022-5193(08)00395-0}, + pmid = {18706428}, + timestamp = {2011.05.05}, + url = {http://dx.doi.org/10.1016/j.jtbi.2008.07.028} +} + +@ARTICLE{Bahi2008bis, + author = {Bahi, J. M. and Michel, C. J.}, + title = {A stochastic model of gene evolution with chaotic mutations}, + journal = {Journal of Theoretical Biology}, + year = {2008}, + volume = {255}, + pages = {53-63}, + owner = {guyeux}, + timestamp = {2009.01.10} +} + +@ARTICLE{Bahi2004, + author = {Jacques M Bahi and Christian J Michel}, + title = {A stochastic gene evolution model with time dependent mutations.}, + journal = {Bull Math Biol}, + year = {2004}, + volume = {66}, + pages = {763--778}, + number = {4}, + month = {Jul}, + abstract = {We develop here a new class of gene evolution models in which the + nucleotide mutations are time dependent. These models allow to study + nonlinear gene evolution by accelerating or decelerating the mutation + rates at different evolutionary times. They generalize the previous + ones which are based on constant mutation rates. The stochastic model + developed in this class determines at some time t the occurrence + probabilities of trinucleotides mutating according to 3 time dependent + substitution parameters associated with the 3 trinucleotide sites. + Therefore, it allows to simulate the evolution of the circular code + recently observed in genes. By varying the class of function for + the substitution parameters, 1 among 12 models retrieves after mutation + the statistical properties of the observed circular code in the 3 + frames of actual genes. In this model, the mutation rate in the 3rd + trinucleotide site increases during gene evolution while the mutation + rates in the 1st and 2nd sites decrease. This property agrees with + the actual degeneracy of the genetic code. This approach can easily + be generalized to study evolution of motifs of various lengths, e.g., + dicodons, etc., with time dependent mutations.}, + doi = {10.1016/j.bulm.2003.10.004}, + institution = {LIFC - FRE CNRS 2661, IUT de Belfort, Université de Franche-Comté, + BP 527, 90016 Belfort Cédex, France. bahi@iut-bm.univ-fcomte.fr}, + keywords = {Codon, genetics; Evolution, Molecular; Genes, genetics; Genetic Code, + genetics; Models, Genetic; Mutation; Stochastic Processes}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pii = {S0092824003001174}, + pmid = {15210317}, + timestamp = {2011.05.05}, + url = {http://dx.doi.org/10.1016/j.bulm.2003.10.004} +} + +@ARTICLE{Banks92, + author = {J. Banks and J. Brooks and G. Cairns and P. Stacey}, + title = {On Devaney's Definition of Chaos}, + journal = {Amer. Math. Monthly}, + year = {1992}, + volume = {99}, + pages = {332--334}, + keywords = {(c+),}, + owner = {guyeux}, + timestamp = {27/01/2008} +} + +@MISC{Nist10, + author = {E. Barker and A. Roginsky}, + title = {DRAFT NIST Special Publication 800-131 Recommendation for the Transitioning + of Cryptographic Algorithms and Key Sizes}, + year = {2010}, + owner = {christophe}, + timestamp = {2010.08.18} +} + +@ARTICLE{BarniBF03, + author = {Mauro Barni and Franco Bartolini and Teddy Furon}, + title = {A general framework for robust watermarking security}, + journal = {Signal Processing}, + year = {2003}, + volume = {83}, + pages = {2069-2084}, + number = {10}, + note = {Special issue on Security of Data Hiding Technologies, invited paper}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + ee = {http://dx.doi.org/10.1016/S0165-1684(03)00168-3}, + owner = {guyeux}, + timestamp = {2009.06.30} +} + +@ARTICLE{Baudet78, + author = {Baudet, G\'{e}rard M.}, + title = {Asynchronous Iterative Methods for Multiprocessors}, + journal = {J. ACM}, + year = {1978}, + volume = {25}, + pages = {226--244}, + number = {2}, + address = {New York, NY, USA}, + doi = {http://doi.acm.org/10.1145/322063.322067}, + issn = {0004-5411}, + publisher = {ACM} +} + +@PHDTHESIS{Baz98, + author = {Didier El Baz}, + title = {Contribution à l'algorithmique parall\`{e}le. Le concept d'asynchronisme + : étude théorique, mise en œuvre, et application}, + school = {Institut national polytechnique de Toulouse}, + year = {1998}, + type = {Habilitation à diriger des recherches}, + owner = {christophe}, + timestamp = {2010.08.24} +} + +@ARTICLE{bhr09c:bl, + author = {Benoit, Anne and Hakem, Mourad and Robert, Yves}, + title = {Contention awareness and fault-tolerant scheduling for precedence + constrained tasks in heterogeneous systems}, + journal = {Parallel Computing}, + year = {2009}, + volume = {35}, + pages = {83--108}, + number = {2}, + classement = {*}, + doi = {10.1016/j.parco.2008.11.001}, + equipe = {and}, + inhal = {no}, + url = {http://dx.doi.org/10.1016/j.parco.2008.11.001} +} + +@INPROCEEDINGS{bhr08b:bl, + author = {Benoit, Anne and Hakem, Mourad and Robert, Yves}, + title = {Fault tolerant scheduling of precedence task graphs on heterogeneous + platforms}, + booktitle = {IPDPS'08}, + year = {2008}, + pages = {1--8}, + publisher = {IEEE Computer Society Press}, + classement = {*}, + equipe = {and}, + inhal = {no} +} + +@INPROCEEDINGS{Berger98, + author = {Berger, Bonnie and Leighton, Tom}, + title = {Protein folding in the hydrophobic-hydrophilic (HP) is NP-complete}, + booktitle = {Proceedings of the second annual international conference on Computational + molecular biology}, + year = {1998}, + series = {RECOMB '98}, + pages = {30--39}, + address = {New York, NY, USA}, + publisher = {ACM}, + acmid = {279080}, + isbn = {0-89791-976-9}, + location = {New York, New York, United States}, + numpages = {10} +} + +@BOOK{Bertsekas89, + title = {Parallel and distributed computation: numerical methods}, + publisher = {Prentice-Hall, Inc.}, + year = {1989}, + author = {Bertsekas, Dimitri P. and Tsitsiklis, John N.}, + address = {Upper Saddle River, NJ, USA}, + isbn = {0-13-648700-9} +} + +@MISC{Bertsekas88paralleland, + author = {Dimitri P. Bertsekas and John N. Tsitsiklis}, + title = {Parallel and distributed iterative algorithms: a selective survey}, + year = {1988} +} + +@UNPUBLISHED{F.a, + author = {F. Blanchard and E. Glasner and S. Kolyada and A.Maass}, + title = {On Li-Yorke pairs}, + note = {Preprint}, + optkey = {2000}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@UNPUBLISHED{F., + author = {F. Blanchard and B. Host and S. Ruette}, + title = {Asymptotic pairs in positive-entropy systems}, + note = {Preprint}, + optannote = {to appear in Ergod. Th. Dynam. Sys.}, + optkey = {2000}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@INPROCEEDINGS{Blum:1985:EPP:19478.19501, + author = {Blum, Manuel and Goldwasser, Shafi}, + title = {An efficient probabilistic public key encryption scheme which hides + all partial information}, + booktitle = {Proceedings of CRYPTO 84 on Advances in cryptology}, + year = {1985}, + pages = {289--302}, + address = {New York, NY, USA}, + publisher = {Springer-Verlag New York, Inc.}, + acmid = {19501}, + isbn = {0-387-15658-5}, + keywords = {chosen cyphertext attack, integer factorization, partial information, + passive adversaries, probabilistic encryption}, + location = {Santa Barbara, California, United States}, + numpages = {14}, + url = {http://dl.acm.org/citation.cfm?id=19478.19501} +} + +@ARTICLE{BFibe, + author = {Dan Boneh and Matt Franklin}, + title = {Identity-Based Encryption from the {Weil} Pairing}, + journal = {SIAM J. of Computing}, + year = {2003}, + volume = {32}, + pages = {586-615}, + number = {3}, + note = {Extended abstract in Crypto'01} +} + +@INCOLLECTION{boneh, + author = {Boneh, Dan and Goh, Eu-Jin and Nissim, Kobbi}, + title = {Evaluating 2-DNF Formulas on Ciphertexts}, + year = {2005}, + pages = {325--341}, + abstract = {Let ψ be a 2-DNF formula on boolean variables x 1,..., x n ∈ {0,1}. + We present a homomorphic public key encryption scheme that allows + the public evaluation of ψ given an encryption of the variables x + 1,..., x n. In other words, given the encryption of the bits x 1,..., + x n, anyone can create the encryption of ψ( x 1,..., x n). More generally, + we can evaluate quadratic multi-variate polynomials on ciphertexts + provided the resulting value falls within a small set. We present + a number of applications of the system: 1 In a database of size n, + the total communication in the basic step of the Kushilevitz-Ostrovsky + PIR protocol is reduced from to . 2 An efficient election system + based on homomorphic encryption where voters do not need to include + non-interactive zero knowledge proofs that their ballots are valid. + The election system is proved secure without random oracles but still + efficient. 3 A protocol for universally verifiable computation.}, + citeulike-article-id = {2719460}, + citeulike-linkout-0 = {http://www.springerlink.com/content/wtt5caxkr94laxkg}, + journal = {Theory of Cryptography}, + keywords = {homomorphic, pairings}, + posted-at = {2008-04-25 21:53:15}, + priority = {2}, + url = {http://www.springerlink.com/content/wtt5caxkr94laxkg} +} + +@ARTICLE{Bonneau01, + author = {Bonneau, Richard and Baker, David}, + title = {AB INITIO PROTEIN STRUCTURE PREDICTION: Progress and Prospects}, + journal = {Annual Review of Biophysics and Biomolecular Structure}, + year = {2001}, + volume = {30}, + pages = {173-189}, + number = {1}, + doi = {10.1146/annurev.biophys.30.1.173} +} + +@ARTICLE{Bowen, + author = {R. Bowen}, + title = {Entropy for group endomorphisms and homogeneous spaces}, + journal = {Trans. Amer. Math. Soc.}, + year = {1971}, + volume = {153}, + pages = {401-414}, + owner = {guyeux}, + timestamp = {15/02/2008} +} + +@ARTICLE{Bowen1971, + author = {R. Bowen}, + title = {Periodic points and measures for Axiom A diffeomorphisms}, + journal = {Trans. Amer. Math. Soc.}, + year = {1971}, + volume = {154}, + pages = {377-397}, + owner = {guyeux}, + timestamp = {15/02/2008} +} + +@ARTICLE{Braxenthaler97, + author = {Michael Braxenthaler and R. Ron Unger and Ditza Auerbach and John + Moult}, + title = {Chaos in protein dynamics}, + journal = {Proteins-structure Function and Bioinformatics}, + year = {1997}, + volume = {29}, + pages = {417--425}, + doi = {10.1002/(SICI)1097-0134(199712)29:4<417::AID-PROT2>3.3.CO;2-O}, + masid = {2824140} +} + +@MISC{google, + author = {Brin, Sergey and Page, Larry}, + title = {Google}, + month = {May}, + year = {2012}, + note = {\texttt{http://www.google.com}} +} + +@MISC{googlePlus, + author = {Brin, Sergey and Page, Larry}, + title = {Google+}, + month = {May}, + year = {2012}, + note = {\texttt{https://plus.google.com}} +} + +@INPROCEEDINGS{Brumley03remotetiming, + author = {David Brumley and Dan Boneh}, + title = {Remote Timing Attacks are Practical}, + booktitle = {Proceedings of the 12th USENIX Security Symposium}, + year = {2003}, + pages = {1--14} +} + +@ARTICLE{Bohm1991375, + author = {Gerald Böhm}, + title = {Protein folding and deterministic chaos: Limits of protein folding + simulations and calculations}, + journal = {Chaos, Solitons \& Fractals}, + year = {1991}, + volume = {1}, + pages = {375 - 382}, + number = {4}, + doi = {DOI: 10.1016/0960-0779(91)90028-8}, + issn = {0960-0779}, + url = {http://www.sciencedirect.com/science/article/B6TJ4-46CBXVT-1X/2/370489c218e4c2732cd9b620ef50c696} +} + +@INCOLLECTION{Cachin2004, + author = {Cachin, Christian}, + title = {An Information-Theoretic Model for Steganography}, + booktitle = {Information Hiding}, + publisher = {Springer Berlin / Heidelberg}, + year = {1998}, + volume = {1525}, + series = {Lecture Notes in Computer Science}, + pages = {306-318}, + affiliation = {MIT Laboratory for Computer Science 545 Technology Square Cambridge + MA 02139 USA} +} + +@ARTICLE{Cam2006, + author = {H. Cam and S. Ozdemir and P. Nair and D. Muthuavinashinappan and + H. O. Sanli}, + title = {ESPDA: Energy-efficient secure pattern based data aggregation for + wireless sensor networks.}, + journal = {Computer Communication journal (29)}, + year = {2006}, + pages = {446-455} +} + +@ARTICLE{CarletCZ98, + author = {Claude Carlet and Pascale Charpin and Victor Zinoviev}, + title = {Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems}, + journal = {Des. Codes Cryptography}, + year = {1998}, + volume = {15}, + pages = {125-156}, + number = {2}, + bibsource = {DBLP, http://dblp.uni-trier.de} +} + +@INPROCEEDINGS{Castelluccia05efficientaggregation, + author = {Claude Castelluccia}, + title = {Efficient aggregation of encrypted data in wireless sensor networks}, + booktitle = {MobiQuitous}, + year = {2005}, + pages = {109--117}, + publisher = {IEEE Computer Society} +} + +@ARTICLE{Cayre2008, + author = {Cayre, F. and Bas, P.}, + title = {Kerckhoffs-Based Embedding Security Classes for WOA Data Hiding}, + journal = {IEEE Transactions on Information Forensics and Security}, + year = {2008}, + volume = {3}, + pages = {1--15}, + number = {1}, + doi = {10.1109/TIFS.2007.916006}, + issn = {1556-6013}, + keywords = {cryptography, random sequences, spread spectrum communication, telecommunication + security, watermarking, Kerckhoffs-based embedding security classes, + WOA Data Hiding, pseudorandom sequences, spread-spectrum techniques, + steganography security, watermark-only-attack, watermarking, Security, + spread-spectrum (SS) watermarking}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@ARTICLE{Cayre2005, + author = {Cayre, F. and Fontaine, C. and Furon, T.}, + title = {Watermarking security: theory and practice}, + journal = {IEEE Transactions on Signal Processing}, + year = {2005}, + volume = {53}, + pages = {3976--3987}, + number = {10}, + doi = {10.1109/TSP.2005.855418}, + issn = {1053-587X}, + keywords = {blind source separation, cryptography, watermarking, Fisher information + matrix, blind source separation, cryptanalysis, information theory, + spread spectrum techniques, substitutive scheme, watermarking security, + Blind source separation, Fisher information matrix, equivocation, + security, watermarking}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@ARTICLE{Chajakis91, + author = {Chajakis, Emmanuel D. and Zenios, Stavros A.}, + title = {Synchronous and asynchronous implementations of relaxation algorithms + for nonlinear network optimization}, + journal = {Parallel Comput.}, + year = {1991}, + volume = {17}, + pages = {873--894}, + number = {8}, + address = {Amsterdam, The Netherlands, The Netherlands}, + doi = {http://dx.doi.org/10.1016/S0167-8191(05)80072-9}, + issn = {0167-8191}, + publisher = {Elsevier Science Publishers B. V.} +} + +@ARTICLE{Chan2007, + author = {Chan, Haowen and Perrig, Adrian and Przydatek, Bartosz and Song, + Dawn}, + title = {SIA: Secure information aggregation in sensor networks}, + journal = {J. Comput. Secur.}, + year = {2007}, + volume = {15}, + pages = {69--102}, + number = {1}, + address = {Amsterdam, The Netherlands, The Netherlands}, + issn = {0926-227X}, + publisher = {IOS Press} +} + +@ARTICLE{Chandramouli06, + author = {R. Chandramouli and S. Bapatla and K.P. Subbalakshmi}, + title = {Battery power-aware encryption}, + journal = {ACM transactions on information and system security}, + year = {2006}, + pages = {162--180}, + owner = {christophe}, + timestamp = {2010.07.31} +} + +@ARTICLE{Charpin85, + author = {Pascale Charpin}, + title = {A description of some extended cyclic codes with application to Reed-Solomon + codes}, + journal = {Discrete Mathematics}, + year = {1985}, + volume = {56}, + pages = {117-124}, + number = {2-3}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + ee = {http://dx.doi.org/10.1016/0012-365X(85)90019-6} +} + +@ARTICLE{Chazan69, + author = {D. Chazan and W. Miranker}, + title = {Chaotic relaxation}, + journal = {Linear algebra and its applications}, + year = {1969}, + pages = {199-222}, + owner = {guyeux}, + timestamp = {2008.05.22} +} + +@ARTICLE{Cheon2006, + author = {Cheon, Jung Hee and Kim, Woo-Hwan and Nam, Hyun Soo}, + title = {Known-plaintext cryptanalysis of the Domingo-Ferrer algebraic privacy + homomorphism scheme}, + journal = {Inf. Process. Lett.}, + year = {2006}, + volume = {97}, + pages = {118--123}, + number = {3}, + address = {Amsterdam, The Netherlands, The Netherlands}, + doi = {http://dx.doi.org/10.1016/j.ipl.2005.09.016}, + issn = {0020-0190}, + publisher = {Elsevier North-Holland, Inc.} +} + +@MISC{Cheon03acryptanalysis, + author = {Jung Hee Cheon and Hyun Soo Nam}, + title = {A Cryptanalysis of the Original Domingo-Ferrer's Algebraic Privacy + Homomorphism}, + year = {2003} +} + +@ARTICLE{Cheung05, + author = {R.C.C. Cheung and N.J. Telle and W. Luk and P.Y.K. Cheung}, + title = {Secure encrypted-data aggregation for wireless sensor networks}, + journal = {IEEE Trans. on Very Large Scale Integration Systems}, + year = {2005}, + volume = {13}, + pages = {1048-1059}, + number = {9} +} + +@ARTICLE{Chivian2005, + author = {Chivian, Dylan and Kim, David E. and Malmström, Lars and Schonbrun, + Jack and Rohl, Carol A. and Baker, David}, + title = {Prediction of CASP6 structures using automated robetta protocols}, + journal = {Proteins}, + year = {2005}, + volume = {61}, + pages = {157--166}, + number = {S7}, + issn = {1097-0134}, + keywords = {Rosetta, fragment assembly, de novo modeling, homology modeling, parametric + alignment ensemble}, + owner = {christophe}, + publisher = {Wiley Subscription Services, Inc., A Wiley Company}, + timestamp = {2011.01.22}, + url = {http://dx.doi.org/10.1002/prot.20733} +} + +@ARTICLE{Zhu06, + author = {Congxu, Zhu and Xuefeng, Liao and Zhihua, Li}, + title = {Chaos-based multipurpose image watermarking algorithm}, + journal = {Wuhan University Journal of Natural Sciences}, + year = {2006}, + volume = {11}, + pages = {1675-1678}, + note = {10.1007/BF02831848}, + abstract = {To achieve the goal of image content authentication and copyright + protection simultaneously, this paper presents a novel image dual + watermarking method based on chaotic map. Firstly, the host image + was split into many nonoverlapping small blocks, and the block-wise + discrete cosine transform (DCT) is computed. Secondly, the robust + watermarks, shuffled by the chaotic sequences, are embedded in the + DC coefficients of blocks to achieve the goal of copyright protection. + The semi-fragile watermarks, generated by chaotic map, are embedded + in the AC coefficients of blocks to obtain the aim of image authentication. + Both of them can be extracted without the original image. Simulation + results demonstrate the effectiveness of our algorithm in terms of + robustness and fragility.}, + affiliation = {Central South University School of Information Science and Engineering + 410083 Changsha, Hunan China}, + issn = {1007-1202}, + issue = {6}, + keyword = {Mathematics, general}, + publisher = {Wuhan University, co-published with Springer}, + url = {http://dx.doi.org/10.1007/BF02831848} +} + +@ARTICLE{Conley1978, + author = {C. Conley}, + title = {Isolated invariant sets and the Morse index}, + journal = {CBMS Regional Conference. AMS.}, + year = {1978}, + optvolume = {38}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@ARTICLE{Coppel55, + author = {Coppel,W. A.}, + title = {The solution of equations by iteration}, + journal = {Mathematical Proceedings of the Cambridge Philosophical Society}, + year = {1955}, + volume = {51}, + pages = {41-43}, + number = {01}, + doi = {10.1017/S030500410002990X}, + eprint = {http://journals.cambridge.org/article_S030500410002990X}, + url = {http://dx.doi.org/10.1017/S030500410002990X} +} + +@ARTICLE{Cornu2002, + author = {Philippe Cornu and André Smolarz}, + title = {Image characterization by texture}, + journal = {Traitement du signal}, + year = {2002}, + volume = {19}, + pages = {29-35}, + file = {:/home/guyeux/Documents/Bibliotheque/These/Watermarking/Caractérisation d'images par textures associées.pdf:PDF}, + owner = {guyeux}, + timestamp = {2008.05.12} +} + +@INPROCEEDINGS{Cox99, + author = {Ingemar Cox and Matt L. Miller and Andrew L. Mckellips}, + title = {Watermarking as Communications With Side Information}, + booktitle = {Proceedings of the IEEE}, + year = {1999}, + pages = {1127--1141}, + owner = {christophe}, + timestamp = {2010.03.06} +} + +@ARTICLE{Cox97securespread, + author = {Ingemar J. Cox and Senior Member and Joe Kilian and F. Thomson Leighton + and Talal Shamoon}, + title = {Secure spread spectrum watermarking for multimedia}, + journal = {IEEE Transactions on Image Processing}, + year = {1997}, + volume = {6}, + pages = {1673--1687} +} + +@ARTICLE{Cramer96, + author = {Christopher Cramer and Erol Gelenbe and Hakan Bakircioglu}, + title = {Video Compression with Random Neural Networks}, + journal = {Neural Networks for Identification, Control, and Robotics, International + Workshop}, + year = {1996}, + volume = {0}, + pages = {0476}, + address = {Los Alamitos, CA, USA}, + isbn = {0-8186-7456-3}, + publisher = {IEEE Computer Society} +} + +@INPROCEEDINGS{Crescenzi98, + author = {Crescenzi, Pierluigi and Goldman, Deborah and Papadimitriou, Christos + and Piccolboni, Antonio and Yannakakis, Mihalis}, + title = {On the complexity of protein folding (extended abstract)}, + booktitle = {Proceedings of the thirtieth annual ACM symposium on Theory of computing}, + year = {1998}, + series = {STOC '98}, + pages = {597--603}, + address = {New York, NY, USA}, + publisher = {ACM}, + acmid = {276875}, + isbn = {0-89791-962-9}, + location = {Dallas, Texas, United States}, + numpages = {7} +} + +@ARTICLE{Dawei2004, + author = {Zhao Dawei and Chen Guanrong and Liu Wenbo}, + title = {A chaos-based robust wavelet-domain watermarking algorithm}, + journal = {Chaos, Solitons and Fractals}, + year = {2004}, + volume = {22}, + pages = {47-54}, + owner = {guyeux}, + timestamp = {2008.10.07} +} + +@MISC{1011.1638, + author = {Anthony Desnos and Robert Erra and Eric Filiol}, + title = {Processor-Dependent Malware... and codes}, + year = {2010}, + comment = {arXiv:1011.1638}, + eprint = {arXiv:1011.1638} +} + +@BOOK{devaney, + title = {An Introduction to Chaotic Dynamical Systems}, + publisher = {Addison-Wesley}, + year = {1989}, + author = {Devaney, Robert L.