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[prng_gpu.git] / prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 7eb93d14dad7c090cf80f7cea66f84cdedbfe846..a57e2a00a6281772530129985688ab776bde082f 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -161,7 +161,7 @@ We show in Section~\ref{sec:security analysis} that, if the inputted
 generator is cryptographically secure, then it is the case too for the
 generator provided by the post-treatment.
 Such a proof leads to the proposition of a cryptographically secure and
 generator is cryptographically secure, then it is the case too for the
 generator provided by the post-treatment.
 Such a proof leads to the proposition of a cryptographically secure and

-chaotic generator on GPU based on the famous Blum Blum Shum
+chaotic generator on GPU based on the famous Blum Blum Shub

 in Section~\ref{sec:CSGPU}, and to an improvement of the
 Blum-Goldwasser protocol in Sect.~\ref{Blum-Goldwasser}.
 This research work ends by a conclusion section, in which the contribution is
 in Section~\ref{sec:CSGPU}, and to an improvement of the
 Blum-Goldwasser protocol in Sect.~\ref{Blum-Goldwasser}.
 This research work ends by a conclusion section, in which the contribution is