}, + address = {Redwood City, CA}, + edition = {2nd} +} + +@ARTICLE{diffie76, + author = {Whitfield Diffie and Martin E. Hellman}, + title = {New Directions in Cryptography}, + journal = {IEEE Transactions on Information Theory}, + year = {1976}, + volume = {IT-22}, + pages = {644--654}, + number = {6}, + date = {November 1976}, + owner = {guyeux}, + timestamp = {2009.06.30}, + url = {citeseer.ist.psu.edu/diffie76new.html} +} + +@INCOLLECTION{Dijk10, + author = {van Dijk, Marten and Gentry, Craig and Halevi, Shai and Vaikuntanathan, + Vinod}, + title = {Fully Homomorphic Encryption over the Integers}, + booktitle = {Advances in Cryptology – EUROCRYPT 2010}, + publisher = {Springer Berlin / Heidelberg}, + year = {2010}, + editor = {Gilbert, Henri}, + volume = {6110}, + series = {Lecture Notes in Computer Science}, + pages = {24-43}, + abstract = {We construct a simple fully homomorphic encryption scheme, using only + elementary modular arithmetic. We use Gentry’s technique to construct + a fully homomorphic scheme from a bootstrappable somewhat homomorphic + scheme. However, instead of using ideal lattices over a polynomial + ring, our bootstrappable encryption scheme merely uses addition and + multiplication over the integers. The main appeal of our scheme is + the conceptual simplicity. We reduce the security of our scheme to + finding an approximate integer gcd – i.e., given a list of integers + that are near-multiples of a hidden integer, output that hidden integer. + We investigate the hardness of this task, building on earlier work + of Howgrave-Graham.}, + affiliation = {MIT CSAIL} +} + +@ARTICLE{Dill1985, + author = {Dill, KA}, + title = {Theory for the folding and stability of globular proteins.}, + journal = {Biochemistry}, + year = {1985}, + volume = {24}, + pages = {1501-9--}, + number = {6}, + month = mar, + abstract = {Using lattice statistical mechanics, we develop theory to account + for the folding of a heteropolymer molecule such as a protein to + the globular and soluble state. Folding is assumed to be driven by + the association of solvophobic monomers to avoid solvent and opposed + by the chain configurational entropy. Theory predicts a phase transition + as a function of temperature or solvent character. Molecules that + are too short or too long or that have too few solvophobic residues + are predicted not to fold. Globular molecules should have a largely + solvophobic core, but there is an entropic tendency for some residues + to be "out of place", particularly in small molecules. For long chains, + molecules comprised of globular domains are predicted to be thermodynamically + more stable than spherical molecules. The number of accessible conformations + in the globular state is calculated to be an exceedingly small fraction + of the number available to the random coil. Previous estimates of + this number, which have motivated kinetic theories of folding, err + by many tens of orders of magnitude.}, + comment = {Research Support, Non-U.S. Gov't,Research Support, U.S. Gov't, P.H.S.,}, + keywords = {Mathematics, Models, Chemical, Polymers, Protein Conformation}, + owner = {christophe}, + timestamp = {2011.01.22}, + url = {http://ukpmc.ac.uk/abstract/MED/3986190} +} + +@ARTICLE{Dill1995, + author = {Dill, KA and Bromberg, S and Yue, K and Fiebig, KM and Yee, DP and + Thomas, PD and Chan, HS}, + title = {Principles of protein folding--a perspective from simple exact models.}, + journal = {Protein Sci}, + year = {1995}, + volume = {4}, + pages = {561-602--}, + number = {4}, + month = apr, + abstract = {General principles of protein structure, stability, and folding kinetics + have recently been explored in computer simulations of simple exact + lattice models. These models represent protein chains at a rudimentary + level, but they involve few parameters, approximations, or implicit + biases, and they allow complete explorations of conformational and + sequence spaces. Such simulations have resulted in testable predictions + that are sometimes unanticipated: The folding code is mainly binary + and delocalized throughout the amino acid sequence. The secondary + and tertiary structures of a protein are specified mainly by the + sequence of polar and nonpolar monomers. More specific interactions + may refine the structure, rather than dominate the folding code. + Simple exact models can account for the properties that characterize + protein folding: two-state cooperativity, secondary and tertiary + structures, and multistage folding kinetics--fast hydrophobic collapse + followed by slower annealing. These studies suggest the possibility + of creating "foldable" chain molecules other than proteins. The encoding + of a unique compact chain conformation may not require amino acids; + it may require only the ability to synthesize specific monomer sequences + in which at least one monomer type is solvent-averse.}, + address = {Department of Pharmaceutical Chemistry, University of California, + San Francisco 94143-1204, USA.}, + comment = {Review,Research Support, Non-U.S. Gov't,Research Support, U.S. Gov't, + Non-P.H.S.,Research Support, U.S. Gov't, P.H.S.,}, + keywords = {Amino Acid Sequence, Biological Evolution, Hydrogen Bonding, Models, + Molecular, Molecular Sequence Data, Mutation, Protein Conformation, + Protein Denaturation, Protein Folding, Temperature, Thermodynamics}, + owner = {christophe}, + timestamp = {2011.01.22}, + url = {http://ukpmc.ac.uk/abstract/MED/7613459} +} + +@INPROCEEDINGS{Dobbertin96, + author = {Dobbertin, Hans}, + title = {Cryptanalysis of MD4}, + booktitle = {Proceedings of the Third International Workshop on Fast Software + Encryption}, + year = {1996}, + pages = {53--69}, + address = {London, UK}, + publisher = {Springer-Verlag}, + isbn = {3-540-60865-6} +} + +@INPROCEEDINGS{DomingoFerrer2002, + author = {Domingo-Ferrer, Josep}, + title = {A Provably Secure Additive and Multiplicative Privacy Homomorphism}, + booktitle = {ISC '02: Proceedings of the 5th International Conference on Information + Security}, + year = {2002}, + pages = {471--483}, + address = {London, UK}, + publisher = {Springer-Verlag}, + isbn = {3-540-44270-7} +} + +@ARTICLE{Dubchak1995, + author = {I. Dubchak and I. Muchnik and S. R. Holbrook and S. H. Kim}, + title = {Prediction of protein folding class using global description of amino + acid sequence.}, + journal = {Proc Natl Acad Sci U S A}, + year = {1995}, + volume = {92}, + pages = {8700--8704}, + number = {19}, + month = {Sep}, + __markedentry = {[guyeux]}, + abstract = {We present a method for predicting protein folding class based on + global protein chain description and a voting process. Selection + of the best descriptors was achieved by a computer-simulated neural + network trained on a data base consisting of 83 folding classes. + Protein-chain descriptors include overall composition, transition, + and distribution of amino acid attributes, such as relative hydrophobicity, + predicted secondary structure, and predicted solvent exposure. Cross-validation + testing was performed on 15 of the largest classes. The test shows + that proteins were assigned to the correct class (correct positive + prediction) with an average accuracy of 71.7\%, whereas the inverse + prediction of proteins as not belonging to a particular class (correct + negative prediction) was 90-95\% accurate. When tested on 254 structures + used in this study, the top two predictions contained the correct + class in 91\% of the cases.}, + institution = {Department of Chemistry, University of California, Berkeley 94720, + USA.}, + keywords = {Amino Acid Sequence; Amino Acids, chemistry; Computer Simulation; + Databases, Factual; Models, Chemical; Neural Networks (Computer); + Protein Folding; Protein Structure, Secondary; Proteins, chemistry/classification; + Reproducibility of Results; Solvents}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pmid = {7568000}, + timestamp = {2011.07.18} +} + +@BOOK{Dudley, + title = {Real analysis and probability}, + publisher = {Cambridge University Press}, + author = {Richard M. Dudley}, + optpages = {209}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@ARTICLE{Tarazi84, + author = {El Tarazi, Mouhamed Nabih}, + title = {Algorithmes mixtes asynchrones. Etude de convergence monotone}, + journal = {Numerische Mathematik}, + year = {1984}, + volume = {44}, + pages = {363-369}, + note = {10.1007/BF01405568}, + affiliation = {Department of Mathematics, Faculty of Science Kuwait University P.O. + Box 5969 Kuwait}, + issn = {0029-599X}, + issue = {3}, + keyword = {Mathematics and Statistics}, + publisher = {Springer Berlin / Heidelberg}, + url = {http://dx.doi.org/10.1007/BF01405568} +} + +@ARTICLE{Tarazi82, + author = {El Tarazi, Mouhamed Nabih}, + title = {Some convergence results for asynchronous algorithms}, + journal = {Numerische Mathematik}, + year = {1982}, + volume = {39}, + pages = {325-340}, + note = {10.1007/BF01407866}, + affiliation = {Department of Mathematics, Faculty of Science Kuwait University P.O. + Box 5969 Kuwait Kuwait}, + issn = {0029-599X}, + issue = {3}, + keyword = {Mathematics and Statistics}, + publisher = {Springer Berlin / Heidelberg}, + url = {http://dx.doi.org/10.1007/BF01407866} +} + +@ARTICLE{Fei2005, + author = {Peng Fei and Qiu Shui-Sheng and Long Min}, + title = {A secure digital signature algorithm based on elliptic curve and + chaotic mappings}, + journal = {Circuits Systems Signal Processing}, + year = {2005}, + volume = {24, No. 5}, + pages = {585--597}, + owner = {guyeux}, + timestamp = {2009.01.16} +} + +@BOOK{Feigenbaum1908, + title = {Universal behavior in nonlinear systems}, + publisher = {Los Alamos Science}, + year = {1908}, + author = {Feigenbaum}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@ARTICLE{Felsenstein1980, + author = {J. Felsenstein}, + title = {A view of population genetics.}, + journal = {Science}, + year = {1980}, + volume = {208}, + pages = {1253}, + number = {4449}, + month = {Jun}, + doi = {10.1126/science.208.4449.1253}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pii = {208/4449/1253}, + pmid = {17830806}, + timestamp = {2011.05.05}, + url = {http://dx.doi.org/10.1126/science.208.4449.1253} +} + +@BOOK{Filiol09, + title = {Les virus informatiques : techniques virales et antivirales avancées}, + year = {2009}, + editor = {Springer}, + author = {Eric Filiol}, + owner = {christophe}, + timestamp = {2010.10.13} +} + +@INPROCEEDINGS{FiliolBlackHat, + author = {Eric Filiol}, + title = {Passive and Active Leakage of Secret Data from Non Networked Computer}, + booktitle = {Black Hat}, + year = {2008}, + owner = {christophe}, + timestamp = {2010.11.28} +} + +@INPROCEEDINGS{Fischlin, + author = {Fischlin, R. and Schnorr, C. P.}, + title = {Stronger security proofs for RSA and rabin bits}, + booktitle = {Proceedings of the 16th annual international conference on Theory + and application of cryptographic techniques}, + year = {1997}, + series = {EUROCRYPT'97}, + pages = {267--279}, + address = {Berlin, Heidelberg}, + publisher = {Springer-Verlag}, + acmid = {1754569}, + isbn = {3-540-62975-0}, + location = {Konstanz, Germany}, + numpages = {13}, + url = {http://dl.acm.org/citation.cfm?id=1754542.1754569} +} + +@PHDTHESIS{Formenti2003, + author = {Enrico Formenti}, + title = {De l'algorithmique du chaos dans les syst\`{e}mes dynamiques discrets}, + school = {Université de Provence}, + year = {2003}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@PHDTHESIS{Formenti1998, + author = {Enrico Formenti}, + title = {Automates cellulaires et chaos : de la vision topologique à la vision + algorithmique}, + school = {\'Ecole Normale Supérieure de Lyon}, + year = {1998}, + optmonth = {Octobre}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@ARTICLE{Frey2006, + author = {Gabriel Frey and Christian J Michel}, + title = {Identification of circular codes in bacterial genomes and their use + in a factorization method for retrieving the reading frames of genes.}, + journal = {Comput Biol Chem}, + year = {2006}, + volume = {30}, + pages = {87--101}, + number = {2}, + month = {Apr}, + abstract = {We developed a statistical method that allows each trinucleotide to + be associated with a unique frame among the three possible ones in + a (protein coding) gene. An extensive gene study in 175 complete + bacterial genomes based on this statistical approach resulted in + identification of 72 new circular codes. Finding a circular code + enables an immediate retrieval of the reading frame locally anywhere + in a gene. No knowledge of location of the start codon is required + and a short window of only a few nucleotides is sufficient for automatic + retrieval. We have therefore developed a factorization method (that + explores previously found circular codes) for retrieving the reading + frames of bacterial genes. Its principle is new and easy to understand. + Neither complex treatment nor specific information on the nucleotide + sequences is necessary. Moreover, the method can be used for short + regions in nucleotide sequences (less than 25 nucleotides in protein + coding genes). Selected additional properties of circular codes and + their possible biological consequences are also discussed.}, + doi = {10.1016/j.compbiolchem.2005.11.001}, + institution = {Equipe de Bioinformatique Théorique, LSIIT (UMR CNRS-ULP 7005), Université + Louis Pasteur de Strasbourg, Pôle API, Boulevard Sébastien Brant, + 67400 Illkirch, France. frey@dpt-info.u-strasbg.fr}, + keywords = {Base Sequence; Computational Biology; Genes, Bacterial; Genome, Bacterial; + Genomics, statistics /&/ numerical data; Models, Genetic; Models, + Statistical; Reading Frames}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pii = {S1476-9271(05)00111-8}, + pmid = {16439185}, + timestamp = {2011.05.05}, + url = {http://dx.doi.org/10.1016/j.compbiolchem.2005.11.001} +} + +@ARTICLE{Frey2006a, + author = {Gabriel Frey and Christian J Michel}, + title = {An analytical model of gene evolution with six mutation parameters: + an application to archaeal circular codes.}, + journal = {Comput Biol Chem}, + year = {2006}, + volume = {30}, + pages = {1--11}, + number = {1}, + month = {Feb}, + abstract = {We develop here an analytical evolutionary model based on a trinucleotide + mutation matrix 64 x 64 with six substitution parameters associated + with the transitions and transversions in the three trinucleotide + sites. It generalizes the previous models based on the nucleotide + mutation matrices 4 x 4 and the trinucleotide mutation matrix 64 + x 64 with three parameters. It determines at some time t the exact + occurrence probabilities of trinucleotides mutating randomly according + to six substitution parameters. An application of this model allows + an evolutionary study of the common circular code COM and the 15 + archaeal circular codes X which have been recently identified in + several archaeal genomes. The main property of a circular code is + the retrieval of the reading frames in genes, both locally, i.e. + anywhere in genes and in particular without a start codon, and automatically + with a window of a few nucleotides. In genes, the circular code is + superimposed on the traditional genetic one. Very unexpectedly, the + evolutionary model demonstrates that the archaeal circular codes + can derive from the common circular code subjected to random substitutions + with particular values for six substitutions parameters. It has a + strong correlation with the statistical observations of three archaeal + codes in actual genes. Furthermore, the properties of these substitution + rates allow proposal of an evolutionary classification of the 15 + archaeal codes into three main classes according to this model. In + almost all the cases, they agree with the actual degeneracy of the + genetic code with substitutions more frequent in the third trinucleotide + site and with transitions more frequent that transversions in any + trinucleotide site.}, + doi = {10.1016/j.compbiolchem.2005.09.001}, + institution = {Equipe de Bioinformatique Théorique, LSIIT (UMR CNRS-ULP 7005), Université + Louis Pasteur de Strasbourg, Pôle API, Boulevard Sébastien Brant, + 67400 Illkirch, France. frey@dpt-info.u-strasbg.fr}, + keywords = {Archaea, genetics; DNA, Circular; Evolution, Molecular; Genetic Code; + Genome, Archaeal; Models, Genetic; Mutation; Trinucleotide Repeats}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pii = {S1476-9271(05)00083-6}, + pmid = {16324886}, + timestamp = {2011.05.05}, + url = {http://dx.doi.org/10.1016/j.compbiolchem.2005.09.001} +} + +@INPROCEEDINGS{fgb11:ip, + author = {Friot, Nicolas and Guyeux, Christophe and Bahi, Jacques}, + title = {Chaotic Iterations for Steganography - Stego-security and chaos-security}, + booktitle = {SECRYPT'2011, Int. Conf. on Security and Cryptography}, + year = {2011}, + pages = {***--***}, + address = {Sevilla, Spain}, + month = jul, + note = {To appear}, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@MISC{Frisch, + author = {Alain Frisch}, + title = {Entropie topologique et définition du chaos}, + year = {1998}, + note = {Rapport de tipe}, + file = {Tipe_Entropie Topologique et Definition du Chaos (Alain Frisch).ps:Chaos/Tipe_Entropie Topologique et Definition du Chaos (Alain Frisch).ps:PDF}, + keywords = {Chaos, Entropie Topologique, Tipe}, + owner = {guyeux}, + timestamp = {2008.01.02}, + url = {http://alain.frisch.fr/math.html} +} + +@MISC{Frisch98, + author = {Alain Frisch}, + title = {Entropie topologique et définition du chaos}, + year = {1998}, + note = {[En ligne; Page disponible le 12-août-2010]}, + url = {\url{http://alain.frisch.fr/math.html}} +} + +@ARTICLE{Frommer97asynchronousweighted, + author = {Andreas Frommer and Hartmut Schwandt and Daniel and Daniel B. Szyld}, + title = {Asynchronous Weighted Additive Schwarz Methods}, + journal = {Electronic Transactions on Numerical Analysis}, + year = {1997}, + volume = {5}, + pages = {48--61} +} + +@MISC{Frommer94asynchronoustwo-stage, + author = {Andreas Frommer and Daniel B. Szyld}, + title = {Asynchronous Two-Stage Iterative Methods}, + year = {1994} +} + +@BOOK{J1992, + title = {Introduction to Chaos and Coherence}, + publisher = {IOP Publishing}, + year = {1992}, + author = {J. Frøyland}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@MISC{Furon2002, + author = {T. Furon}, + title = {Security analysis}, + year = {2002}, + note = {European Project IST-1999-10987 CERTIMARK, Deliverable D.5.5}, + owner = {guyeux}, + timestamp = {2009.06.30} +} + +@ARTICLE{Furon08, + author = {Furon, Teddy and Bas, Patrick}, + title = {Broken arrows}, + journal = {EURASIP J. Inf. Secur.}, + year = {2008}, + volume = {2008}, + pages = {1--13}, + address = {New York, NY, United States}, + doi = {http://dx.doi.org/10.1155/2008/597040}, + issn = {1687-4161}, + owner = {christophe}, + publisher = {Hindawi Publishing Corp.}, + timestamp = {2010.03.06} +} + +@ARTICLE{P1150442004, + author = {G.S.El-Taweel and H.M. Onsi and M.Samy and M.G. Darwish}, + title = {Secure and Non-Blind Watermarking Scheme for Color Images Based on + DWT}, + journal = {ICGST International Journal on Graphics, Vision and Image Processing}, + year = {2005}, + volume = {05}, + pages = {1--5}, + month = {April}, + issue = {4}, + owner = {christophe}, + timestamp = {2010.03.07} +} + +@INPROCEEDINGS{Gentry09, + author = {Gentry, Craig}, + title = {Fully homomorphic encryption using ideal lattices}, + booktitle = {STOC '09: Proceedings of the 41st annual ACM symposium on Theory + of computing}, + year = {2009}, + pages = {169--178}, + address = {New York, NY, USA}, + publisher = {ACM}, + doi = {http://doi.acm.org/10.1145/1536414.1536440}, + isbn = {978-1-60558-506-2}, + location = {Bethesda, MD, USA} +} + +@INPROCEEDINGS{Girao04, + author = {J. Girao and M. Schneider and D. Westhoff}, + title = {CDA: Concealed data aggregation in wireless sensor networks}, + booktitle = {Proceedings of the ACM Workshop on Wireless Security}, + year = {2004}, + owner = {christophe}, + timestamp = {2010.07.31} +} + +@ARTICLE{Goldreich86, + author = {Goldreich, Oded and Goldwasser, Shafi and Micali, Silvio}, + title = {How to construct random functions}, + journal = {J. ACM}, + year = {1986}, + volume = {33}, + pages = {792--807}, + month = {August}, + acmid = {6503}, + address = {New York, NY, USA}, + doi = {http://doi.acm.org/10.1145/6490.6503}, + issn = {0004-5411}, + issue = {4}, + numpages = {16}, + publisher = {ACM}, + url = {http://doi.acm.org/10.1145/6490.6503} +} + +@CONFERENCE{Gotsman88, + author = {C. Gotsman and D. Lehmann and E. Shamir}, + title = {Asynchronous Dynamics of Random Boolean Networks}, + booktitle = {San Diego '88 Neural Networks Conference}, + year = {1988}, + owner = {guyeux}, + timestamp = {30/03/2008} +} + +@ARTICLE{Guckenheimer1979, + author = {J. Guckenheimer}, + title = {Sensitive dependence to initial conditions for one-dimensional maps}, + journal = {Comm. Math. Phys.}, + year = {1979}, + optpages = {133-160}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@BOOK{J.1983, + title = {Nonlinear oscillations, dynamical systems, and bifurcations of vector + fields}, + publisher = {Springer Verlag}, + year = {1983}, + author = {J. Guckenheimer and P. Holmes}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@ARTICLE{Guo20093201, + author = {Wei Guo and Xiaoming Wang and Dake He and Yang Cao}, + title = {Cryptanalysis on a parallel keyed hash function based on chaotic + maps}, + journal = {Physics Letters A}, + year = {2009}, + volume = {373}, + pages = {3201 - 3206}, + number = {36}, + abstract = {This Letter analyzes the security of a novel parallel keyed hash function + based on chaotic maps, proposed by Xiao et al. to improve the efficiency + in parallel computing environment. We show how to devise forgery + attacks on Xiao's scheme with differential cryptanalysis and give + the experiment results of two kinds of forgery attacks firstly. Furthermore, + we discuss the problem of weak keys in the scheme and demonstrate + how to utilize weak keys to construct collision.}, + issn = {0375-9601}, + keywords = {Cryptanalysis} +} + +@PHDTHESIS{GuyeuxThese10, + author = {Christophe Guyeux}, + title = {Le d\'{e}sordre des it\'{e}rations chaotiques et leur utilit\'{e} + en s\'{e}curit\'{e} informatique}, + school = {Universit\'{e} de Franche-Comt\'{e}}, + year = {2010}, + owner = {christophe}, + timestamp = {2010.12.21} +} + +@MISC{gb11:onp, + author = {Guyeux, Christophe and Bahi, Jacques}, + title = {\'Etude topologique de l'\'etalement de spectre}, + howpublished = {Journ\'ees Codes et St\'eganographie, \'Ecoles Militaires de Saint-Cyr, + Co\"etquidan}, + month = jan, + year = {2011}, + classement = {COM}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@INPROCEEDINGS{bg10:ip, + author = {Guyeux, Christophe and Bahi, Jacques}, + title = {An improved watermarking algorithm for Internet applications}, + booktitle = {INTERNET'2010. The 2nd Int. Conf. on Evolving Internet}, + year = {2010}, + pages = {119--124}, + address = {Valencia, Spain}, + month = sep, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@INPROCEEDINGS{gfb10:ip, + author = {Guyeux, Christophe and Friot, Nicolas and Bahi, Jacques}, + title = {Chaotic iterations versus Spread-spectrum: chaos and stego security}, + booktitle = {IIH-MSP'10, 6-th Int. Conf. on Intelligent Information Hiding and + Multimedia Signal Processing}, + year = {2010}, + pages = {208--211}, + address = {Darmstadt, Germany}, + month = oct, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@ARTICLE{friot10, + author = {Christophe Guyeux and Nicolas Friot and Jacques M. Bahi}, + title = {A more secure information hiding scheme than spread-spectrum obtained + by chaos-security}, + journal = {arXiv 0032565}, + year = {2010}, + owner = {guyeux}, + timestamp = {2010.04.30} +} + +@BOOK{ECC, + title = {Guide to Elliptic Curve Cryptography}, + publisher = {Springer Professional Computing}, + year = {2004}, + editor = {Springer}, + author = {D. Hankerson and A. Menezes and S. Vanstone}, + owner = {christophe}, + timestamp = {2010.07.31} +} + +@ARTICLE{Hasegawa1985, + author = {M. Hasegawa and H. Kishino and T. Yano}, + title = {Dating of the human-ape splitting by a molecular clock of mitochondrial + DNA.}, + journal = {J Mol Evol}, + year = {1985}, + volume = {22}, + pages = {160--174}, + number = {2}, + abstract = {A new statistical method for estimating divergence dates of species + from DNA sequence data by a molecular clock approach is developed. + This method takes into account effectively the information contained + in a set of DNA sequence data. The molecular clock of mitochondrial + DNA (mtDNA) was calibrated by setting the date of divergence between + primates and ungulates at the Cretaceous-Tertiary boundary (65 million + years ago), when the extinction of dinosaurs occurred. A generalized + least-squares method was applied in fitting a model to mtDNA sequence + data, and the clock gave dates of 92.3 +/- 11.7, 13.3 +/- 1.5, 10.9 + +/- 1.2, 3.7 +/- 0.6, and 2.7 +/- 0.6 million years ago (where the + second of each pair of numbers is the standard deviation) for the + separation of mouse, gibbon, orangutan, gorilla, and chimpanzee, + respectively, from the line leading to humans. Although there is + some uncertainty in the clock, this dating may pose a problem for + the widely believed hypothesis that the pipedal creature Australopithecus + afarensis, which lived some 3.7 million years ago at Laetoli in Tanzania + and at Hadar in Ethiopia, was ancestral to man and evolved after + the human-ape splitting. Another likelier possibility is that mtDNA + was transferred through hybridization between a proto-human and a + proto-chimpanzee after the former had developed bipedalism.}, + keywords = {Animals; Biological Evolution; DNA, Mitochondrial, genetics; Genes; + Haplorhini, genetics; Humans; Mathematics; Models, Genetic; Nucleic + Acid Hybridization; Primates, genetics; Proteins, genetics; Species + Specificity}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pmid = {3934395}, + timestamp = {2011.05.05} +} + +@BOOK{R1994, + title = {A First Course in Discrete Dynamical Systems}, + publisher = {Springer-Verlag}, + year = {1994}, + author = {R. Homlgren}, + optpages = {106}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@INCOLLECTION{Hoque09, + author = {Hoque, Md. and Chetty, Madhu and Sattar, Abdul}, + title = {Genetic Algorithm in Ab Initio Protein Structure Prediction Using + Low Resolution Model: A Review}, + booktitle = {Biomedical Data and Applications}, + publisher = {Springer Berlin Heidelberg}, + year = {2009}, + editor = {Sidhu, Amandeep and Dillon, Tharam}, + volume = {224}, + series = {Studies in Computational Intelligence}, + pages = {317-342}, + affiliation = {IIIS, Griffith University, Nathan, QLD-4111 Australia} +} + +@CONFERENCE{Houmansadr09, + author = {A. Houmansadr and N. Kiyavash and N. Borisov}, + title = {Rainbow: A robust and invisible non-blind watermark for network flows}, + booktitle = {NDSS’09: 16th Annual Network and Distributed System Security Symposium}, + year = {2009}, + owner = {christophe}, + timestamp = {2010.03.07} +} + +@ARTICLE{Huang10, + author = {Huang, Shih-I and Shieh, Shiuhpyng and Tygar, J.}, + title = {Secure encrypted-data aggregation for wireless sensor networks}, + journal = {Wireless Networks}, + abstract = {Abstract\ \ This paper proposes a secure encrypted-data + aggregation scheme for wireless sensor networks. Our design for data + aggregation eliminates redundant sensor readings without using encryption + and maintains data secrecy and privacy during transmission. Conventional + aggregation functions operate when readings are received in plaintext. + If readings are encrypted, aggregation requires decryption creating + extra overhead and key management issues. In contrast to conventional + schemes, our proposed scheme provides security and privacy, and duplicate + instances of original readings will be aggregated into a single packet. + Our scheme is resilient to known-plaintext attacks, chosen-plaintext + attacks, ciphertext-only attacks and man-in-the-middle attacks. Our + experiments show that our proposed aggregation method significantly + reduces communication overhead and can be practically implemented + in on-the-shelf sensor platforms.}, + citeulike-article-id = {4499496}, + citeulike-linkout-0 = {http://dx.doi.org/10.1007/s11276-009-0177-y}, + citeulike-linkout-1 = {http://www.springerlink.com/content/g573138072642u63}, + doi = {10.1007/s11276-009-0177-y}, + posted-at = {2009-05-10 09:55:44}, + url = {http://dx.doi.org/10.1007/s11276-009-0177-y} +} + +@ARTICLE{W.2001, + author = {W. Huang and X. Ye}, + title = {Homeomorphisms with the whole compacta being scrambled sets}, + journal = {Ergod. Th. Dynam. Systems}, + year = {2001}, + optnumber = {1}, + optpages = {77-91}, + optvolume = {21}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@ARTICLE{Hurley1982, + author = {M. Hurley}, + title = {Attractors, persistence and density of their bassin}, + journal = {Transactions of AMS}, + year = {1982}, + optpages = {247-271}, + optvolume = {269}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@INPROCEEDINGS{Islam:2009:NMA:1695134.1695181, + author = {Islam, Md. Kamrul and Chetty, Madhu}, + title = {Novel Memetic Algorithm for Protein Structure Prediction}, + booktitle = {Proceedings of the 22nd Australasian Joint Conference on Advances + in Artificial Intelligence}, + year = {2009}, + series = {AI '09}, + pages = {412--421}, + address = {Berlin, Heidelberg}, + publisher = {Springer-Verlag}, + acmid = {1695181}, + isbn = {978-3-642-10438-1}, + keywords = {Guided search space, Memetic Algorithm, Modified fitness function, + Pair-wise-interchange, Schema preservation, Tabu Search}, + location = {Melbourne, Australia}, + numpages = {10} +} + +@PHDTHESIS{Jacquemard77, + author = {C. Jacquemard}, + title = {Contribution à l'étude d'algorithmes à convergence monotone}, + school = {Université de Franche-Comté}, + year = {1977}, + owner = {christophe}, + timestamp = {2010.08.25} +} + +@BOOK{Jukes69, + title = {{Evolution of Protein Molecules}}, + publisher = {Academy Press}, + year = {1969}, + editor = {Munro, H. N.}, + author = {Jukes, T. H. and Cantor, C. R.}, + booktitle = {Evolution of Protein Molecules}, + citeulike-article-id = {1673661}, + keywords = {compbio, fresco}, + posted-at = {2007-09-19 06:23:18}, + priority = {2} +} + +@INPROCEEDINGS{Kalker2001, + author = {Kalker, T.}, + title = {Considerations on watermarking security}, + year = {2001}, + pages = {201--206}, + abstract = {In this paper we address the usually implicit assumption that digital + watermarking has as its main target copyright and copy protection + applications. From these target applications a great many conclusions + are drawn about the required security of a watermarking system, and + in fact, a considerably percentage of the watermarking literature + has this very topic as its main focus of attention. In this paper + we take a step back, and try to do a more careful analysis of the + 'watermarking-is-for-security-applications' paradigm. The intention + of this paper is to discuss the meaning of the concept security in + the context of watermarking, and try to show that one has to be careful + in using analogies from the related field of cryptography}, + citeulike-article-id = {1226513}, + journal = {2001 IEEE Fourth Workshop on Multimedia Signal Processing}, + keywords = {security, wateramarking}, + owner = {guyeux}, + posted-at = {2007-04-14 14:30:06}, + priority = {2}, + timestamp = {2009.06.30} +} + +@ARTICLE{Kerckhoffs83, + author = {Kerckhoffs, Auguste}, + title = {La cryptographie militaire}, + journal = {Journal des sciences militaires}, + year = {1883}, + volume = {IX}, + pages = {5--83}, + month = {January}, + abstract = {pp. 161–191, Feb. 1883.}, + citeulike-article-id = {505508}, + keywords = {cryptography, master}, + owner = {guyeux}, + posted-at = {2006-02-15 04:49:15}, + priority = {2}, + timestamp = {2009.06.30} +} + +@ARTICLE{Kimura80, + author = {Kimura, Motoo}, + title = {A simple method for estimating evolutionary rates of base substitutions + through comparative studies of nucleotide sequences}, + journal = {Journal of Molecular Evolution}, + year = {1980}, + volume = {16}, + pages = {111-120}, + note = {10.1007/BF01731581}, + affiliation = {National Institute of Genetics 411 Mishima Japan}, + issn = {0022-2844}, + issue = {2}, + keyword = {Biomedical and Life Sciences}, + publisher = {Springer New York}, + url = {http://dx.doi.org/10.1007/BF01731581} +} + +@ARTICLE{Knudsen94, + author = {Knudsen}, + title = {Chaos Without Nonperiodicity}, + journal = {Amer. Math. Monthly}, + year = {1994}, + volume = {101}, + owner = {guyeux}, + timestamp = {27/01/2008} +} + +@PHDTHESIS{Knudsen1994a, + author = {C. Knudsen}, + title = {Aspects of noninvertible dynamics and chaos}, + school = {Technical University of Denmark}, + year = {1994}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@BOOK{Knuth97, + title = {Seminumerical Algorithms}, + publisher = {Addison-Wesley, Reading, MA, USA}, + year = {1997}, + author = {D. E. Knuth}, + volume = {3}, + edition = {Third Edition}, + owner = {guyeux}, + timestamp = {2012.02.15} +} + +@ARTICLE{Kocarev06, + author = {L. Kocarev and J. Szczepanski and J.M. Amigo and I. Tomovski}, + title = {Discrete Chaos - I: Theory}, + journal = {IEEE Trans. on Circuits Systems}, + year = {2006}, + volume = {53}, + pages = {1300-1309}, + owner = {christophe}, + timestamp = {2010.10.10} +} + +@INPROCEEDINGS{Kocher95cryptanalysisof, + author = {Paul C. Kocher}, + title = {Cryptanalysis of Diffie-Hellman, RSA, DSS, and Other Systems Using + Timing Attacks (Extended Abstract)}, + booktitle = {Advances in Cryptology, CRYPTO '95: 15th Annual International Cryptology + Conference}, + year = {1995}, + pages = {27--31}, + publisher = {Springer-Verlag} +} + +@ARTICLE{Kullback1951, + author = {Kullback, Solomon and Leibler, Richard A.}, + title = {On Information and Sufficiency}, + journal = {The Annals of Mathematical Statistics}, + year = {1951}, + volume = {22}, + pages = {79--86}, + number = {1}, + citeulike-article-id = {3245942}, + keywords = {file-import-08-09-12}, + owner = {guyeux}, + posted-at = {2008-09-12 14:30:37}, + priority = {2}, + timestamp = {2009.06.29} +} + +@ARTICLE{Lang08, + author = {Lang, Gregory I. and Murray, Andrew W.}, + title = {Estimating the Per-Base-Pair Mutation Rate in the Yeast Saccharomyces + cerevisiae}, + journal = {Genetics}, + year = {January 2008}, + volume = {178}, + pages = {67-82}, + number = {1}, + abstract = {Although mutation rates are a key determinant of the rate of evolution + they are difficult to measure precisely and global mutations rates + (mutations per genome per generation) are often extrapolated from + the per-base-pair mutation rate assuming that mutation rate is uniform + across the genome. Using budding yeast, we describe an improved method + for the accurate calculation of mutation rates based on the fluctuation + assay. Our analysis suggests that the per-base-pair mutation rates + at two genes differ significantly (3.80 × 10−10 at URA3 and 6.44 + × 10−10 at CAN1) and we propose a definition for the effective target + size of genes (the probability that a mutation inactivates the gene) + that acknowledges that the mutation rate is nonuniform across the + genome.}, + doi = {10.1534/genetics.107.071506}, + eprint = {http://www.genetics.org/content/178/1/67.full.pdf+html}, + url = {http://www.genetics.org/content/178/1/67.abstract} +} + +@MISC{ledoux, + author = {Eshter Ledoux}, + title = {Introduction à la théorie du chaos}, + year = {2002}, + note = {[En ligne; Page disponible le 12-août-2010]}, + url = {\url{http://www.nux.be/eledoux/mem/node1.html}} +} + +@BOOK{Lehning1997, + title = {Analyse en dimension finie}, + publisher = {Masson}, + year = {1997}, + author = {Lehning}, + optpages = {28}, + optvolume = {4}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@ARTICLE{Lenstra01, + author = {A.K. Lenstra and E.R. Verheul}, + title = {Selecting Cryptographic Key Sizes}, + journal = {Jour. of the International Association for Cryptologic Research}, + year = {2001}, + volume = {14}, + pages = {255-293}, + number = {4} +} + +@ARTICLE{Pitts59, + author = {Lettvin, J.Y. and Maturana, H.R. and McCulloch, W.S. and Pitts, W.H.}, + title = {What the Frog's Eye Tells the Frog's Brain}, + journal = {Proceedings of the IRE}, + year = {1959}, + volume = {47}, + pages = {1940--51}, + number = {11}, + owner = {christophe}, + timestamp = {2010.12.21} +} + +@PHDTHESIS{Li11, + author = {Ming Li}, + title = {User-Centric Security and Privacy Mechanisms in Untrusted Networking + and Computing Environments}, + school = {Worcester Polytechnic Institute}, + year = {2011}, + owner = {guyeux}, + timestamp = {2012.05.04} +} + +@ARTICLE{Li75, + author = {T. Y. Li and J. A. Yorke}, + title = {Period three implies chaos}, + journal = {Amer. Math. Monthly}, + year = {1975}, + volume = {82}, + pages = {985--992}, + number = {10}, + owner = {guyeux}, + timestamp = {27/01/2008} +} + +@ARTICLE{Xiao10, + author = {Li, Yantao and Deng, Shaojiang and Xiao, Di}, + title = {A novel Hash algorithm construction based on chaotic neural network}, + journal = {Neural Computing and Applications}, + year = {2010}, + pages = {1-9}, + affiliation = {Chongqing University College of Computer Science 400044 Chongqing + China}, + issn = {0941-0643}, + keyword = {Computer Science}, + publisher = {Springer London} +} + +@INPROCEEDINGS{Lin09, + author = {Lin, Hua-Yi and Chiang, Tzu-Chiang}, + title = {Cooperative secure data aggregation in sensor networks using elliptic + curve based cryptosystems}, + booktitle = {CDVE'09: Proceedings of the 6th international conference on Cooperative + design, visualization, and engineering}, + year = {2009}, + pages = {384--387}, + address = {Berlin, Heidelberg}, + publisher = {Springer-Verlag}, + isbn = {3-642-04264-3, 978-3-642-04264-5}, + location = {Luxembourg, Luxembourg} +} + +@INPROCEEDINGS{Liu2008, + author = {Liu, An and Ning, Peng}, + title = {TinyECC: A Configurable Library for Elliptic Curve Cryptography in + Wireless Sensor Networks}, + booktitle = {7th International Conference on Information Processing in Sensor + Networks (IPSN 2008)}, + year = {2008}, + pages = {245--256}, + month = {April}, + citeulike-article-id = {3041699}, + howpublished = {SPOTS Track}, + keywords = {hagg}, + posted-at = {2008-07-25 05:25:05}, + priority = {2} +} + +@ARTICLE{Liu2007bis, + author = {Shao-Hui Liu and Hong-Xun Yao and Wen Gao and Yong-Liang Liu}, + title = {An image fragile watermark scheme based on chaotic image pattern + and pixel-pairs}, + journal = {Applied Mathematics and Computation}, + year = {2007}, + volume = {185}, + pages = {869-882}, + owner = {guyeux}, + timestamp = {2008.10.07} +} + +@INPROCEEDINGS{Liu07, + author = {Liu, Zhen and Xi, Lifeng}, + title = {Image Information Hiding Encryption Using Chaotic Sequence}, + booktitle = {KES '07: Knowledge-Based Intelligent Information and Engineering + Systems and the XVII Italian Workshop on Neural Networks on Proceedings + of the 11th International Conference}, + year = {2007}, + pages = {202--208}, + address = {Berlin, Heidelberg}, + publisher = {Springer-Verlag}, + doi = {http://dx.doi.org/10.1007/978-3-540-74827-4_26}, + isbn = {978-3-540-74826-7}, + location = {Vietri sul Mare, Italy} +} + +@ARTICLE{Liu2007, + author = {Zhen Liu and Lifeng Xi}, + title = {Image Information Hiding Encryption Using Chaotic Sequence}, + journal = {LNAI}, + year = {2007}, + volume = {4693}, + pages = {202-208}, + owner = {guyeux}, + timestamp = {11/04/2008} +} + +@ARTICLE{Lubachevsky86, + author = {Lubachevsky, Boris and Mitra, Debasis}, + title = {A chaotic asynchronous algorithm for computing the fixed point of + a nonnegative matrix of unit spectral radius}, + journal = {J. ACM}, + year = {1986}, + volume = {33}, + pages = {130--150}, + number = {1}, + address = {New York, NY, USA}, + doi = {http://doi.acm.org/10.1145/4904.4801}, + issn = {0004-5411}, + publisher = {ACM} +} + +@ARTICLE{Larger10, + author = {{L}arger, {L}. and {D}udley, {J}.{M}.}, + title = { {N}onlinear dynamics {O}ptoelectronic chaos}, + journal = {{N}ature }, + year = {2010}, + volume = {465 }, + pages = {41-42 }, + number = {7294 }, + month = {05}, + abstract = {{O}ptoelectronic circuits with delayed feedback provide a convenient + bench-top platform to study a wide range of nonlinear dynamic systems, + from ultrastable clocks to complex chaotic devices.}, + affiliation = {{F}ranche-{C}omt{\'e} {\'E}lectronique {M}{\'e}canique, {T}hermique + et {O}ptique - {S}ciences et {T}echnologies - {FEMTO}-{ST} - {CNRS} + : {UMR}6174 - {U}niversit{\'e} de {F}ranche-{C}omt{\'e} - {U}niversit{\'e} + de {T}echnologie de {B}elfort-{M}ontbeliard - {E}cole {N}ationale + {S}up{\'e}rieure de {M}{\'e}canique et des {M}icrotechniques }, + audience = {internationale }, + day = {05}, + doi = {10.1038/465041a }, + hal_id = {hal-00517696}, + language = {{A}nglais}, + url = {http://hal.archives-ouvertes.fr/hal-00517696/en/} +} + +@INPROCEEDINGS{Mahoney00, + author = {Mahoney, Matthew V.}, + title = {Fast Text Compression with Neural Networks}, + booktitle = {Proceedings of the Thirteenth International Florida Artificial Intelligence + Research Society Conference}, + year = {2000}, + pages = {230--234}, + publisher = {AAAI Press}, + acmid = {707654}, + isbn = {1-57735-113-4}, + numpages = {5} +} + +@INPROCEEDINGS{msp10:bl, + author = {Makhoul, Abdallah and Saadi, Rachid and Pham, Congduc}, + title = {Risk Management in Intrusion Detection Applications with Wireless + Video Sensor Networks}, + booktitle = {WCNC'10 IEEE Int. Conf.}, + year = {2010}, + pages = {***--***}, + address = {Sydney, Australia}, + month = apr, + note = {To appear}, + classement = {*}, + equipe = {and}, + inhal = {no} +} + +@ARTICLE{Malvar03, + author = {H.S. Malvar and D. Florêncio}, + title = {Improved Spread Spectrum: A New Modulation Technique for Robust Watermarking}, + journal = {IEEE Trans. Signal Proceeding}, + year = {2003}, + volume = {53}, + pages = {898--905}, + owner = {christophe}, + timestamp = {2010.03.07} +} + +@ARTICLE{Marsaglia2003, + author = {G. Marsaglia}, + title = {Xorshift RNGs}, + journal = {Journal of Statistical Software}, + year = {2003}, + volume = {8(14)}, + pages = {1--6}, + owner = {qianxue}, + timestamp = {2009.10.28} +} + +@ARTICLE{Marsaglia1996, + author = {G. Marsaglia}, + title = {DIEHARD: a battery of tests of randomness.}, + journal = {http://stat.fsu.edu/~geo/diehard.html}, + year = {1996}, + owner = {qianxue}, + timestamp = {2009.11.09} +} + +@ARTICLE{DefiningChaos, + author = {M. Martelli and M. Dang and T. Seph}, + title = {Defining chaos}, + journal = {Mathematics Magazine}, + year = {1998}, + volume = {71}, + pages = {112--122}, + owner = {christophe}, + timestamp = {2010.08.11} +} + +@ARTICLE{Michel2007c, + author = {Christian J Michel}, + title = {An analytical model of gene evolution with 9 mutation parameters: + an application to the amino acids coded by the common circular code.}, + journal = {Bull Math Biol}, + year = {2007}, + volume = {69}, + pages = {677--698}, + number = {2}, + month = {Feb}, + abstract = {We develop here an analytical evolutionary model based on a trinucleotide + mutation matrix 64 x 64 with nine substitution parameters associated + with the three types of substitutions in the three trinucleotide + sites. It generalizes the previous models based on the nucleotide + mutation matrices 4 x 4 and the trinucleotide mutation matrix 64 + x 64 with three and six parameters. It determines at some time t + the exact occurrence probabilities of trinucleotides mutating randomly + according to these nine substitution parameters. An application of + this model allows an evolutionary study of the common circular code + [Formula: see text] of eukaryotes and prokaryotes and its 12 coded + amino acids. The main property of this code [Formula: see text] is + the retrieval of the reading frames in genes, both locally, i.e. + anywhere in genes and in particular without a start codon, and automatically + with a window of a few nucleotides. However, since its identification + in 1996, amino acid information coded by [Formula: see text] has + never been studied. Very unexpectedly, this evolutionary model demonstrates + that random substitutions in this code [Formula: see text] and with + particular values for the nine substitutions parameters retrieve + after a certain time of evolution a frequency distribution of these + 12 amino acids very close to the one coded by the actual genes.}, + doi = {10.1007/s11538-006-9147-z}, + institution = {Equipe de Bioinformatique Théorique, LSIIT (UMR CNRS-ULP 7005), Université + Louis Pasteur de Strasbourg, Pôle API, Boulevard Sébastien Brant, + 67400 Illkirch, France. michel@dpt-info.u-strasbg.fr}, + keywords = {Amino Acids, genetics; Codon, genetics; Eukaryotic Cells; Evolution, + Molecular; Models, Genetic; Prokaryotic Cells}, + language = {eng}, + medline-pst = {ppublish}, + owner = {guyeux}, + pmid = {16952018}, + timestamp = {2011.05.05}, + url = {http://dx.doi.org/10.1007/s11538-006-9147-z} +} + +@ARTICLE{Miellou75, + author = {J.-C. Miellou}, + title = {Algorithmes de relaxation chaotique \`{a} retards}, + journal = {Rairo}, + year = {1975}, + volume = {R1}, + pages = {148-162}, + owner = {guyeux}, + timestamp = {2008.05.22} +} + +@ARTICLE{Miellou75b, + author = {Miellou, J.-C.}, + title = {Itérations chaotiques à retards, étude de la convergence dans le + cas d'espaces partiellement ordonnés}, + journal = {C.R.A.S. Paris}, + year = {1975}, + volume = {280}, + pages = {233--236}, + owner = {christophe}, + timestamp = {2010.08.17} +} + +@ARTICLE{Spiteri85, + author = {Jean-Claude Miellou and Pierre Spitéri}, + title = {Un crit\`{e}re de convergence pour des méthodes générales de point + fixe}, + journal = {Rairo -- Modélisation mathématique et analyse numérique}, + year = {1985}, + volume = {19}, + pages = {645--669}, + number = {4}, + owner = {christophe}, + timestamp = {2010.10.13} +} + +@ARTICLE{Mooney08, + author = {Aidan Mooney and John G. Keating and Ioannis Pitas}, + title = {A comparative study of chaotic and white noise signals in digital + watermarking}, + journal = {Chaos, Solitons and Fractals}, + year = {2008}, + volume = {35}, + pages = {913-921}, + owner = {christophe}, + timestamp = {2010.03.01} +} + +@ARTICLE{Nakashima2003, + author = {Nakashima, Y. and Tachibana, R. and Babaguchi, N.}, + title = {Watermarked Movie Soundtrack Finds the Position of the Camcorder + in a Theater}, + journal = {IEEE Transactions on Multimedia}, + year = {2009}, + note = {Accepted for future publication Multimedia} +} + +@INCOLLECTION{springerlink:10.1007/978-3-642-04431-1_16, + author = {Nelson, Michael and Nahapetian, Ani and Koushanfar, Farinaz and Potkonjak, + Miodrag}, + title = {SVD-Based Ghost Circuitry Detection}, + booktitle = {Information Hiding}, + publisher = {Springer Berlin / Heidelberg}, + year = {2009}, + editor = {Katzenbeisser, Stefan and Sadeghi, Ahmad-Reza}, + volume = {5806}, + series = {Lecture Notes in Computer Science}, + pages = {221-234}, + note = {10.1007/978-3-642-04431-1_16}, + affiliation = {Computer Science Department, UCLA, Los Angeles, CA 90095, USA}, + url = {http://dx.doi.org/10.1007/978-3-642-04431-1_16} +} + +@INPROCEEDINGS{Perez-Hernandez09, + author = {P\'{e}rez-Hern\'{a}ndez, Luis Germ\'{a}n and Rodr\'{\i}guez-V\'{a}zquez, + Katya and Gardu\~{n}o-Ju\'{a}rez, Ram\'{o}n}, + title = {Parallel particle swarm optimization applied to the protein folding + problem}, + booktitle = {Proceedings of the 11th Annual conference on Genetic and evolutionary + computation}, + year = {2009}, + series = {GECCO '09}, + pages = {1791--1792}, + address = {New York, NY, USA}, + publisher = {ACM}, + acmid = {1570163}, + isbn = {978-1-60558-325-9}, + keywords = {bioinformatics, biology and chemistry, combinatorial optimization, + parallelization, swarm intelligence}, + location = {Montreal, Qu\&\#233;bec, Canada}, + numpages = {2} +} + +@INPROCEEDINGS{Paillier99, + author = {Paillier, Pascal}, + title = {Public-key cryptosystems based on composite degree residuosity classes}, + booktitle = {Proceedings of the 17th international conference on Theory and application + of cryptographic techniques}, + year = {1999}, + series = {EUROCRYPT'99}, + pages = {223--238}, + address = {Berlin, Heidelberg}, + publisher = {Springer-Verlag}, + acmid = {1756146}, + isbn = {3-540-65889-0}, + location = {Prague, Czech Republic}, + numpages = {16}, + url = {http://dl.acm.org/citation.cfm?id=1756123.1756146} +} + +@PHDTHESIS{Pellegrin1986, + author = {D. Pellegrin}, + title = {Algorithmique discr\`{e}te et r\'{e}seaux d'automates}, + school = {Grenoble}, + year = {1986}, + owner = {guyeux}, + timestamp = {2008.05.22} +} + +@ARTICLE{Peng2005, + author = {F. Peng and S.-S. Qiu and M. Long}, + title = {One way Hash function construction based on two-dimensional hyperchaotic + mappings}, + journal = {Acta Phys. Sinici.}, + year = {2005}, + volume = {54}, + pages = {98--104}, + owner = {guyeux}, + timestamp = {2009.01.16} +} + +@INPROCEEDINGS{Perez06, + author = {Luis Perez-Freire and F. Pérez-gonzalez and Pedro Comesaña}, + title = {Secret Dither Estimation in Lattice-Quantization Data Hiding: A Set-Membership + Approach}, + booktitle = {Security, Steganography, and Watermarking of Multimedia Contents}, + year = {2006}, + editor = {Edward J. Delp and Ping W. Wong}, + address = {San Jose, California, USA}, + month = {January}, + organization = {SPIE}, + owner = {guyeux}, + timestamp = {2009.06.30} +} + +@INPROCEEDINGS{Perez-Freire06, + author = {Luis Perez-Freire and Pedro Comesana and Juan Ramon Troncoso-Pastoriza + and Fernando Perez-Gonzalez}, + title = {Watermarking Security: a Survey}, + booktitle = {LNCS Transactions on Data Hiding and Multimedia Security}, + year = {2006}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@PROCEEDINGS{Peter07, + title = {On Concealed Data Aggregation for WSNs}, + year = {2007}, + author = {Peter, Steffen and Piotrowski, Krzysztof and Langendoerfer, Peter}, + booktitle = {Consumer Communications and Networking Conference, 2007. CCNC 2007. + 4th IEEE}, + citeulike-article-id = {2281643}, + citeulike-linkout-0 = {http://dx.doi.org/10.1109/CCNC.2007.45}, + citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=4199133}, + doi = {10.1109/CCNC.2007.45}, + journal = {Consumer Communications and Networking Conference, 2007. CCNC 2007. + 4th IEEE}, + keywords = {hagg}, + pages = {192--196}, + posted-at = {2008-01-23 19:36:19}, + priority = {3}, + url = {http://dx.doi.org/10.1109/CCNC.2007.45} +} + +@ARTICLE{pms11:ij, + author = {Pham, Congduc and Makhoul, Abdallah and Saadi, Rachid}, + title = {Risk-based Adaptive Scheduling in Randomly Deployed Video Sensor + Networks for Critical Surveillance Applications}, + journal = {Journal of Network and Computer Applications}, + year = {2011}, + volume = {*}, + pages = {***--***}, + number = {*}, + note = {Accepted manuscript. To appear}, + classement = {ACLI}, + equipe = {and}, + impact-factor = {1.111}, + inhal = {no}, + isi-acro = {J NETW COMPU APPL}, + publisher = {Springer} +} + +@MISC{Poe, + author = {Edgar Alan Poe}, + title = {The Raven}, + month = {April}, + year = {1839}, + note = {American Museum (Baltimore)}, + owner = {christophe}, + timestamp = {2010.11.23} +} + +@INPROCEEDINGS{Przydatek03sia:secure, + author = {Bartosz Przydatek and Dawn Song and Adrian Perrig}, + title = {SIA: Secure Information Aggregation in Sensor Networks}, + year = {2003}, + pages = {255--265}, + publisher = {ACM Press} +} + +@ARTICLE{Perez-Freire2006:Security, + author = {L. P{\'e}rez-Freire and F. P{\'e}rez-González and T. Furon and P. + Comesaña}, + title = {Security of lattice-based data hiding against the known message attack}, + journal = {IEEE Trans. on Information Forensics and Security}, + year = {2006}, + volume = {1}, + pages = {421-439}, + number = {4}, + month = {dec}, + owner = {guyeux}, + timestamp = {2009.12.06} +} + +@MISC{Quisquater02sidechannel, + author = {J-J. Quisquater and D. Samyde and Université Catholique De Louvain + and Groupe Crypto}, + title = {Side Channel Cryptanalysis}, + year = {2002} +} + +@ARTICLE{Raynal2001, + author = {Frédéric Raynal and Fabien A. P. Petitcolas and Caroline Fontaine}, + title = {Evaluation automatique des méthodes de tatouage}, + journal = {Traitement du signal}, + year = {2001}, + volume = {18}, + pages = {271-282}, + owner = {guyeux}, + timestamp = {2008.05.21} +} + +@MISC{rijmen05, + author = {Vincent Rijmen and Elisabeth Oswald}, + title = {Update on SHA-1}, + howpublished = {Cryptology ePrint Archive, Report 2005/010}, + year = {2005}, + note = {\url{http://eprint.iacr.org/}} +} + +@BOOK{Robert, + title = {Discrete Iterations, a Metric Study}, + publisher = {Springer-Verlag}, + year = {1986}, + editor = {Berlin Heidelberg New-York}, + author = {François Robert}, + volume = {6}, + series = {Series in Computational Mathematics} +} + +@BOOK{Robert1986, + title = {Discrete Iterations: A Metric Study}, + year = {1986}, + editor = {Springer-Verlag}, + author = {F. Robert}, + volume = {6}, + series = {Springer Series in Computational Mathematics}, + owner = {guyeux}, + timestamp = {17/02/2008} +} + +@ARTICLE{Rudenko08, + author = {Rudenko, O. and Snytkin, M.}, + title = {Image compression based on the neural network art}, + journal = {Cybernetics and Systems Analysis}, + year = {2008}, + volume = {44}, + pages = {797-802}, + affiliation = {Kharkov National University of Radio Electronics Kharkov Ukraine}, + issn = {1060-0396}, + issue = {6}, + keyword = {Computer Science}, + publisher = {Springer New York} +} + +@PHDTHESIS{Ruette2001, + author = {Sylvie Ruette}, + title = {Chaos en dynamique topologique, en particulier sur l'intervalle, + mesures d'entropie maximale}, + school = {Université d'Aix-Marseille II}, + year = {2001}, + optmonth = {Novembre}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@MASTERSTHESIS{Saulnier02, + author = {Boris Saulnier}, + title = {Entropie topologique}, + school = {DEA Sémantique, Preuves et Langages, Paris 7}, + year = {2002}, + owner = {christophe}, + timestamp = {2010.08.12} +} + +@ARTICLE{Schmitz2001, + author = {Roland Schmitz}, + title = {Use of chaotic dynamical systems in cryptography}, + journal = {Journal of Franklin Institute}, + year = {2001}, + volume = {338}, + pages = {429-441}, + owner = {guyeux}, + timestamp = {17/02/2008} +} + +@BOOK{Schwartz80, + title = {Analyse: topologie g\'{e}n\'{e}rale et analyse fonctionnelle}, + publisher = {Hermann}, + year = {1980}, + editor = {Hermann}, + author = {Laurent Schwartz}, + owner = {christophe}, + timestamp = {2010.09.15} +} + +@ARTICLE{Shannon49, + author = {Shannon, Claude E.}, + title = {Communication Theory of Secrecy Systems}, + journal = {Bell Systems Technical Journal}, + year = {1949}, + volume = {28}, + pages = {656--715}, + citeulike-article-id = {507362}, + keywords = {master, secrecy\_systems, teoria-informacao, theory\_communication, + theory\_cryptography}, + owner = {guyeux}, + posted-at = {2006-02-16 23:24:09}, + priority = {2}, + timestamp = {2009.06.29} +} + +@ARTICLE{Shmygelska05, + author = {Shmygelska, Alena and Hoos, Holger}, + title = {An ant colony optimisation algorithm for the 2D and 3D hydrophobic + polar protein folding problem}, + journal = {BMC Bioinformatics}, + year = {2005}, + volume = {6}, + pages = {30}, + number = {1}, + abstract = {BACKGROUND:The protein folding problem is a fundamental problems in + computational molecular biology and biochemical physics. Various + optimisation methods have been applied to formulations of the ab-initio + folding problem that are based on reduced models of protein structure, + including Monte Carlo methods, Evolutionary Algorithms, Tabu Search + and hybrid approaches. In our work, we have introduced an ant colony + optimisation (ACO) algorithm to address the non-deterministic polynomial-time + hard (NP-hard) combinatorial problem of predicting a protein's conformation + from its amino acid sequence under a widely studied, conceptually + simple model - the 2-dimensional (2D) and 3-dimensional (3D) hydrophobic-polar + (HP) model.RESULTS:We present an improvement of our previous ACO + algorithm for the 2D HP model and its extension to the 3D HP model. + We show that this new algorithm, dubbed ACO-HPPFP-3, performs better + than previous state-of-the-art algorithms on sequences whose native + conformations do not contain structural nuclei (parts of the native + fold that predominantly consist of local interactions) at the ends, + but rather in the middle of the sequence, and that it generally finds + a more diverse set of native conformations.CONCLUSIONS:The application + of ACO to this bioinformatics problem compares favourably with specialised, + state-of-the-art methods for the 2D and 3D HP protein folding problem; + our empirical results indicate that our rather simple ACO algorithm + scales worse with sequence length but usually finds a more diverse + ensemble of native states. Therefore the development of ACO algorithms + for more complex and realistic models of protein structure holds + significant promise.}, + doi = {10.1186/1471-2105-6-30}, + issn = {1471-2105}, + pubmedid = {15710037} +} + +@OTHER{Shmygelska2005Feb, + __markedentry = {[christophe]}, + abstract = {Abstract Background The protein folding problem is a fundamental problems + in computational molecular biology and biochemical physics. Various + optimisation methods have been applied to formulations of the ab-initio + folding problem that are based on reduced models of protein structure, + including Monte Carlo methods, Evolutionary Algorithms, Tabu Search + and hybrid approaches. In our work, we have introduced an ant colony + optimisation (ACO) algorithm to address the non-deterministic polynomial-time + hard (NP-hard) combinatorial problem of predicting a protein's conformation + from its amino acid sequence under a widely studied, conceptually + simple model – the 2-dimensional (2D) and 3-dimensional (3D) hydrophobic-polar + (HP) model. Results We present an improvement of our previous ACO + algorithm for the 2D HP model and its extension to the 3D HP model. + We show that this new algorithm, dubbed ACO-HPPFP-3, performs better + than previous state-of-the-art algorithms on sequences whose native + conformations do not contain structural nuclei (parts of the native + fold that predominantly consist of local interactions) at the ends, + but rather in the middle of the sequence, and that it generally finds + a more diverse set of native conformations. Conclusions The application + of ACO to this bioinformatics problem compares favourably with specialised, + state-of-the-art methods for the 2D and 3D HP protein folding problem; + our empirical results indicate that our rather simple ACO algorithm + scales worse with sequence length but usually finds a more diverse + ensemble of native states. Therefore the development of ACO algorithms + for more complex and realistic models of protein structure holds + significant promise.}, + author = {Shmygelska, Alena and Hoos, Holger H}, + journal = {BMC Bioinformatics. 2005 Feb 14}, + number = {1}, + owner = {christophe}, + pages = {30}, + timestamp = {2011.01.24}, + title = {An ant colony optimisation algorithm for the 2D and 3D hydrophobic + polar protein folding problem}, + volume = {6}, + year = {2005 Feb} +} + +@ARTICLE{Shujun1, + author = {Li Shujun and Li Qi and Li Wenmin and Mou Xuanqin and Cai Yuanlong}, + title = {Statistical Properties of Digital Piecewise Linear Chaotic Maps and + Their Roles in Cryptography and Pseudo-Random Coding}, + journal = {Proceedings of the 8th IMA International Conference on Cryptography + and Coding}, + year = {2001}, + volume = {1}, + pages = {205--221}, + owner = {christophe}, + timestamp = {2010.03.06} +} + +@ARTICLE{Simard07testu01:a, + author = {Richard Simard and Université De Montréal}, + title = {TestU01: A C library for empirical testing of random number generators}, + journal = {ACM Transactions on Mathematical Software}, + year = {2007}, + pages = {2007} +} + +@INPROCEEDINGS{Simmons83, + author = {Gustavus J. Simmons}, + title = {The Prisoners' Problem and the Subliminal Channel}, + booktitle = {Advances in Cryptology, Proc. CRYPTO'83}, + year = {1984}, + pages = {51--67}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@ARTICLE{Solak2004389, + author = {Ercan Solak}, + title = {On the security of a class of discrete-time chaotic cryptosystems}, + journal = {Physics Letters A}, + year = {2004}, + volume = {320}, + pages = {389 - 395}, + number = {5-6}, + doi = {DOI: 10.1016/j.physleta.2003.11.008}, + issn = {0375-9601}, + keywords = {Communication using chaos}, + owner = {guyeux}, + timestamp = {2009.12.12}, + url = {http://www.sciencedirect.com/science/article/B6TVM-4B22RC9-2/2/99a0af737c9b6ba8af47ae4d3c7a326d} +} + +@PHDTHESIS{Spiteri74, + author = {Pierre Spitéri}, + title = {Contribution à l'étude de la stabilite au sens de liapounov de certains + systemes differentiels non lineaires}, + school = {Université de Franche-Comté}, + year = {1974}, + owner = {christophe}, + timestamp = {2010.10.13} +} + +@BOOK{Stewart1989, + title = {Does God Play Dices ?: the mathematics of chaos}, + publisher = {Penguin}, + year = {1989}, + author = {Ian Stewart}, + owner = {guyeux}, + timestamp = {2008.01.02} +} + +@BOOK{Stinson02, + title = {Cryptography: Theory and Practice, Second Edition}, + publisher = {{Chapman \& Hall/CRC}}, + year = {2002}, + author = {Stinson, Douglas R.}, + month = {February}, + abstract = {{Douglas R. Stinson's Cryptography: Theory and Practice is + a mathematically intensive examination of cryptography, including + ciphers, the Data Encryption Standard (DES), public key cryptography, + one-way hash functions, and digital signatures. Stinson's explication + of "zero-sum proofs"--a process by which one person lets another + person know that he or she has a password without actually revealing + any information--is especially good.

If you are new to the math + behind cryptography but want to tackle it, the author covers all + of the required background to understand the real mathematics here. + Cryptography includes extensive exercises with each chapter + and makes an ideal introduction for any math-literate person willing + to get acquainted with this material.} {

Major advances over the + last five years precipitated this major revision of the bestselling + Cryptography: Theory and Practice. With more than 40 percent new + or updated material, the second edition now provides an even more + comprehensive treatment of modern cryptography. It focuses on the + new Advanced Encryption Standards and features an entirely new chapter + on that subject. Another new chapter explores the applications of + secret sharing schemes, including ramp schemes, visual cryptography, + threshold cryptography, and broadcast encryption. This is an ideal + introductory text for both computer science and mathematics students + and a valuable reference for professionals.

}}, + citeulike-article-id = {2401855}, + day = {27}, + howpublished = {Hardcover}, + isbn = {1584882069}, + keywords = {security}, + posted-at = {2008-02-20 08:28:49}, + priority = {0}, + url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20\&path=ASIN/1584882069} +} + +@ARTICLE{Tamura92, + author = {Tamura, K}, + title = {Estimation of the number of nucleotide substitutions when there are + strong transition-transversion and G+C-content biases.}, + journal = {Molecular Biology and Evolution}, + year = {1992}, + volume = {9}, + pages = {678-687}, + number = {4}, + abstract = {A simple mathematical method is developed to estimate the number of + nucleotide substitutions per site between two DNA sequences, by extending + Kimura's (1980) two-parameter method to the case where a G+C-content + bias exists. This method will be useful when there are strong transition-transversion + and G+C-content biases, as in the case of Drosophila mitochondrial + DNA.}, + eprint = {http://mbe.oxfordjournals.org/content/9/4/678.full.pdf+html}, + url = {http://mbe.oxfordjournals.org/content/9/4/678.abstract} +} + +@ARTICLE{Tamura93, + author = {Tamura, K and Nei, M}, + title = {Estimation of the number of nucleotide substitutions in the control + region of mitochondrial DNA in humans and chimpanzees.}, + journal = {Molecular Biology and Evolution}, + year = {1993}, + volume = {10}, + pages = {512-526}, + number = {3}, + abstract = {Examining the pattern of nucleotide substitution for the control region + of mitochondrial DNA (mtDNA) in humans and chimpanzees, we developed + a new mathematical method for estimating the number of transitional + and transversional substitutions per site, as well as the total number + of nucleotide substitutions. In this method, excess transitions, + unequal nucleotide frequencies, and variation of substitution rate + among different sites are all taken into account. Application of + this method to human and chimpanzee data suggested that the transition/transversion + ratio for the entire control region was approximately 15 and nearly + the same for the two species. The 95% confidence interval of the + age of the common ancestral mtDNA was estimated to be 80,000-480,000 + years in humans and 0.57-2.72 Myr in common chimpanzees.}, + eprint = {http://mbe.oxfordjournals.org/content/10/3/512.full.pdf+html}, + url = {http://mbe.oxfordjournals.org/content/10/3/512.abstract} +} + +@INPROCEEDINGS{Takana90, + author = {K. Tanaka and Y. Nakamura and K. Matsui}, + title = {Embedding Secret Information into a Dithered Multi-level Image}, + booktitle = {IEEE Military Communications Conference}, + year = {1990}, + owner = {christophe}, + timestamp = {2010.08.05} +} + +@PHDTHESIS{ElTarazi81, + author = {M. N. El Tarazi}, + title = {Contraction et ordre partiel pour l'étude d'algorithmes synchrones + et asynchrones en analyse numérique}, + school = {Faculté des Sciences et Techniques de l'Université de Franche-Comté, + Besançon}, + year = {1981}, + owner = {christophe}, + timestamp = {2010.08.17} +} + +@INPROCEEDINGS{Unger93, + author = {Unger, Ron and Moult, John}, + title = {Genetic Algorithm for 3D Protein Folding Simulations}, + booktitle = {Proceedings of the 5th International Conference on Genetic Algorithms}, + year = {1993}, + pages = {581--588}, + address = {San Francisco, CA, USA}, + publisher = {Morgan Kaufmann Publishers Inc.}, + acmid = {657747}, + isbn = {1-55860-299-2}, + numpages = {8} +} + +@MISC{Van93electronicwater, + author = {Tirkel Rankin Van}, + title = {Electronic Water Mark}, + year = {1993} +} + +@ARTICLE{Venkatesan2007397, + author = {R.C. Venkatesan}, + title = {Encryption of covert information into multiple statistical distributions}, + journal = {Physics Letters A}, + year = {2007}, + volume = {370}, + pages = {397 - 404}, + number = {5-6}, + doi = {DOI: 10.1016/j.physleta.2007.05.117}, + issn = {0375-9601}, + keywords = {Statistical encryption/decryption}, + owner = {guyeux}, + timestamp = {2009.12.12}, + url = {http://www.sciencedirect.com/science/article/B6TVM-4P4FV2M-1/2/cd11a2ec144526e3c4552d2a7e7906cc} +} + +@ARTICLE{pitas, + author = {G. Voyatzis and I. Pitas}, + title = {Chaotic watermarks for embedding in the spatial digital image domain}, + journal = {Proceedings of IEEE ICIP}, + year = {1998}, + volume = {2}, + pages = {432-436}, + owner = {christophe}, + timestamp = {2010.03.06} +} + +@INCOLLECTION{Wagner03, + author = {Wagner, David}, + title = {Cryptanalysis of an Algebraic Privacy Homomorphism}, + booktitle = {Information Security}, + publisher = {Springer Berlin, Heidelberg}, + year = {2003}, + volume = {2851}, + series = {Lecture Notes in Computer Science}, + pages = {234-239}, + abstract = {We use linear algebra to show that an algebraic privacy homomorphism + proposed by Domingo-Ferrer is insecure for some parameter settings.}, + affiliation = {University of California, Berkeley USA} +} + +@INPROCEEDINGS{Wagner03cryptanalysisof, + author = {David Wagner}, + title = {Cryptanalysis of an Algebraic Privacy Homomorphism}, + booktitle = {Proc. Sixth Information Security Conf. (ISC03}, + year = {2003}, + pages = {234--239} +} + +@ARTICLE{Wang_ellipticcurve, + author = {Haodong Wang and Bo Sheng and Qun Li}, + title = {Elliptic curve cryptography-based access control in sensor networks}, + journal = {Int. J. Security and Networks} +} + +@INPROCEEDINGS{wbg10:ip, + author = {Wang, Qianxue and Bahi, Jacques and Guyeux, Christophe and Fang, + Xiaole}, + title = {Randomness quality of {CI} chaotic generators. Application to Internet + security}, + booktitle = {INTERNET'2010. The 2nd Int. Conf. on Evolving Internet}, + year = {2010}, + pages = {125--130}, + address = {Valencia, Spain}, + month = sep, + publisher = {IEEE Computer Society Press}, + note = {Best Paper award}, + classement = {ACTI}, + domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO}, + equipe = {and}, + inhal = {no} +} + +@ARTICLE{Wang2003, + author = {X. M. Wang and J. S. Zhang and W. F. Zhang}, + title = {One-way hash function construction based on the extended chaotic + maps switch}, + journal = {Acta Phys. Sinici.}, + year = {2003}, + volume = {52, No. 11}, + pages = {2737--2742}, + owner = {guyeux}, + timestamp = {2009.01.16} +} + +@ARTICLE{Girao06, + author = {Westhoff, Dirk and Girao, Joao and Acharya, Mithun}, + title = {Concealed Data Aggregation for Reverse Multicast Traffic in Sensor + Networks: Encryption, Key Distribution, and Routing Adaptation}, + journal = {IEEE Transactions on Mobile Computing}, + year = {2006}, + volume = {5}, + pages = {1417--1431}, + number = {10}, + address = {Piscataway, NJ, USA}, + doi = {http://dx.doi.org/10.1109/TMC.2006.144}, + issn = {1536-1233}, + publisher = {IEEE Educational Activities Department} +} + +@MISC{web:lyapunov, + author = {Wikipédia}, + title = {Exposant de Lyapunov -- Site web d'André Lévesque}, + year = {2010}, + note = {[En ligne; Page disponible le 9-septembre-2010]}, + url = {\url{http://math.cmaisonneuve.qc.ca/alevesque/chaos_fract/Lyapunov/Exposant.html}} +} + +@MISC{wiki:complet, + author = {Wikipédia}, + title = {Espace complet --- Wikipédia{,} l'encyclopédie libre}, + year = {2010}, + note = {[En ligne; Page disponible le 9-août-2010]}, + url = {\url{https://secure.wikimedia.org/wikipedia/fr/w/index.php?title=Espace_complet&oldid=52734266}} +} + +@MISC{wiki:densite, + author = {Wikipédia}, + title = {Densité (mathématiques) --- Wikipédia{,} l'encyclopédie libre}, + year = {2010}, + note = {[En ligne; Page disponible le 8-août-2010]}, + url = {\url{https://secure.wikimedia.org/wikipedia/fr/w/index.php?title=Densit%C3%A9_(math%C3%A9matiques)&oldid=53938121}} +} + +@MISC{wiki:fisher, + author = {Wikipédia}, + title = {Information de Fisher --- Wikipédia{,} l'encyclopédie libre}, + year = {2010}, + note = {[En ligne; Page disponible le 5-août-2010]}, + url = {\url{https://secure.wikimedia.org/wikipedia/fr/w/index.php?title=Information_de_Fisher&oldid=52877871}} +} + +@MISC{wiki:Kerkhoffs, + author = {Wikipédia}, + title = {Principe de Kerckhoffs --- Wikipédia{,} l'encyclopédie libre}, + year = {2010}, + note = {[En ligne; Page disponible le 20-août-2010]}, + url = {\url{https://secure.wikimedia.org/wikipedia/fr/w/index.php?title=Principe_de_Kerckhoffs&oldid=52133114}} +} + +@MISC{wiki:sarkovskii, + author = {Wikipédia}, + title = {Théor\`{e}me de Sarkovskii --- Wikipédia{,} l'encyclopédie libre}, + year = {2010}, + note = {[En ligne; Page disponible le 8-août-2010]}, + url = {\url{https://secure.wikimedia.org/wikipedia/fr/w/index.php?title=Th%C3%A9or%C3%A8me_de_Sarkovskii&oldid=54196167}} +} + +@MISC{wiki:steganographie, + author = {Wikipédia}, + title = {Stéganographie --- Wikipédia{,} l'encyclopédie libre}, + year = {2010}, + note = {[En ligne; Page disponible le 5-août-2010]}, + url = {\url{https://secure.wikimedia.org/wikipedia/fr/w/index.php?title=St%C3%A9ganographie&oldid=54724435}} +} + +@MISC{wiki:tatouage, + author = {Wikipédia}, + title = {Tatouage numérique --- Wikipédia{,} l'encyclopédie libre}, + year = {2010}, + note = {[En ligne; Page disponible le 5-août-2010]}, + url = {https://secure.wikimedia.org/wikipedia/fr/w/index.php?title=Tatouage_num%C3%A9rique&oldid=55484940} +} + +@MISC{wiki:testsHypothese, + author = {Wikipédia}, + title = {Test d'hypoth\`{e}se --- Wikipédia{,} l'encyclopédie libre}, + year = {2010}, + note = {[En ligne; Page disponible le 5-août-2010]}, + url = {\url{https://secure.wikimedia.org/wikipedia/fr/w/index.php?title=Test_d%27hypoth%C3%A8se&oldid=55344108}} +} + +@MISC{gowalla, + author = {Williams, Josh and Raymond, Scott}, + title = {Gowalla}, + month = {April}, + year = {2012}, + note = {\texttt{http://gowalla.com}} +} + +@ARTICLE{Wu2007bis, + author = {Xianyong Wu and Zhi-Hong Guan}, + title = {A novel digital watermark algorithm based on chaotic maps}, + journal = {Physics Letters A}, + year = {2007}, + volume = {365}, + pages = {403 - 406}, + number = {5-6}, + doi = {DOI: 10.1016/j.physleta.2007.01.034}, + issn = {0375-9601}, + keywords = {Watermarking}, + url = {http://www.sciencedirect.com/science/article/B6TVM-4MY0MF3-8/2/0b4d1298fa84337d2e59b3fefe26f583} +} + +@INPROCEEDINGS{Wu2007, + author = {Wu, Xianyong and Guan, Zhi-Hong and Wu, Zhengping}, + title = {A Chaos Based Robust Spatial Domain Watermarking Algorithm}, + booktitle = {ISNN '07: Proceedings of the 4th international symposium on Neural + Networks}, + year = {2007}, + pages = {113--119}, + address = {Berlin, Heidelberg}, + publisher = {Springer-Verlag}, + doi = {http://dx.doi.org/10.1007/978-3-540-72393-6_15}, + isbn = {978-3-540-72392-9}, + location = {Nanjing, China} +} + +@ARTICLE{Xiao20092288, + author = {Di Xiao and Xiaofeng Liao and Yong Wang}, + title = {Parallel keyed hash function construction based on chaotic neural + network}, + journal = {Neurocomputing}, + year = {2009}, + volume = {72}, + pages = {2288 - 2296}, + number = {10-12}, + note = {Lattice Computing and Natural Computing (JCIS 2007) / Neural Networks + in Intelligent Systems Designn (ISDA 2007)}, + abstract = {Recently, various hash functions based on chaos or neural networks + were proposed. Nevertheless, none of them works efficiently in parallel + computing environment. In this paper, an algorithm for parallel keyed + hash function construction based on chaotic neural network is proposed. + The mechanism of changeable-parameter and self-synchronization establishes + a close relation between the hash value bit and message, and the + algorithm structure ensures the uniform sensitivity of the hash value + to the message blocks at different positions. The proposed algorithm + can satisfy the performance requirements of hash function. These + properties make it a promising choice for hashing on parallel computing + platform.}, + issn = {0925-2312}, + keywords = {Chaotic neural network} +} + +@ARTICLE{Xiao20094346, + author = {Di Xiao and Xiaofeng Liao and Yong Wang}, + title = {Improving the security of a parallel keyed hash function based on + chaotic maps}, + journal = {Physics Letters A}, + year = {2009}, + volume = {373}, + pages = {4346 - 4353}, + number = {47}, + issn = {0375-9601}, + keywords = {Hash function}, + owner = {guyeux}, + timestamp = {2009.12.12} +} + +@ARTICLE{Xiao20102254, + author = {Di Xiao and Frank Y. Shih and Xiaofeng Liao}, + title = {A chaos-based hash function with both modification detection and + localization capabilities}, + journal = {Communications in Nonlinear Science and Numerical Simulation}, + year = {2010}, + volume = {15}, + pages = {2254 - 2261}, + number = {9}, + abstract = {Recently, a variety of chaos-based hash functions have been proposed. + Nevertheless, none of them can realize modification localization. + In this paper, a hash function with both modification detection and + localization capabilities is proposed, which can also support the + parallel processing mode. By using the mechanism of changeable-parameter + and self-synchronization, the keystream can establish a close relation + with the algorithm key, the content, and the order of each message + unit. Theoretical analysis and computer simulation indicate that + the proposed algorithm can satisfy the performance requirements of + hash functions.}, + issn = {1007-5704}, + keywords = {Hash function} +} + +@ARTICLE{yang94, + author = {Yang, Z.}, + title = {Estimating the pattern of nucleotide substitution}, + journal = {Journal of Molecular Evolution}, + year = {1994}, + volume = {10}, + pages = {105-111}, + added-at = {2009-01-22T02:55:58.000+0100}, + biburl = {http://www.bibsonomy.org/bibtex/27da68ebb5221b9e97c5f9567cbd72bb5/stephane.guindon}, + interhash = {951d2d6b98320cb775fd695a0c058092}, + intrahash = {7da68ebb5221b9e97c5f9567cbd72bb5}, + keywords = {imported}, + timestamp = {2009-01-22T02:55:58.000+0100} +} + +@INPROCEEDINGS{Yao82, + author = {Yao, Andrew C.}, + title = {Theory and application of trapdoor functions}, + booktitle = {Proceedings of the 23rd Annual Symposium on Foundations of Computer + Science}, + year = {1982}, + series = {SFCS '82}, + pages = {80--91}, + address = {Washington, DC, USA}, + publisher = {IEEE Computer Society}, + acmid = {1382790}, + doi = {http://dx.doi.org/10.1109/SFCS.1982.95}, + numpages = {12}, + url = {http://dx.doi.org/10.1109/SFCS.1982.95} +} + +@INPROCEEDINGS{Yu06, + author = {Yu, Yu and Leiwo, Jussipekka and Premkumar, Benjamin}, + title = {A Study on the Security of Privacy Homomorphism}, + booktitle = {ITNG '06: Proceedings of the Third International Conference on Information + Technology: New Generations}, + year = {2006}, + pages = {470--475}, + address = {Washington, DC, USA}, + publisher = {IEEE Computer Society}, + doi = {http://dx.doi.org/10.1109/ITNG.2006.19}, + isbn = {0-7695-2497-4} +} + +@ARTICLE{Zhang2008658, + author = {Wei Zhang and Yonghe Liu and Sajal K. Das and Pradip De}, + title = {Secure data aggregation in wireless sensor networks: A watermark + based authentication supportive approach}, + journal = {Pervasive and Mobile Computing}, + year = {2008}, + volume = {4}, + pages = {658 - 680}, + number = {5}, + doi = {DOI: 10.1016/j.pmcj.2008.05.005}, + issn = {1574-1192}, + keywords = {Wireless sensor networks}, + url = {http://www.sciencedirect.com/science/article/B7MF1-4SKB3MD-1/2/b73948dcaa3eb63a2c21d09041882625} +} + +@ARTICLE{Zhang2005, + author = {Zhang, Yang and Arakaki, Adrian K. and Skolnick, Jeffrey}, + title = {TASSER: An automated method for the prediction of protein tertiary + structures in CASP6}, + journal = {Proteins}, + year = {2005}, + volume = {61}, + pages = {91--98}, + number = {S7}, + issn = {1097-0134}, + keywords = {comparative modeling, threading, ab initio prediction, TASSER, PROSPECTOR_3}, + owner = {christophe}, + publisher = {Wiley Subscription Services, Inc., A Wiley Company}, + timestamp = {2011.01.22}, + url = {http://dx.doi.org/10.1002/prot.20724} +} + +@ARTICLE{Zhou1997429, + author = {Chang-song Zhou and Tian-lun Chen}, + title = {Extracting information masked by chaos and contaminated with noise: + Some considerations on the security of communication approaches using + chaos}, + journal = {Physics Letters A}, + year = {1997}, + volume = {234}, + pages = {429 - 435}, + number = {6}, + issn = {0375-9601}, + keywords = {Communication}, + owner = {guyeux}, + timestamp = {2009.12.12} +} + +@ARTICLE{Zhou96, + author = {Zhou, Huai-bei and Wang, Lu}, + title = {Chaos in Biomolecular Dynamics}, + journal = {The Journal of Physical Chemistry}, + year = {1996}, + volume = {100}, + pages = {8101-8105}, + number = {20}, + doi = {10.1021/jp953409x} +} + +@PROCEEDINGS{DBLP:conf/iwdw/2005, + title = {IWDW'05: 4th International Workshop on Digital Watermarking}, + year = {2005}, + editor = {Mauro Barni and Ingemar J. Cox and Ton Kalker and Hyoung Joong Kim}, + volume = {3710}, + series = {Lecture Notes in Computer Science}, + address = {Siena, Italy}, + publisher = {Springer}, + month = {September 15-17}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {IWDW}, + isbn = {3-540-28768-X}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@PROCEEDINGS{DBLP:conf/ih/2006, + title = {IH 2006: Information Hiding, 8th International Workshop}, + year = {2007}, + editor = {Jan Camenisch and Christian S. Collberg and Neil F. Johnson and Phil + Sallee}, + volume = {4437}, + series = {Lecture Notes in Computer Science}, + address = {Alexandria, VA, USA}, + publisher = {Springer}, + month = {July}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {Information Hiding}, + isbn = {978-3-540-74123-7}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@PROCEEDINGS{DBLP:conf/ih/2007, + title = {Information Hiding, 9th International Workshop, IH 2007, Saint Malo, + France, June 11-13, 2007, Revised Selected Papers}, + year = {2008}, + editor = {Teddy Furon and Fran\c{c}ois Cayre and Gwena{\"e}l J. Do{\"e}rr and + Patrick Bas}, + volume = {4567}, + series = {Lecture Notes in Computer Science}, + publisher = {Springer}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {Information Hiding}, + isbn = {978-3-540-77369-6}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@PROCEEDINGS{DBLP:conf/iccsa/2006-1, + title = {Computational Science and Its Applications - ICCSA 2006, International + Conference, Glasgow, UK, May 8-11, 2006, Proceedings, Part I}, + year = {2006}, + editor = {Marina L. Gavrilova and Osvaldo Gervasi and Vipin Kumar and Chih + Jeng Kenneth Tan and David Taniar and Antonio Lagan{\`a} and Youngsong + Mun and Hyunseung Choo}, + volume = {3980}, + series = {Lecture Notes in Computer Science}, + publisher = {Springer}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {ICCSA (1)}, + isbn = {3-540-34070-X} +} + +@PROCEEDINGS{DBLP:conf/secrypt/2010, + title = {SECRYPT 2010 - Proceedings of the International Conference on Security + and Cryptography, Athens, Greece, July 26-28, 2010, SECRYPT is part + of ICETE - The International Joint Conference on e-Business and Telecommunications}, + year = {2010}, + editor = {Sokratis K. Katsikas and Pierangela Samarati}, + publisher = {SciTePress}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {SECRYPT}, + isbn = {978-989-8425-18-8} +} + +@BOOK{Katzenbeisser00, + title = {Information Hiding Techniques for Steganography and Digital Watermarking}, + publisher = {Artech House, Inc.}, + year = {2000}, + editor = {Katzenbeisser, Stefan and Petitcolas, Fabien A.}, + address = {Norwood, MA, USA}, + isbn = {1580530354} +} + +@PROCEEDINGS{DBLP:conf/ih/1999, + title = {IH'99: 3rd International Workshop on Information Hiding}, + year = {2000}, + editor = {Andreas Pfitzmann}, + volume = {1768}, + series = {Lecture Notes in Computer Science}, + address = {Dresden, Germany}, + publisher = {Springer}, + month = {September 29 - October 1.}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {Information Hiding}, + isbn = {3-540-67182-X}, + owner = {guyeux}, + timestamp = {2009.06.29} +} + +@PROCEEDINGS{DBLP:conf/indocrypt/2000, + title = {Progress in Cryptology - INDOCRYPT 2000, First International Conference + in Cryptology in India, Calcutta, India, December 10-13, 2000, Proceedings}, + year = {2000}, + editor = {Bimal K. Roy and Eiji Okamoto}, + volume = {1977}, + series = {Lecture Notes in Computer Science}, + publisher = {Springer}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {INDOCRYPT}, + isbn = {3-540-41452-5} +} + +@BOOK{DBLP:reference/icsec/2010, + title = {Handbook of Information and Communication Security}, + publisher = {Springer}, + year = {2010}, + editor = {Peter P. Stavroulakis and Mark Stamp}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {Handbook of Information and Communication Security}, + ee = {http://dx.doi.org/10.1007/978-3-642-04117-4}, + isbn = {978-3-642-04116-7} +} + +@PROCEEDINGS{DBLP:conf/isnn/2004-2, + title = {Advances in Neural Networks - ISNN 2004, International Symposium + on Neural Networks, Dalian, China, August 19-21, 2004, Proceedings, + Part II}, + year = {2004}, + editor = {Fuliang Yin and Jun Wang and Chengan Guo}, + volume = {3174}, + series = {Lecture Notes in Computer Science}, + publisher = {Springer}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {ISNN (2)}, + isbn = {3-540-22843-8} +} + +@PROCEEDINGS{DBLP:conf/adhocnets/2010, + title = {Ad Hoc Networks - Second International Conference, ADHOCNETS 2010, + Victoria, BC, Canada, August 18-20, 2010, Revised Selected Papers}, + year = {2010}, + editor = {Jun Zheng and David Simplot-Ryl and Victor C. M. Leung}, + volume = {49}, + series = {Lecture Notes of the Institute for Computer Sciences, Social Informatics + and Telecommunications Engineering}, + publisher = {Springer}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {ADHOCNETS}, + ee = {http://dx.doi.org/10.1007/978-3-642-17994-5}, + isbn = {978-3-642-17993-8} +} + +@MISC{Delicious, + title = {Delicious social bookmarking, http://delicious.com/}, + comment = {http://delicious.com/}, + type = {web page}, + url = {http://delicious.com/} +} + +@MISC{Frick, + title = {The Frick Collection, http://www.frick.org/}, + comment = {http://www.frick.org/}, + type = {web page}, + url = {http://www.frick.org/} +} + +@PROCEEDINGS{2010, + title = {Proceedings of the IEEE Congress on Evolutionary Computation, CEC + 2010, Barcelona, Spain, 18-23 July 2010}, + year = {2010}, + publisher = {IEEE}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {IEEE Congress on Evolutionary Computation} +} + +@PROCEEDINGS{DBLP:conf/cec/2010, + title = {Proceedings of the IEEE Congress on Evolutionary Computation, CEC + 2010, Barcelona, Spain, 18-23 July 2010}, + year = {2010}, + publisher = {IEEE}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {IEEE Congress on Evolutionary Computation} +} + +@PROCEEDINGS{DBLP:conf/date/2010, + title = {Design, Automation and Test in Europe, DATE 2010, Dresden, Germany, + March 8-12, 2010}, + year = {2010}, + publisher = {IEEE}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {DATE} +} + +@PROCEEDINGS{DBLP:conf/cse/2009, + title = {Proceedings IEEE CSE'09, 12th IEEE International Conference on Computational + Science and Engineering, August 29-31, 2009, Vancouver, BC, Canada}, + year = {2009}, + publisher = {IEEE Computer Society}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {CSE} +} + +@PROCEEDINGS{DBLP:conf/icumt/2009, + title = {Proceedings of the International Conference on Ultra Modern Telecommunications, + ICUMT 2009, 12-14 October 2009, St. Petersburg, Russia}, + year = {2009}, + publisher = {IEEE}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {ICUMT} +} + +@PROCEEDINGS{DBLP:conf/focs/2008, + title = {49th Annual IEEE Symposium on Foundations of Computer Science, FOCS + 2008, October 25-28, 2008, Philadelphia, PA, USA}, + year = {2008}, + publisher = {IEEE Computer Society}, + bibsource = {DBLP, http://dblp.uni-trier.de}, + booktitle = {FOCS} +} + +@comment{jabref-meta: selector_publisher:} + +@comment{jabref-meta: selector_author:} + +@comment{jabref-meta: selector_journal:} + +@comment{jabref-meta: selector_keywords:Chaos;Entropie Topologique;Tip +e;} + diff --git a/review_prng.tex b/review_prng.tex index c6ab2f1..d4acd30 100644 --- a/review_prng.tex +++ b/review_prng.tex @@ -1,6 +1,1998 @@ \documentclass{article} +\usepackage[utf8x]{inputenc} +\usepackage[standard]{ntheorem} +\usepackage[english]{babel} + + +\usepackage{amsmath} +\usepackage{color} +\usepackage{dsfont} + + + +\title{A Review of Chaotic Iteration Based Pseudorandom Number Generators} +\author{Jacques M. Bahi, Jean-Fran\c cois Couchot, Raphaël Couturier, and Christophe Guyeux~\thanks{Authors in alphabetic order}} + + \begin{document} +\maketitle + +\begin{abstract} + +\end{abstract} + + +\section{Introduction} + + +\section{Topology} + +\subsection{Historical context} + +Pseudorandom number generators are recurrent sequences having a disordered behavior. + +Recurrent sequences, also called discrete dynamical systems, of the form +\begin{equation} +\label{sdd} +u^0 \in \mathds{R}, u^{n+1} = f(u^n), +\end{equation} +with +$f$ continuous, have been well studied since the early years of mathematical +analysis. They are widely used, for instance to resolve equations using a +Newton method, or when approximating the solutions to differential equations +using finite difference equations to approximate derivatives. +The context study was the seek for convergence, which is for instance guarantee +when using monotonic functions or contractions. +In the middle of the last century, Coppel has +established a link between this desire of convergence +and the existence of a cycle in iterations~\cite{Coppel55}. +More precisely, his theorem states that, considering Eq.~\eqref{sdd} with a function +$f:I \longrightarrow I$ continuous on the line segment $I$, the absence of +any 2-cycle implies the convergence of the discrete dynamical system. + + +% +% +% \begin{block}{Convergence} +% \begin{itemize} +% \item $f$ monotone +% \item Applications contractantes +% \item Coppel: Pas de 2-cycle $\Rightarrow$ convergence +% \end{itemize} +% \end{block} +%} + + + +%\frame{ +% \frametitle{3-cycle implique chaos} +% \begin{alertblock}{Period Three Implies Chaos (Li et Yorke, 1975)} +%S'il y a un point de période 3, alors il y a un point de n'importe quelle période +% \end{alertblock} +% +% \uncover<2->{ +% \begin{exampleblock}{Remarques} +% \begin{itemize} +% \item Désordre lié à la multiplicité des périodes +% \item \`A AND, on étudie des ``systèmes itératifs'' pour le calcul distribué, généralisation des suites récurrentes +% \end{itemize} +% \end{exampleblock} +% } +%} + + + + + +%%\subsection*{Réécriture des systèmes itératifs} + +%%\frame{ +%% \frametitle{Les systèmes itératifs: généralisation} +%% \begin{block}{Les systèmes itératifs en toute généralité} +%% La formulation suivante englobe tous les modes d'itérations imaginables: +%% $$\left\{ +%% \begin{array}{l} +%% x^0 \in \mathcal{X}\\ +%% x^{n+1} = f^n(x^0, \hdots, x^n) +%% \end{array} +%% \right.$$ +%% où $f^n:\mathcal{X}^{n+1}\rightarrow \mathcal{X}$ +%% \end{block} +%%\uncover<2->{ +%%Différents modes d'itérations: séries, parallèles, chaotiques, asynchrones... +%%} +%%} + + + + + + + + + + +%\subsection*{Cas des Itérations chaotiques} +%\frame{ +% \frametitle{Les « itérations chaotiques »} +% \begin{block}{Définition (Itérations chaotiques)} +% Soient $f: \mathds{B}^\mathsf{N} \longrightarrow \mathds{B}^\mathsf{N}$ et $S \subset \mathcal{P} \left(\llbracket1,\mathsf{N}\rrbracket\right)^\mathds{N}$. Les \emph{itérations chaotiques} sont: +%$$\left\{ +%\begin{array}{l} +%x^0 \in \mathds{B}^\mathsf{N} \\ +%\forall n \in \mathds{N}^*, \forall i \in \llbracket 1; \mathsf{N} \rrbracket, x^{n}_i = \left\{ +%\begin{array}{ll} +%x^{n-1}_{i} & \textrm{ si } i \notin S^n\\ +%f(x^{n-1})_{i} & \textrm{ si } i \in S^n +%\end{array} +%\right. +%\end{array} +%\right.$$ +%\end{block} +%%\uncover<2->{ +%%Itérations chaotiques et théorie du chaos: a priori, rien à voir. +%%} +%%\uncover<3->{Y a-t-il un lien ?}\uncover<4->{ Pour quoi faire ?} +%} + + + + + +%\frame{ +% \frametitle{Non-convergence des IC} +% \begin{alertblock}{Théorème (Condition nécessaire de non-convergence)} +% % Soit $f : \mathds{B}^\mathsf{N} \to \mathds{B}^\mathsf{N}$ et $S \in \mathcal{S}$. +% Si les itérations chaotiques $\left(f,(x^0,S)\right)$ sont non convergentes, alors: +%\begin{itemize} +%\item soit $f$ n'est pas contractante, +%\item soit $S$ n'est pas pseudo-périodique (complète). +%\end{itemize} +% \end{alertblock} +% \uncover<2->{ +% Quelle quantité de désordre ? +% } +%} + + + + + + + + + + +%\frame{ +%\frametitle{Présentation du problème} + +%\begin{tabular}{c||c} +%MATHS DISCRÈTES & TOPOLOGIE MATHÉMATIQUE \tabularnewline +%\hline +%\multirow{2}{5cm}{\centering $f: \mathds{B}^\mathsf{N} \to \mathds{B}^\mathsf{N}$} & $(\mathcal{X},\tau)$ espace topologique\\ +%& $f : \mathcal{X} \to \mathcal{X}$ continue pour $\tau$\\ +%\hline +%$S \in \mathcal{S} = \llbracket 1,\mathsf{N}\rrbracket^\mathds{N}$ & \multirow{2}{5cm}{\centering $x^0 \in \mathcal{X}$} \\ +%$x^0 \in \mathds{B}^\mathds{N}$ & \\ +%\hline +%$x_i^{n+1} = \left\{ \begin{array}{ll} x^{n}_{i} & \textrm{ si } i \neq S^n\\ f(x^{n})_{i} & \textrm{ si } i = S^n \end{array} \right.$ & $\forall n \in \mathds{N}, x^{n+1} = f(x^n)$ \\ +%\end{tabular} + +%} + + + + + + +%\frame{ +%\frametitle{Définitions et notations} +%\begin{block}{Introduisons quelques fonctions...} +%\begin{itemize} +%\item décalage: $\sigma : \mathcal{S} \longrightarrow \mathcal{S}, (S^n)_{n \in \mathds{N}} \mapsto (S^{n+1})_{n \in \mathds{N}}$. +%\item initiale: $i : \mathcal{S} \longrightarrow \llbracket 1 ; \mathsf{N} \rrbracket, (S^n)_{n \in \mathds{N}} \mapsto S^0$ +%\item $F_f : \llbracket 1 ; \mathsf{N} \rrbracket \times \mathds{B}^\mathsf{N} \longrightarrow \mathds{B}^\mathsf{N},$ $$(k,E) \longmapsto \left( E_j.\delta(k,j) + f(E)_k.\overline{\delta (k,j)} \right)_{j \in \llbracket 1 ; \mathsf{N} \rrbracket}$$ +%\end{itemize} +%où $\delta(x,y) = \left\{\begin{array}{ll} +%0 & \textrm{ si } x=y, \\ +%1 & \textrm{ sinon.} +% \end{array}\right. +%$ +%\end{block} +%} + + + + +%\frame{ +%\frametitle{Modélisation des IC} +%\begin{alertblock}{Modélisation des IC en topologie} +%Soit $\mathcal{X} = \llbracket 1 ; \mathsf{N} \rrbracket^\mathds{N} \times \mathds{B}^\mathsf{N},$ et $G_f\left(S,E\right) = \left(\sigma(S), F_f(i(S),E)\right).$ + + +%On modélise les itérations chaotiques $\left(f, (S,x^0)\right)$ par le système dynamique discret: +%$$\left\{ +%\begin{array}{l} +%X^0 = (S,x^0) \in \mathcal{X}, \\ +%\forall k \in \mathds{N}, X^{k+1} = G_f(X^k). +%\end{array} +%\right.$$ +%\end{alertblock} + +% \uncover<2>{ +% On peut donc étudier leur désordre topologique. +% } +%} + + + + + +%\frame{ +% \frametitle{Métrique et continuité} + +%Distance sur $\mathcal{X}:$ +%$$d((S,E);(\check{S};\check{E})) = d_e(E,\check{E}) + d_s(S,\check{S})$$ + +%\noindent où $\displaystyle{d_e(E,\check{E}) = \sum_{k=1}^\mathsf{N} \delta (E_k, \check{E}_k)}$, ~~et~ $\displaystyle{d_s(S,\check{S}) = \dfrac{9}{\textsf{N}} \sum_{k = 1}^\infty \dfrac{|S^k-\check{S}^k|}{10^k}}$. +%%\end{block} + +%\vspace{0.5cm} + +%\begin{alertblock}{Théorème} +%La fonction $G_f : (\mathcal{X},d) \to (\mathcal{X},d)$ est continue. +%\end{alertblock} + +%} + + + +% \frame{ +% \frametitle{\'Etude de $(\mathcal{X},d)$} +% \begin{block}{Propriétés de $(\mathcal{X},d)$} +% \begin{itemize} +% \item $\mathcal{X}$ est infini indénombrable +% \vspace{0.15cm} +% \item $(\mathcal{X},d)$ est un espace métrique compact, complet et parfait +% \end{itemize} +% \end{block} +% +% \vspace{0.5cm} +% +% \begin{block}{\'Etude de $G_{f_0}$} +% $G_{f_0}$ est surjective, mais pas injective \vspace{0.3cm}\newline $\Rightarrow (\mathcal{X},G_{f_0})$ pas réversible. +% \end{block} + +% } + + + +%%\frame{ +%% \frametitle{Etude des périodes} +%% \begin{block}{Multiplicité des périodes ?} +%% Soit $f_0:\mathds{B}^\mathsf{N} \rightarrow \mathds{B}^\mathsf{N}$ la négation vectorielle. +%% \begin{itemize} +%% \item $\forall k \in \mathds{N}, Per_{2k+1}(G_{f_0}) = \varnothing, card\left(Per_{2k+2}(G_{f_0})\right)>0$ \vspace{0.3cm} \linebreak $\Rightarrow G_{f_0}$ pas chaotique sur $\mathcal{X}$ +%% \item Cependant : +%% \begin{itemize} +%% \item Il y a chaos sur $\mathcal{X}^G = \mathcal{P}\left(\llbracket 1,\mathsf{N}\rrbracket\right)^\mathds{N}\times \mathds{B}^\mathsf{N}$. +%% \item $G_{f_0}$ possède plus de $n^2$ points périodiques de période $2n$. +%% \end{itemize} +%% \end{itemize} +%% \end{block} +%% \uncover<2->{ +%% Cette multiplicité des périodes n'est pas le désordre complet... +%% } +%%} + + + +%\subsection*{Approche type Devaney/Knudsen} + +%\frame{ +% \frametitle{Les approches Devaney et Knudsen} +% \begin{block}{3 propriétés pour de l'imprévisibilité} +% \begin{enumerate} +% \item \emph{Indécomposabilité.} On ne doit pas pouvoir simplifier le système +% \begin{itemize} +% \item Impossible de diviser pour régner +% \item Des orbites doivent visiter tout l'espace +% \end{itemize} +% \item \emph{Élément de régularité.} +% \begin{itemize} +% \item Contrecarre l'effet précédent +% \item Des points proches \textit{peuvent} se comporter complètement différemment +% \end{itemize} +% \item \emph{Sensibilité.} Des points proches \textit{peuvent} finir éloignés +% \end{enumerate} +% \end{block} +%} + + +%\frame{ +% \frametitle{Exemple : définition de Devaney} +%\begin{enumerate} +%\item \emph{Transitivité:} Pour chaque couple d'ouverts non vides $A,B \subset \mathcal{X}$, il existe $k \in \mathbb{N}$ tel que $f^{(k)}(A)\cap B \neq \varnothing$ +%\item \emph{Régularité:} Les points périodiques sont denses +%\item \emph{Sensibilité aux conditions initiales:} Il existe $\varepsilon>0$ tel que $$\forall x \in \mathcal{X}, \forall \delta >0, \exists y \in \mathcal{X}, \exists n \in \mathbb{N}, d(x,y)<\delta \textrm{ et } d(f^{(n)}(x),f^{(n)}(y)) \geqslant \varepsilon$$ +%\end{enumerate} +%} + +%\frame{ +% \frametitle{Systèmes intrinsèquement compliqués} +% \begin{block}{Définitions de l'indécomposabilité} +% \begin{itemize} +% \item \emph{Indécomposable}: pas la réunion de deux parties non vides, fermées et t.q. $f(A) \subset A$ +% \item \emph{Totalement transitive}: $\forall n \geqslant 1$, l'application composée $f^{(n)}$ est transitive. +% \item \emph{Fortement transitif}: +%$\forall x,y \in \mathcal{X},$ $\forall r>0,$ $\exists z \in B(x,r),$ $\exists n \in \mathbb{N},$ $f^{(n)}(z)=y.$ +% \item \emph{Topologiquement mélangeant}: pour toute paire d'ouverts disjoints et non vides $U$ et $V$, il existe $n_0 \in \mathbb{N}$ tel que $\forall n \geqslant n_0, f^{(n)}(U) \cap V \neq \varnothing$. +% \end{itemize} +% \end{block} +%} + + + + +%\frame{ +%\frametitle{Stabilité et expansivité} +% \begin{block}{Définitions de la sensibilité} +% \begin{itemize} +% \item $(\mathcal{X},f)$ est \emph{instable} si tous ses points le sont: $\forall x \in \mathcal{X},$ $\exists \varepsilon >0,$ $\forall \delta > 0,$ $\exists y \in \mathcal{X},$ $\exists n \in \mathbb{N},$ $d(x,y)<\delta$ et $d(f^{(n)}(x),f^{(n)}(y)) \geqslant \varepsilon$ +% \item $(\mathcal{X},f)$ est \emph{expansif} si +%$\exists \varepsilon >0,$ $\forall x \neq y,$ $\exists n \in \mathbb{N},$ $d(f^{(n)}(x),f^{(n)}(y)) \geqslant \varepsilon$ +% \end{itemize} +% \end{block} +%} + +%%\frame{ +%% \frametitle{Des systèmes imprévisibles} +%% \begin{block}{Définitions des systèmes dynamiques désordonnés} +%% \begin{itemize} +%% \item \emph{Devaney:} $(\mathcal{X},f)$ est sensible aux conditions initiales, régulier et transitif +%% \item \emph{Wiggins:} $(\mathcal{X},f)$ est transitif et sensible aux conditions initiales +%% \item \emph{Knudsen:} $(\mathcal{X},f)$ a une orbite dense et s'il est sensible aux conditions initiales +%% \item \emph{expansif:} $(\mathcal{X},f)$ est transitif, régulier et expansif +%% \end{itemize} +%% \end{block} +%%} + + + +%\subsection*{Autres approches} + + +%\frame{ +% \frametitle{Selon Li et Yorke} +% \begin{block}{Définitions} +% \begin{description} +%\item[Couple de Li-Yorke.] $(x,y)$ en est un quand: $\limsup_{n \rightarrow +\infty} d(f^{(n)}(x), f^{(n)}(y))>0$ et $\liminf_{n \rightarrow +\infty} d(f^{(n)}(x), f^{(n)}(y))=0.$ + +%\item[Ensemble brouillé.] $B \subset \mathcal{X}$ en est un si tout couple de points distincts de $B$ est de Li-Yorke. + +%\item[Systèmes de Li-Yorke.] $\mathcal{X}$ est compact et contient un ensemble brouillé indénombrable. +%\end{description} +%\end{block} +%} + + + + + + +%\frame{ +% \frametitle{Approche entropie topologique} +% \begin{block}{Entropie topologique} +% \begin{itemize} +% \item $x,y \in \mathcal{X}$ sont ~$\varepsilon-$\emph{séparés en temps $n$} s'il existe $k \leqslant n$ tel que $d\left(f^{(k)}(x),f^{(k)}(y)\right)>\varepsilon$. +% \item Les ensembles $(n,\varepsilon)-$séparé sont des ensembles de points qui seront tous $\varepsilon-$séparés en temps $n$ +% \item $s_n(\varepsilon,Y)$: cardinal maximal d'un ensemble $(n,\varepsilon)-$séparé $$h_{top}(\mathcal{X},f) = \displaystyle{\lim_{\varepsilon \rightarrow 0} \Big[ \limsup_{n \rightarrow +\infty} \dfrac{1}{n} \log s_n(\varepsilon,\mathcal{X})\Big]}$$ +% \end{itemize} +% \end{block} +%} + + + + +%\frame{ +% \frametitle{Exposant de Lyapunov} +%\begin{block}{L'exposant de Lyapunov} +%$$\lambda(x^0) = \displaystyle{\lim_{n \to +\infty} \dfrac{1}{n} \sum_{i=1}^n \ln \left| ~f'\left(x^{i-1}\right)\right|}$$ +%Il doit être positif pour multiplier les erreurs +%\end{block} +%} + + + + + +%\subsection*{Etude des systèmes itératifs} + +%%\frame{ +%% \frametitle{IC et propriété de Devaney} +%%\begin{alertblock}{Théorème} +%%$G_{f_0}$ est régulier et transitif (Devaney). + +%%Sa sensibilité est $\geqslant \mathsf{N}-1$. +%%\end{alertblock} + +%%\uncover<2->{ +%% \begin{exampleblock}{Question} +%% $f_0$ est-elle la seule fonction dont le système itératif vérifie la condition de Devaney ? +%% \end{exampleblock} +%% +%% \vspace{0.5cm} + +%%Pour y répondre, nous avons utilisé le graphe de tous les possibles par itérations chaotiques : le GTPIC.} +%%} + + + + +%%\frame{ +%% \frametitle{Nombre de fonctions imprévisibles} +%% \begin{alertblock}{Caractérisation des IC imprévisibles selon Devaney} +%%$G_f$ vérifie l'hypothèse de Devaney $\Leftrightarrow$ Son graphe des possibles est fortement connexe. + +%%$\Rightarrow$ Il y a $\left(2^\mathsf{N}\right)^{2^\mathsf{N}}$ IC chaotiques. +%%\end{alertblock} +%%} + + + + + + + +%\frame{ +% \frametitle{Etude topologique} +% \begin{exampleblock}{Etude topologique des ICs} +% \begin{itemize} +% \item $\forall f \in \mathcal{C}$, $Per\left(G_f\right)$ est infini dénombrable, $G_f$ est fortement transitive, est chaotique selon Knudsen, +% \item $\left(\mathcal{X}, G_{f_0}\right)$ est topologiquement mélangeant, expansif (constante 1), est chaotique selon Li-Yorke, a une entropie topologique infinie, un exposant de Lyapunov de $ln(\mathsf{N})$ +% \item Indécomposabilité, instabilité, chaos de Wiggins, de la multiplicité des périodes... +% \end{itemize} +% \end{exampleblock} +%} + + + + + + + +%\frame{ +% \frametitle{Graphe de tous les possibles par IC} +% \begin{center} +% \includegraphics[scale=0.55]{14.Caracterisation_des_IC_chaotiques_selon_Devaney/grapheTPICver2.pdf} +% \end{center} +%} + + + + + + + + + + + + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\section*{Topologie des programmes} +%\frame{ +%% 'transition': Crossfade, +% \begin{center} +% \Huge{Topologie des programmes} +% +% \end{center} +%} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +%%\frame{ +%% \frametitle{Premières questions} +%% \begin{exampleblock}{Le chaos dans mon PC ?} +%% Le désordre, l'imprévisibilité (vrai, sans perte) sont-ils possibles sur un ordinateur ? +%%\begin{itemize} +%% \item Il n'y a pas de réels sur mon PC +%% \item Toute machine ayant un nombre fini d'états finit par entrer dans un cycle. +%%\end{itemize} +%% \end{exampleblock} +%%} + + + + + + + + + +%%\frame{ +%% \frametitle{Mode d'emploi} +%% \begin{alertblock}{Chaos sur machine: quelques règles} +%% \begin{enumerate} +%% \item Ne pas laisser la machine travailler en vase clos %\newline +%% %$\Rightarrow$ Une nouvelle entrée à chaque itérée +%% \item Utiliser les médias sur lesquels on travaille %\newline +%% %$\Rightarrow$ Ensemble infini dénombrable +%% \item Ne manipuler que des entiers +%% \item \'Eviter les tailles fixes %(graine, nombre d'itérations, etc.) +%% \end{enumerate} +%% \end{alertblock} +%%} + + + + + +%\frame{ +% \frametitle{Introduction} +% \begin{block}{Deux cas de figure} +% \begin{itemize} +% \item En vase clos : +% \begin{itemize} +% \item 4 Go de mémoire $\Rightarrow 2^{4000000000}$ états possibles... +% \item Lemme de filature/lemme fantôme +% \end{itemize} +% \item $\mathcal{X}=\mathds{B}^\mathsf{N}\times \mathcal{P}\left(\llbracket 1;\mathsf{N}\rrbracket\right)^\mathds{N}$: +% \begin{itemize} +% \item Pas de réels, que des entiers bornés par $\mathsf{N}$ +% \item On peut utiliser le média à chaque itérée +% \end{itemize} +% \end{itemize} +% \end{block} +%} + + + + + + +%\frame{ +% \frametitle{Introduction} +% \begin{exampleblock}{Deux questions} +%% Vos ICs sont chaotiques, mais pour moi c'est pas ça une machine, un programme. +%\begin{itemize} +% \item Peut-on construire des automates chaotiques ? +% \item Peut-on évaluer si un programme est chaotique ? +%\end{itemize} +% \end{exampleblock} +%} + + + + + +%\frame{ +% \frametitle{Une machine de Moore chaotique} +% \begin{center} +% \includegraphics[scale=0.55]{14.Caracterisation_des_IC_chaotiques_selon_Devaney/grapheTPICver2.pdf} +% \end{center} +%} + + + + + +%\frame{ +%\frametitle{Le chaos d'un programme} +%\begin{block}{Machines de Turing et systèmes itératifs} +%Soit $(w,i,q)$ la configuration actuelle de la machine de Turing\\ +%\begin{center} +%\includegraphics[scale=0.3]{Steganalyse/Medias/Turing.pdf} +%\end{center} +%\begin{itemize} +%\item $w=\sharp^{-\omega} w(0) \hdots w(k)\sharp^{\omega}$ est la bande de lecture, +%\item $i$ est la position de la tête de lecture, +%\item $q$ décrit l'état de la machine, +%\item et $\delta$ est sa fonction de transition. +%\end{itemize} +%\end{block} +%} + + + +%\frame{ +%\frametitle{Le chaos d'un programme} +%\begin{block}{Machines de Turing et systèmes itératifs} +%On définit $f$ par: + +%\begin{itemize} +%\item Si $\delta(q;w(i)) = (q'; a; \rightarrow)$, alors $f(w(0) \hdots w(k);i;q) = ( w(0) \hdots w(i-1) ~ a ~ w(i+1) \hdots w(k); i+1; q')$ +%\item Si $\delta(q;w(i)) = (q'; a; \leftarrow)$, alors $f( w(0) \hdots w(k);i;q) = (w(0) \hdots w(i-1) ~ a ~ w(i+1) \hdots w(k); i-1; q')$ +%\end{itemize} + +%La machine peut être écrite sous la forme $x^{n+1}=f(x^n)$ +%\end{block} +%} + + + + + + + +%\frame{ +% \frametitle{A quoi ça sert ?} +% \begin{exampleblock}{Un programme chaotique, pour quoi faire ?} +%\begin{itemize} +% \item Se placer dans de bonnes conditions lors de conception de nouveaux algorithmes +% \item Renforcer les attaques (virus chaotique) +% \item Simuler numériquement des processus chaotiques +% \item Renforcer la sécurité +% \item Battre l'intelligence artificielle +%\end{itemize} +% \end{exampleblock} +% +%% \uncover<3->{ +%% Tentons une première illustration +%% } +%} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\section{Applications aux PRNGs} +%\subsection*{PRNGs} +%\begin{frame}{Applications} +%% 'transition': Crossfade, +% \begin{center} +% \Huge{Applications} + +%\medskip +% \huge{Générateurs pseudo-aléatoires} +% \end{center} +%\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%\frame{ +% \frametitle{Chaos et aléas} +% \begin{block}{Motivations: La batterie du NIST} +% \begin{itemize} +%\item \textbf{Transitivités} +% \begin{itemize} +% \item \textbf{Random Excursions Variant Test.} To detect deviations from the expected number of visits to various states in the random walk. +% \item \textbf{Random Excursions Test.} To determine if the number of visits to a particular state within a cycle deviates from what one would expect for a random sequence. +% \end{itemize} +%\item \textbf{Chaos selon Li-Yorke} +% \begin{itemize} +% \item \textbf{Runs Test.} To determine whether the number of runs of ones and zeros of various lengths is as expected for a random sequence. In particular, this test determines whether the oscillation between such zeros and ones is too fast or too slow. +% \end{itemize} +%\end{itemize} +%\end{block} +%} + +%\frame{ +% \frametitle{Chaos et aléas} +% \begin{block}{Motivations: La batterie du NIST} +% \begin{itemize} +% \item \textbf{Régularité} +% \begin{itemize} +% \item \textbf{Non-overlapping Template Matching Test} To detect generators that produce too many occurrences of a given non-periodic (aperiodic) pattern (m is the length in bits of each template which is the target string). +% \item \textbf{Discrete Fourier Transform (Spectral) Test} To detect periodic features (i.e., repetitive patterns that are near each other) in the tested sequence that would indicate a deviation from the assumption of randomness. +% \end{itemize} +% \item \textbf{Entropie} +% \begin{itemize} +%\item \textbf{Approximate Entropy Test} To compare the frequency of overlapping blocks of two consecutive/adjacent lengths (m and m+1) against the expected result for a random sequence (m is the length of each block). +% \end{itemize} +% \end{itemize} +%\end{block} +%} + +%\frame{ +% \frametitle{Chaos et aléas} +% \begin{block}{Motivations: La batterie du NIST} +% \begin{itemize} +% \item \textbf{Non-linéarité, complexité} +% \begin{itemize} +%\item \textbf{Binary Matrix Rank Test} To check for linear dependence among fixed length substrings of the original sequence. +%\item \textbf{Linear Complexity Test} To determine whether or not the sequence is complex enough to be considered random (M is the length in bits of a block). +% \end{itemize} +%\end{itemize} +% \end{block} +%} + + +%\subsection*{Le Old CI PRNG} +%\frame{ +% \frametitle{Notre PRNG} +% \begin{alertblock}{Le PRNG $CI_f(PRNG_1,PRNG_2)$} +% \begin{description} +%\item[\underline{Paramètres:}] Une fonction $f: \mathds{B}^\mathsf{N} \rightarrow \mathds{B}^\mathsf{N}$, et deux PRNGs:\\ +%\begin{itemize} +%\item $S\in\llbracket 1,\mathsf{N}\rrbracket^\mathds{N}$ +%\item et $m\in S^\mathds{N}, S \subset \mathds{N}$ +%\end{itemize} +%\item[\underline{Graine:}] Les graines de $S$ et $m$, et $E\in \mathds{B}^\mathsf{N}$\\ +%\item[\underline{PRNG:}] $\left(G_f(E,S)^{m^i}\right)_{i\in\mathds{N}}$ +%\end{description} +% \end{alertblock} +% +%% \uncover<2->{ +%% \begin{exampleblock}{Exemple: $X^{n+1} = X^n \oplus Y^n$} +%% où $Y \in \llbracket 0, 2^{\mathsf{N}}-1 \rrbracket^\mathds{N}$ +%% \end{exampleblock} +%% } +%} + + + +%%\frame{ +%% \frametitle{Old CI PRNG: Illustration} +%% \begin{block}{} +%%\begin{figure} +%%\centering +%% \includegraphics[scale=0.4]{OldCI1.png} +%% \caption{Le Old CI PRNG} +%% \end{figure} +%% \end{block} +%%} + + + +%%\frame{ +%% \frametitle{Old CI PRNG: Illustration} +%% \begin{block}{} +%%\begin{figure} +%%\centering +%% \includegraphics[scale=0.41]{OldCI2.png} +%% \caption{Le Old CI PRNG} +%% \end{figure} +%% \end{block} +%%} + + +%%\frame{ +%% \frametitle{Old CI PRNG: Illustration} +%% \begin{block}{} +%%\begin{figure} +%%\centering +%% \includegraphics[scale=0.4]{OldCI3.png} +%% \caption{Le Old CI PRNG} +%% \end{figure} +%% \end{block} +%%} + + + + +%%\frame{ +%% \frametitle{Old CI PRNG: Illustration} +%% \begin{block}{} +%%\begin{figure} +%%\centering +%% \includegraphics[scale=0.4]{OldCI4.png} +%% \caption{Le Old CI PRNG} +%% \end{figure} +%% \end{block} +%%} + + + +%%\frame{ +%% \frametitle{Old CI PRNG: Illustration} +%% \begin{block}{} +%%\begin{figure} +%%\centering +%% \includegraphics[scale=0.4]{OldCI5.png} +%% \caption{Le Old CI PRNG} +%% \end{figure} +%% \end{block} +%%} + + + + +%%\frame{ +%% \frametitle{Graphe de tous les possibles par IC} +%% \begin{center} +%% \includegraphics[scale=0.55]{14.Caracterisation_des_IC_chaotiques_selon_Devaney/grapheTPICver2.pdf} +%% \end{center} +%%} + + + + + +%\begin{frame}{Le Old $CI_{f_0}$(logistic,logistic)} +%\begin{block}{} +%\begin{tabular}{llllllllll} +%m (logistic map):&\uncover<1->{2} &\uncover<3->{~} &\uncover<4->{~} &\uncover<5->{~1}&\uncover<8->{~4}&\uncover<9->{~}&\uncover<10->{~}&\uncover<11->{~}& \uncover<13->{...}\\ +%S (logistic map):&\uncover<2->{1} &\uncover<3->{~3} &\uncover<4->{~} &\uncover<6->{~2}&\uncover<9->{~1}&\uncover<10->{~1}&\uncover<11->{~2}&\uncover<12->{~1}& \uncover<14->{...}\\ +%\end{tabular} +%\end{block} +% +%\begin{block}{\'Etat interne du système x:} +%\begin{equation} +%\label{Basic equations} +%\begin{array}{r@{\;}l} +%\ \textbf{0}\uncover<2->{\rightarrow \textbf{1}} \uncover<3->{\rightarrow 1} \uncover<6->{\rightarrow 1} \uncover<9->{\rightarrow \textbf{0}} \uncover<10->{\rightarrow \textbf{1}} \uncover<11->{\rightarrow 1} \uncover<12->{\rightarrow \textbf{0}} \uncover<14->{...}\\ +%\ \textbf{0}\uncover<2->{\rightarrow 0} \uncover<3->{\rightarrow 0} \uncover<6->{\rightarrow \textbf{1}} \uncover<9->{\rightarrow 1} \uncover<10->{\rightarrow 1} \uncover<11->{\rightarrow \textbf{0}} \uncover<12->{\rightarrow 0} \uncover<14->{...}\\ +%\ \textbf{0}\uncover<2->{\rightarrow 0} \uncover<3->{\rightarrow \textbf{1}} \uncover<6->{\rightarrow 1} \uncover<9->{\rightarrow 1}\uncover<10->{\rightarrow 1} \uncover<11->{\rightarrow 1} \uncover<12->{\rightarrow 1} \uncover<14->{...}\\ +%\ \textbf{0}\uncover<2->{\rightarrow 0} \uncover<3->{\rightarrow 0} \uncover<6->{\rightarrow 0} \uncover<9->{\rightarrow 0} \uncover<10->{\rightarrow 0} \uncover<11->{\rightarrow 0} \uncover<12->{\rightarrow 0} \uncover<14->{...}\\ +%\end{array} +%\end{equation} +%\end{block} + +%\begin{block}{} + +%\alert{Sortie:} \uncover<4->{1 0 1 0 }\uncover<7->{1 1 1 0 }\uncover<13->{0 0 1 0 }\uncover<14->{...} + +%\end{block} +%\end{frame} + + + + +%\begin{frame}{Choix de l'ensemble $\mathcal{M}$} +% \begin{figure}[!t] +% \centering +% \includegraphics[width=3.5in,height=2in]{lesM.png} +% \DeclareGraphicsExtensions. +% \caption{Nombre d'itérations entre deux sorties} +% \label{Premiers tests élémentaires} +% \end{figure} +%\end{frame} + + + + +%\begin{frame}{Choix de l'ensemble $\mathcal{M}$} +% \begin{figure}[!t] +% \centering +% \includegraphics[width=3.5in,height=2in]{leM.png} +% \DeclareGraphicsExtensions. +% \caption{Choix de $\mathcal{M}$} +% \end{figure} +%\end{frame} + + + + + +%\frame{ +%\frametitle{Résultats} +%\begin{alertblock}{Premiers résultats} +%\begin{enumerate} +% \item Générateur chaotique dès que le GTPIC de $G_f$ est fortement connexe +% \item Toutes les autres propriétés de chaos +% \item Sortie uniforme si la matrice d'adjacence réduite du GTPIC est doublement stochastique +% \item Les résultats aux tests statistiques sont meilleurs (DieHARD, NIST, TestU01) +%\end{enumerate} +%\end{alertblock} +%} + + + + +%\begin{frame}{Premiers tests comparatifs} +% \begin{figure}[!t] +% \centering +% \includegraphics[width=3.5in,height=2in]{1.pdf} +% \DeclareGraphicsExtensions. +% \caption{Premiers tests élémentaires} +% \label{Premiers tests élémentaires} +% \end{figure} +%\end{frame} + + +%\begin{frame}{NIST pour les PRNG en entrée} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.27]{NistSeul.png} +% \DeclareGraphicsExtensions. +% \caption{Le NIST pour 3 PRNG} +% \end{figure} +%\end{frame} + + + +%\begin{frame}{NIST pour le Old CI} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.27]{NistAvec.png} +% \DeclareGraphicsExtensions. +% \caption{Résultats du Old CI PRNG} +% \end{figure} +%\end{frame} + + + +%\begin{frame}{DieHard pour les PRNG en entrée} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.27]{DieHardSeul.png} +% \DeclareGraphicsExtensions. +% \caption{DieHard pour 3 PRNG} +% \end{figure} +%\end{frame} + + + + +%\begin{frame}{DieHard pour le Old CI} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.24]{DieHarda.png} +% \DeclareGraphicsExtensions. +% \caption{Résultats du Old CI PRNG} +% \end{figure} +%\end{frame} + + + + +%\begin{frame}{TestU01 pour les PRNG en entrée} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.3]{TestUSeul.png} +% \DeclareGraphicsExtensions. +% \caption{TestU01 pour 3 PRNG} +% \end{figure} +%\end{frame} + + + + + + + + +%\begin{frame}{TestU01 pour le Old CI} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.25]{TestUAvec.png} +% \DeclareGraphicsExtensions. +% \caption{Résultats du Old CI PRNG} +% \end{figure} +%\end{frame} + + + +%\subsection*{Le New CI PRNG} +%\frame{ +% \frametitle{Variantes} +% \begin{block}{Quelques variantes du CI PRNG} +% \begin{itemize} +% \item $New ~CI_f(PRNG_1,PRNG_2)$: éviter de changer deux fois de suite un même bit entre deux outputs +% \begin{itemize} +% \item Ne plus compter le nombre d'itérées entre deux outputs +% \item Mais le nombre de bits à changer +% \end{itemize} +% \item $Xor CI PRNG$: $S^{n+1}=S^n \oplus PRNG^n$ +% \item etc. +% \end{itemize} +% \end{block} +%} + + + + + + +%\begin{frame}{La suite $m$ du New CI} +%Supposons que $x_0 = (0, 0, 0)$. Alors $m_0 \in \llbracket 0, 3 \rrbracket$: on +%peut changer de 0 à 3 bits dans cet état pour produire $x_1$. +%\begin{itemize} +% \item Si $m_0 = 0$, alors aucun bit ne changera entre la première et la +% seconde sortie de notre générateur. Et donc $x_1 = (0, 0, 0)$. +% \item Si $m_0 = 1$, alors exactement 1 bit changera, ce qui conduit à trois +% valeurs possibles pour $x_1$, à savoir (1, 0, 0), (0, 1, 0) et (0, 0, 1). +% \item etc. +%\end{itemize} +%\end{frame} + + + +%\begin{frame}{La suite $m$ du New CI} +%\begin{equation} +%\label{Formula} +%m^n = f(y^n)= +%\left\{ +%\begin{array}{l} +%0 \text{ si }0 \leqslant\frac{y^n}{2^{32}}<\frac{C^0_N}{2^N},\\ +%1 \text{ si }\frac{C^0_N}{2^N} \leqslant\frac{y^n}{2^{32}}<\sum_{i=0}^1\frac{C^i_N}{2^N},\\ +%2 \text{ si }\sum_{i=0}^1\frac{C^i_N}{2^N} \leqslant\frac{y^n}{2^{32}}<\sum_{i=0}^2\frac{C^i_N}{2^N},\\ +%\vdots~~~~~ ~~\vdots~~~ ~~~~\\ +%N \text{ si }\sum_{i=0}^{N-1}\frac{C^i_N}{2^N} \leqslant\frac{y^n}{2^{32}}<1.\\ +%\end{array} +%\right. +%\end{equation} +%\end{frame} + + + + + +%\begin{frame}{Stratégie chaotique} +%Une suite de marquage controlera la suite du XORshift $b$ ainsi: +%\begin{itemize} +%\item si $d^{b^j} \neq 1$, alors $S^k=b^j$, $d^{b^j} = 1$ et $k = k+1$ +%\item si $d^{b^j}=1$, alors $b^j$ est écarté. +%\end{itemize} +%Par exemple, si $b = 142\underline{2}334 +%142\underline{1} \underline{1}\underline{2}\underline{2}34...$ et $m = +%4241...$, alors $S=1423~34~1423~4...$ +%\end{frame} + + + + + + +%%\subsection*{Chaotic iterations as pseudo-random generator} +%% \begin{frame}{CI(XORshift, XORshift) algorithm} +%% \begin{tiny} +%% \begin{table} +%% \centering +%% \begin{tabular}{|l|} +%% \hline +%% ~\textbf{Input}: the internal state $x$ (an array of $\mathsf{N}$ bits)\\ +%% \hline +%% ~\textbf{Output}: a state $r$ of $\mathsf{N}$ bits \\ +%% \hline +%% ~\textbf{for} $i=0,\dots,N$ \textbf{do}\\ +%% ~~~~~~ $d_i\leftarrow{0}$;\\ +%% ~\textbf{end for}\\ +%% ~$a\leftarrow{XORshift1(~)}$;\\ +%% ~$m\leftarrow{f(a)}$\;\\ +%% ~$k\leftarrow{m}$\;\\ +%% ~\textbf{for} $i=0,\dots,k$ \textbf{do}\\ +%% ~~~~~~ $b\leftarrow{XORshift2() mod ~ N}$;\\ +%% ~~~~~~ $S\leftarrow{b}$;\\ +%% ~~~~~~~\textbf{if} $d_S=0$ \textbf{then}\\ +%% ~~~~~~~~~~~~ $x_S\leftarrow{ \overline{x_S}}$;\\ +%% ~~~~~~~~~~~~ $d_S\leftarrow{1}$;\\ +%% ~~~~~~~\textbf{end}\\ +%% ~~~~~~~\textbf{else if} $d_S=1$ \textbf{then}\\ +%% ~~~~~~~~~~~~ $k\leftarrow{k+1}$;\\ +%% ~~~~~~~\textbf{end}\\ +%% ~\textbf{end for}\\ +%% ~$r\leftarrow{x}$\;\\ +%% ~\textbf{return} $r$;\\ +%% \hline +%% +%% \end{tabular} +%% \caption{An arbitrary round of the proposed generator} +%% \label{Chaotic iteration} +%% \end{table} +%% \end{tiny} +%% +%% \end{frame} +%% + + + + + + + + + + + + + + + + +%%\begin{frame}{Exemple du New CI} +%%\begin{block}{} +%%\begin{tabular}{llllll} +%%m:&\uncover<2->{0~} &\uncover<4->{4~~} &\uncover<6->{2 } &\uncover<8->{2}&\uncover<10->{...}\\ +%%k:&\uncover<2->{0~} &\uncover<4->{4~~~~~~+1~} &\uncover<6->{2 } &\uncover<8->{2~+1}&\uncover<10->{...}\\ +%%b:&\uncover<2->{~~} &\uncover<4->{1~4~2~\underline{2}~3} &\uncover<6->{3~4} &\uncover<8->{1~\underline{1}~~~4}&\uncover<10->{...}\\ +%%S:&\uncover<2->{~~} &\uncover<4->{1~4~2~~~~3} &\uncover<6->{3~4} &\uncover<8->{1~~~~~~4}&\uncover<10->{...} +%%\end{tabular} +%%\end{block} +%% +%%\begin{block}{x:} +%%\begin{equation} +%%\label{Basic equations} +%%% \left\{ +%%\begin{array}{r@{\;}l} +%%\ \textbf{0}\uncover<2->{\rightarrow \textbf{0}} \uncover<4->{\rightarrow \textbf{1}\rightarrow 1\rightarrow 1\rightarrow \textbf{1}} \uncover<6->{\rightarrow 1\rightarrow \textbf{1}} \uncover<8->{\rightarrow \textbf{0}\rightarrow \textbf{0}} \uncover<10->{...}\\ +%%\ \textbf{1}\uncover<2->{\rightarrow \textbf{1}} \uncover<4->{\rightarrow 1\rightarrow 1\rightarrow \textbf{0}\rightarrow \textbf{0}} \uncover<6->{\rightarrow 0\rightarrow \textbf{0}} \uncover<8->{\rightarrow 0\rightarrow \textbf{0}} \uncover<10->{...}\\ +%%\ \textbf{0}\uncover<2->{\rightarrow \textbf{0}} \uncover<4->{\rightarrow 0\rightarrow 0\rightarrow 0\rightarrow \textbf{1}} \uncover<6->{\rightarrow \textbf{0}\rightarrow \textbf{0}} \uncover<8->{\rightarrow 0\rightarrow \textbf{0}} \uncover<10->{...}\\ +%%\ \textbf{0}\uncover<2->{\rightarrow \textbf{0}} \uncover<4->{\rightarrow 0\rightarrow \textbf{1}\rightarrow 1\rightarrow \textbf{1}} \uncover<6->{\rightarrow 1\rightarrow \textbf{0}} \uncover<8->{\rightarrow 0\rightarrow \textbf{1}} \uncover<10->{...} +%%\end{array} +%%% \right. +%%\end{equation} +%%\end{block} + +%%\begin{block}{} + +%%\alert{Sortie:} 0 1 0 0 \uncover<3->{0 1 0 0 }\uncover<5->{1 0 1 1 +%%}\uncover<7->{1 0 0 0 }\uncover<9->{0 0 0 1 }\uncover<10->{...} + +%%\end{block} + +%%\end{frame} + + + + + +%\begin{frame}{Nouvelle version de $CI_f(PRNG_1,PRNG_2)$} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.25]{newCI.png} +% \DeclareGraphicsExtensions. +% \caption{Le NEW CI PRNG} +% \end{figure} +%\end{frame} + + + +%\begin{frame}{NIST pour le New CI} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.27]{NistNew.png} +% \DeclareGraphicsExtensions. +% \caption{Résultats du New CI PRNG (Nist)} +% \end{figure} +%\end{frame} + + + + +%\begin{frame}{DieHard pour le New CI} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.24]{DieHardNew.png} +% \DeclareGraphicsExtensions. +% \caption{Résultats du New CI PRNG (DieHard)} +% \end{figure} +%\end{frame} + + + + + + + +%\begin{frame}{TestU01 pour le New CI} +% \begin{figure}[!t] +% \centering +% \includegraphics[scale=0.37]{TestUNew.png} +% \DeclareGraphicsExtensions. +% \caption{Résultats du New CI PRNG (TestU01)} +% \end{figure} +%\end{frame} + + + + + + + +%%\begin{frame}{Premiers tests comparatifs} +%%\begin{tiny} +%%\begin{table}[!t] +%%\renewcommand{\arraystretch}{1.3} +%%\caption{Comparaison avec $2 \times 10^5$ bits} +%%\label{Comparison2} +%%\centering +%% \begin{tabular}{ccccccc} +%% \hline +%%Method & Monobit & Serial & Poker & Runs & Autocorrelation & Time \\ \hline +%%Logistic map &0.1280&0.1302&240.2893&26.5667&0.0373&0.965s \\ +%%XORshift &1.7053&2.1466&248.9318&18.0087&-0.5009&0.096s \\ +%%Old CI(Logistic, Logistic) &1.0765&1.0796&258.1069&20.9272&-1.6994&0.389s \\ +%%New CI(XORshift,XORshift) &0.3328&0.7441&262.8173&16.7877&-0.0805&0.197s\\ +%% \hline +%% \end{tabular} +%%\end{table} +%%\end{tiny} +%%\end{frame} + + + + + + + + +%%\frame{ +%% \frametitle{Résultats au TestU01} +%% \begin{center} +%% \begin{tabular}{|c|c|} +%% \hline +%% PRNG & Échecs (sur 516 tests) \\ +%% \hline +%% Suite logistique & 261 \\ +%% XORshift & 146 \\ +%% ISAAC & 0 \\ +%% \hline +%% Old CI(Logistic,Logistic) & 138 \\ +%% Old CI(XORshift,XORshift) & 9 \\ +%% Old CI(ISAAC,XORshift) & 0 \\ +%% Old CI(ISAAC,ISAAC) & 0 \\ +%% \hline +%% New CI(Logistic,Logistic) & 0 \\ +%% New CI(ISAAC,XORshift) & 0 \\ +%% New CI(ISAAC,ISAAC) & 0 \\ +%% \hline +%% \end{tabular} +%% \end{center} +%%% \begin{figure} +%%% \centering +%%% \includegraphics[scale=0.35]{testU010.png} +%%% \caption{Score de quelques PRNGs au TestU01} +%%% \end{figure} +%%} + + + +%%\frame{ +%% \frametitle{Résultats} +%% \begin{figure} +%% \centering +%% \includegraphics[scale=0.35]{testU011.png} +%% \caption{Améliorations via le $Old CI(PRNG_1,PRNG_2)$} +%% \end{figure} +%%} + + + +%%\frame{ +%% \frametitle{Résultats} +%% \begin{figure} +%% \centering +%% \includegraphics[scale=0.35]{testU012.png} +%% \caption{Améliorations via le $New CI(PRNG_1,PRNG_2)$} +%% \end{figure} +%%} + + + +%\frame{ +% \frametitle{Résultats} +% \begin{figure} +% \centering +% \includegraphics[scale=0.27]{prngs.png} +% \caption{Autres résultats} +% \end{figure} +% } + + + +%\frame{ +% \frametitle{Résultats} +% \begin{figure} +% \centering +% \includegraphics[scale=0.27]{vitesse.png} +% \caption{Perte de vitesse} +% \end{figure} +% } + + +%%\frame{ +%% \frametitle{A quel prix ?} +%% \begin{figure} +%% \centering +%% \includegraphics[scale=0.35]{rapide.png} +%% \caption{Dégradation de la vitesse} +%% \end{figure} +%%} + + + + + + +%\subsection*{Une famille pour le Old CI} + + + +%\frame{ +% \frametitle{Définition d'une famille de Old CI} +%\begin{block}{La matrice associée à $f$} +%Matrice de taille $N\times 2^N$ dont l'élément $(p,q)$ est +%l'entier ayant la décompistion binaire: +%$$q_N, \hdots, q_{N-p}, f(q)_{N-p+1}, q_{N-p+2}, \hdots, q_1$$ +%avec $q_i$: $i-$ième chiffre en base 2 de $q$. +%\end{block} +% + +%\begin{block}{Vecteur des images} +%Le vecteur des images de $f$ est: +%$$\mathcal{F}(f)=(f(0), f(1), \hdots, f(2^N-1)) \in \llbracket 0, 2^N-1 \rrbracket^{2^N}$$ +%\end{block} +%} + + + + +%\frame{ +% \frametitle{Exemple de matrice associée} +% \begin{figure} +% \centering +% \includegraphics[scale=0.27]{mappingMatrix.png} +% \caption{Matrice associée et vecteur des images pour $f_0$} +% \end{figure} +% +%} + + + +%\frame{ +% \frametitle{Une règle pour le Old CI PRNG} +% \begin{itemize} +% \item Supposons que $\mathcal{F}(f)=(f(0), f(1), \hdots, f(2^N-1)) \in \llbracket 0, 2^N-1 \rrbracket^{2^N}$, avec $Old~ CI_f$ équilibré +% \item Si on veut changer $\mathcal{F}(f)_j$ en $C$, alors il faut aussi que $\mathcal{F}(f)_{2^N-C}=2^N-j$ +% \end{itemize} +% +%} + + + + +%\frame{ +% \frametitle{Exemple de fonctions pour le Old CI} +% \begin{figure} +% \centering +% \includegraphics[scale=0.27]{mappingF0.png} +% \caption{Création de nouvelles fonctions équilibrées} +% \end{figure} +% } + + +%\frame{ +% \frametitle{Un théorème pour l'équilibrage} +%\begin{alertblock}{Théorème} +%Soit $f: \mathds{B}^{n} \rightarrow \mathds{B}^{n}$, $\Gamma(f)$ son graphe d'itération, +%$\check{M}$ sa matrice d'adjacence. + +%Si $\Gamma(f)$ est fortement connexe, alors la sortie produite par le Old CI PRNG +%suit une loi qui tend vers l'uniforme répartition si et seulement si $M$ est +%doublement stochastique. +%\end{alertblock} +%} + + + + +%\frame{ +% \frametitle{D'autres Old CI chaotiques} +% \begin{block}{Pour obtenir d'autres Old CI chaotiques} +% \begin{enumerate} +% \item Partir du graphe de tous les possibles de $f_0$ +% \item Tant que le taux ne suppression n'est pas atteint: +% \begin{itemize} +% \item tirer une arête au sort +% \item la supprimer si le graphe reste fortement connexe (algorithme de Tarjan) +% \end{itemize} +% \end{enumerate} +% (Problème avec les graphes isomorphes) +% \end{block} +%} + + +%\frame{ +% \frametitle{Exemple de fonctions pour le Old CI} +% \begin{figure} +% \centering +% \includegraphics[scale=0.27]{SCC.png} +% \caption{Création de nouvelles fonctions au générateur chaotique} +% \end{figure} +% +%} + + + +%\frame{ +% \frametitle{Condition suffisante de chaoticité} +%\begin{alertblock}{Théorème} +%Soit $f$ une fonction de $\mathds{B}^n$ dans lui-même telle que: +%\begin{enumerate} +%\item +%Le graphe de connexion $G(f)$ n'a pas de cycle de longueur au moins 2; +%\item +%Chaque arête de $G(f)$ ayant une boucle positive a aussi une boucle négative; +%\item +%Chaque arête de $G(f)$ est joignable à partir d'un noeud ayant une boucle négative. +%\end{enumerate} +%Alors $\Gamma(f)$ est fortement connexe. +%\end{alertblock} +%} + + + +%%\begin{theorem} +%% Let $f: \mathds{B}^{n} \rightarrow \mathds{B}^{n}$, $\Gamma(f)$ its +%% iteration graph, $\check{M}$ its adjacency +%% matrix and $M$ a $n\times n$ matrix defined as in the previous lemma. +%% If $\Gamma(f)$ is SCC then +%% the output of the PRNG detailed in Algorithm~\ref{CI Algorithm} follows +%% a law that tends to the uniform distribution +%% if and only if $M$ is a double stochastic matrix. +%%\end{theorem} + + +%\subsection*{PRNG cryptographiquement sûr} +% + +%\frame{ +%\frametitle{Les PRNG cryptographiquement sûrs} +%\begin{block}{Définition: Générateur $G$ \emph{cryptographiquement sûr}} +%%Pour tout +%%algorithme probabiliste polynomial en temps $\mathcal{D}$, pour tout +%%polynome $\mathfrak{p}>0$, et pour tout $n$ suffisamment large, +%$$\left| \mathrm{Pr}[\mathcal{D}(\mathcal{G}(\mathfrak{U}_n))=1]-Pr[\mathcal{D}(\mathfrak{U}_{\ell_\mathcal{G}(n)})=1]\right|< \frac{1}{\mathfrak{p}(n)},$$ +%%où $\mathfrak{U}_r$ est la loi de probabilité uniforme sur $\{0,1\}^r$ et les +%%probabilités sont prises sur $\mathfrak{U}_n$, $\mathfrak{U}_{\ell_G(n)}$ de la même manière +%%que pour le lancer d'une pièce de monnaie dans $\mathcal{D}$. +%\end{block} +%} + + + +%\subsection*{Version GPU} + +%\frame{ +%\frametitle{Derniers Résultats} +%\begin{alertblock}{Nos derniers résultats} +%\begin{enumerate} +% \item Si le premier PRNG en entrée est polynomialement indistinguable d'une suite aléatoire, alors notre PRNG l'est aussi +% \item Implantation sur GPU $\Rightarrow$ 20 milliards de nombres (32 bits) par seconde sur un PC +% \item Utilisation de BBS $\Rightarrow$ 1 milliards de nombres sûrs par seconde +% \item Version chaotique du cryptosystème asymétrique probabiliste de Blum-Goldwasser +% \item Mixage avec dispositif optique (Larger, OPTO) +%\end{enumerate} +%\end{alertblock} +%} + + + + + +%%\frame{ +%% \frametitle{Notre générateur GPU} +%% \begin{figure} +%% \centering +%% \includegraphics[scale=0.3]{gpu.png} +%%% \caption{Version GPU de notre générateur} +%% \end{figure} +%%} + + + + +%%\frame{ +%% \frametitle{Notre générateur GPU} +%% \begin{figure} +%% \centering +%% \includegraphics[scale=0.25]{bbs.png} +%% % \caption{Version GPU de notre générateur, avec bbs} +%% \end{figure} +%%} + + + +%\frame{ +% \frametitle{Notre générateur GPU} +% \begin{tabular}{cc} +% \includegraphics[scale=0.3]{gpu.png} & \includegraphics[scale=0.275]{bbs.png} +% \end{tabular} +%} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\section{Nouvelles pistes} +%%\subsection*{PRNGs} +%\begin{frame}{} +%% 'transition': Crossfade, +% \begin{center} +% \Huge{Nouvelles pistes} + +%\medskip +% %\huge{soulevés par l'approche} +% \end{center} +%\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + + + + +%\frame{ +% \frametitle{Le générateur optique} +% \begin{block}{Côté OPTO} +% \begin{figure} +% \centering +% \includegraphics[scale=0.5]{setup_opto_RNG.eps} +% \caption{Générateur optique (laser chaotique)} +% \end{figure} +% \end{block} +%} + + + + + + + + + + + +%\frame{ +% \frametitle{Le générateur mixé} +% \begin{block}{Côté DISC} +% \begin{figure} +% \centering +% \includegraphics[scale=0.5]{improve.eps} +% \caption{Mixage analogique-numérique} +% \end{figure} +% \end{block} +%} + + + + + +%\frame{ +% \frametitle{Le générateur mixé} +% \begin{block}{Améliorations (NIST)} +% \begin{figure} +% \centering +% \includegraphics[scale=0.35]{NistLaurent.png} +% \caption{Résultat au NIST} +% \end{figure} +% \end{block} +%} + + + + + +%\frame{ +% \frametitle{Le générateur mixé} +% \begin{block}{Améliorations (DieHARD)} +% \begin{figure} +% \centering +% \includegraphics[scale=0.25]{DieHardLaurent.png} +% \caption{Résultat au DieHARD} +% \end{figure} +% \end{block} +%} + + + +%\frame{ +% \frametitle{Le générateur mixé} +% \begin{block}{Côté DISC} +% \begin{figure} +% \centering +% \includegraphics[scale=0.35]{method.eps} +% \caption{Premier PRNG mixé réalisé} + +% \end{figure} +% \end{block} +%} + + +%\frame{ +% \frametitle{Premiers résultats} +% \begin{tabular}{|l||c|c|c|c|c|} +% \hline +%\textbf{Tests} {\textbf{$n$}}&1 &10&20&30&40 \\ \hline\hline +%NIST suite & 0/15 &14/15 & 15/15 & 15/15 & 15/15\\ \hline +%DieHARD suite &1/18 &11/18 & 14/18 &18/18&18/18\\ \hline +% \end{tabular} +%} + + +%\frame{ +% \frametitle{Le générateur mixé} +% \begin{block}{Côté DISC} +% \begin{figure} +% \centering +% \includegraphics[scale=0.25]{paralel.png} +% \caption{Deuxième PRNG mixé réalisé} +% \end{figure} +% \end{block} +%} + + +%\frame{ +% \frametitle{Une piste ?} +% $$X^{mn+1} = X^{mn} \oplus O^{mn} \oplus C^m$$ +%} + + + + + + + + + +%\begin{frame}{} +% \begin{center} +% \huge{Merci pour votre attention} +% \end{center} +%\end{frame} + + + + + + + + +%%\frame{ +%%% 'transition': Crossfade, +%% \frametitle{Une menace en guise d'illustration} +%% \begin{block}{Les attaques par canal auxiliaire} +%% \begin{enumerate} +%%\item Certains processeurs peuvent laisser fuire de l'information. \newline $\Rightarrow$ En 2006 [Acimez07], 508 bits d'une clé d'authentification sur 512. +%%\item Variation de tension appliquée au processeur [Pellegrini10]\newline $\Rightarrow$ \'Emission d'une signature (RSA 1024) corrompue. +%%\item Mesure du temps de déchiffrement [Kocher95] \newline $\Rightarrow$ Obtention de la clé de déchiffrement. +%%\item Optimisations appliquées au théorème des restes chinois [Brumley03] \newline $\Rightarrow$ Factorisation RSA trouvée. +%%\end{enumerate} +%%\end{block} +%%} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +%%\frame{ +%%% 'transition': Crossfade, +%% \frametitle{Une menace en guise d'illustration} +%% \begin{block}{Les attaques par canal auxiliaire} +%% \begin{itemize} +%% \item Failles matérielles ou logicielles +%% \item Une partie du secret +%% \item Algorithmes prouvés sûrs +%% \end{itemize} +%% \end{block} +%% +%% \vspace{0.25cm} +%% \uncover<2->{ +%% \begin{exampleblock}{Tentatives de solution} +%% \begin{itemize} +%% \item Ne plus répondre au cas par cas +%% \item Une sécurité complémentaire ? +%% \item Pourquoi ne pas utiliser des programmes imprédictibles ? +%% \end{itemize} +%% \end{exampleblock} +%%} +%%} + + + + + + + + +%%\frame{ +%% \frametitle{Nos contributions} +%%\begin{block}{Nos contributions} +%%\begin{itemize} +%%\item Construire des machines, des programmes imprévisibles +%%\item Etudier des algorithmes existants sous d'autres aspects (comparaison, autres menaces ?) +%%\item Rajouter des propriétés (topologiques) à des outils préexistants, \emph{sans perte de sécurité} +%% \end{itemize} +%%\end{block} +%%} + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\section*{Problèmes} +%\begin{frame}{} +%% 'transition': Crossfade, +% \begin{center} +% \Huge{Problèmes} + +%\medskip +% \huge{soulevés par l'approche} +% \end{center} +%\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + + + + +%% %%%%%%%%%%%%% 16. De la relativité du chaos %%%%%%%%%%%%%%% +%\subsection*{Tout est relatif (est-ce encore vrai ?)} + +%% \frame{ +%% \frametitle{Problème soulevé par l'approche} +%% \begin{block}{Quels problèmes pose cette approche ?} +%% \begin{itemize} +%% \item Rôle prépondérant de la topologie +%% \item De sa finesse dépendent les propriétés de désordre +%% \item Comment bien la choisir ? +%% \end{itemize} +%% $\Rightarrow$ Se ramener à la topologie de l'ordre sur $\mathds{R}$ +%% \end{block} +%% } + + +%\frame{ +% \frametitle{De l'importance de la topologie} +%%\begin{block}{Les questions qui se posent} +%%\begin{enumerate} +%%\item Si un système $(\mathcal{X},f)$ est chaotique, et pour quelle topologie. +%%\item Si un système $(\mathcal{X},f)$ est plus chaotique qu'un système $(\mathcal{Y},g)$. +%%\end{enumerate} +%%\end{block} + +%%\vspace{0.5cm} +%%\uncover<2>{ +%\begin{exampleblock}{Problèmes soulevés} +%\begin{enumerate} +%\item Le désordre dépend de la topologie (?) +%\item Comparaison de deux systèmes: +%\begin{itemize} +%\item Les ensembles $\mathcal{X}$ et $\mathcal{Y}$ ne sont pas forcément les mêmes. +%\item Les topologies ne sont pas forcément les mêmes. +%\item Sont-elles comparables ? Et quelles conséquences ? +%\end{itemize} +%\end{enumerate} +%\end{exampleblock} +%%} +%} + + + +%\frame{ +% \frametitle{Mon désordre n'est pas le tien} +% \begin{exampleblock}{Théorème: Impact de la finesse de la topologie} +% Soient $\tau, \tau'$ deux topologies sur $\mathcal{X}$ telles que $\tau \subset \tau'$. + +%Si $(\mathcal{X}_{\tau'},f)$ satisfait Devaney, alors $(\mathcal{X}_\tau,f)$ aussi. +% \end{exampleblock} +%} + +%\frame{ +% \frametitle{Mon désordre n'est pas le tien} +% \begin{exampleblock}{Un système peut toujours être chaotique} +% Soit $\mathcal{X}$ un ensemble non vide, et $f: \mathcal{X} \to \mathcal{X}$ une application possédant au moins un point fixe. +%Alors $f$ est $\tau_0-$chaotique, où $\tau_0$ est la topologie grossière sur $\mathcal{X}$. +% \end{exampleblock} +% +% \vspace{0.5cm} +% +% \begin{exampleblock}{Un système peut toujours ne jamais être chaotique} +%Soit $\mathcal{X}$ un ensemble, et $f: \mathcal{X} \to \mathcal{X}$ une application. +%Si $\mathcal{X}$ est infini, alors $\left( \mathcal{X}_{\tau_\infty}, f\right)$ n'est pas chaotique selon Devaney, où $\tau_\infty$ désigne la topologie discrète. +% \end{exampleblock} +%} + + + + + +%\frame{ +% \frametitle{Réflexions autour d'un désordre absolu} +% \begin{block}{Reformulation des problèmes} +% \begin{itemize} +% \item $(\mathcal{X},f)$ peut ou non être chaotique, suivant la richesse de la topologie. +% \item L'ensemble des topologies sur $\mathcal{X}$, muni de la relation « être plus fine que » est un espace réticulé. +% \end{itemize} +% \end{block} +% +% \vspace{0.4cm} +% +% \begin{block}{Quelques pistes} +% \begin{enumerate} +% \item La plus fine topologie rendant une fonction imprédictible +% \item \^Etre imprédictible, c'est l'être pour la topologie de l'ordre. +% \begin{itemize} +% \item Approche légitime (mais, pour quel ordre ?) +% \item Peut conduire à se ramener à $\mathds{R}$ +% \end{itemize} +% \end{enumerate} +% \end{block} +%} + + +%%%%%%%%%%%%%%% 17. Une semi-conjugaison topologique %%%%%%%% +%%%%%%%%%% ou comment passer de X à un intervalle réel %%%%%% +%\subsection*{Une semi-conjugaison topologique} + + + +%\frame{ +% \frametitle{Une semi-conjugaison topologique} +% +% +%\begin{exampleblock}{Une semi-conjugaison topologique} +%IC $G_{f_0}$ sur $\mathcal{X}$ = IC $g$ sur $\mathds{R}$: +%\begin{equation*} +%\begin{CD} +%\left(~\mathcal{S}_{10} \times\mathds{B}^{10}, d~\right) @>G_{f_0}>> \left(~\mathcal{S}_{10} \times\mathds{B}^{10}, d~\right)\\ +% @V{\varphi}VV @VV{\varphi}V\\ +%\left( ~\big[ 0, 2^{10} \big[, D~\right) @>>g> \left(~\big[ 0, 2^{10} \big[, D~\right) +%\end{CD} +%\end{equation*} +%\begin{enumerate} +%\item Prendre la première décimale $d$ de $x \in \big[ 0, 2^{10} \big[$ +%\item Nier le bit numéro $d$ de $E(x)$ +%\item Supprimer $d$ +%\end{enumerate} +%\end{exampleblock} +%} + + + + +%\frame{ +% \frametitle{Comparaison des distances} + +%\begin{exampleblock}{Comparaison de distances} +%$D$ est plus fine que la distance euclidienne. +%\end{exampleblock} + +%\begin{figure}[t] +%\begin{center} +% \subfigure[Application $x \to dist(x;1,234)$.]{\includegraphics[scale=.25]{17.Semi_conjugaison_topologique/distances/DvsEuclidien.pdf}}\quad +% \subfigure[Application $x \to dist(x;3) $.]{\includegraphics[scale=.25]{17.Semi_conjugaison_topologique/distances/DvsEuclidien2.pdf}} +%\end{center} +%\caption{Comparaison des distances $D$ et euclidienne.} +%\label{fig:comparaison de distances} +%\end{figure} +%} + + + + + + + + +%\frame{ +% \frametitle{\'Etude des ICs sur $\mathds{R}$} +% \begin{exampleblock}{Analyse des itérations chaotiques réelles} +%Les itérations chaotiques $g$ définies sur $\mathds{R}$ sont: +%\begin{itemize} +%\item Infiniment dérivables sur $\big[ 0, 2^{10} \big[$, sauf aux 10241 points de l'ensemble $I$ défini par $\left\{ \dfrac{n}{10} ~\big/~ n \in \llbracket 0;2^{10}\times 10\rrbracket \right\}$. +%\item Affine, de pente 10, sur chaque sous-intervalle. +%\end{itemize} +%\end{exampleblock} +%} + + + +%%\frame{ +%% \frametitle{Exemples de fonctions chaotiques} +%%\begin{figure}[t] +%%\begin{center} +%% \subfigure[Doublement de l'angle.]{\includegraphics[scale=.16]{17.Semi_conjugaison_topologique/fonctions/doublement.pdf}}\quad +%% \subfigure[Fonction logistique.]{\includegraphics[scale=.16]{17.Semi_conjugaison_topologique/fonctions/logistique.pdf}}\quad +%% \subfigure[Fonction tente.]{\includegraphics[scale=.16]{17.Semi_conjugaison_topologique/fonctions/tente.pdf}} +%%\end{center} +%%\caption{Exemples de fonctions chaotiques.} +%%\end{figure} +%%} + + + + + +%\frame{ +% \frametitle{Les itérations chaotiques $G_{f_0}$ sur $\mathds{R}$} +%\begin{figure}[t] +%\begin{center} +%% \subfigure[Sur (0,9 ; 1).]{\includegraphics[scale=.16]{17.Semi_conjugaison_topologique/fonctions/ICs09a1.pdf}}\quad +% \subfigure[Sur (0,7 ; 1).]{\includegraphics[scale=.16]{17.Semi_conjugaison_topologique/fonctions/ICs07a95.pdf}}\quad +% \subfigure[Sur (0 ; 1).]{\includegraphics[scale=.19]{17.Semi_conjugaison_topologique/fonctions/ICs0a1.pdf}}\quad +% \subfigure[Sur (510 ; 514).]{\includegraphics[scale=.19]{17.Semi_conjugaison_topologique/fonctions/ICs510a514.pdf}}\quad +% \subfigure[Sur (1000 ; 1008).]{\includegraphics[scale=.19]{17.Semi_conjugaison_topologique/fonctions/ICs1000a1008.pdf}} +%\end{center} +%\caption{Les itérations chaotiques.} +%\end{figure} +%} + + + + +%\frame{ +% \frametitle{Les itérations chaotiques sur $\mathds{R}$} +%\begin{figure}[t] +%\begin{center} +% \subfigure[Sur (510 ; 514).]{\includegraphics[scale=.16]{17.Semi_conjugaison_topologique/fonctions/ICs510a514.pdf}}\quad +% \subfigure[Sur (1000 ; 1008).]{\includegraphics[scale=.16]{17.Semi_conjugaison_topologique/fonctions/ICs1000a1008.pdf}}\quad +% \subfigure[Sur (40 ; 70).]{\includegraphics[scale=.16]{17.Semi_conjugaison_topologique/fonctions/ICs40a70.pdf}} +%\end{center} +%\caption{Les itérations chaotiques.} +%\end{figure} +%} + + + + + + +% \frame{ +% \frametitle{Chaos des IC $G_{f_0}$ sur $\mathds{R}$} +% \begin{exampleblock}{Chaos de Devaney sur $\mathds{R}$} +% Les IC sur $\mathds{R}$ sont chaotiques selon Devaney, quand $\mathds{R}$ a sa topologie usuelle. +% \end{exampleblock} + +% \vspace{0.5cm} + +% \begin{exampleblock}{Exposant de Lyapunov} +% %$\forall x^0 \in \mathcal{L}$, l'exposant de Lyapunov des itérations chaotiques ayant $x^0$ pour condition initiale vaut +% $$\forall x^0 \in \mathcal{L}, \lambda(x^0) = \displaystyle{\lim_{n \to +\infty} \dfrac{1}{n} \sum_{i=1}^n \ln \left| ~g'\left(x^{i-1}\right)\right|} = \ln (10).$$ +% \end{exampleblock} +% } + + + + + + + + + + + + +%\frame{ +% \frametitle{Systèmes itératifs et suites récurrentes} +% \begin{alertblock}{Les systèmes itératifs sont des suites récurrentes} +% On pose $F:\mathcal{X}^\mathds{N} \longleftrightarrow\mathcal{X}^\mathds{N}$, qui à la suite $(x^k)_{k \in \mathds{N}}$ associe $\left(x^0, f^0(x^0), f^1(x^0,x^1), f^2(x^0,x^1,x^0),\hdots\right)$. Alors le système +% $$\left\{ +% \begin{array}{l} +% X^0 = (x^0,0,0, \hdots) \in \mathcal{X}^\mathds{N}\\ +% X^{n+1} = F(X^n) +% \end{array} +% \right.$$ +% tend vers la suite $(x^0,x^1,x^2,\hdots)$. +% \end{alertblock} +% \uncover<2->{ +% Etudions un cas particulier : les « Itérations chaotiques »} +%} + +\section{Conclusion} + + +\bibliographystyle{plain} +\bibliography{mabase} \end{document}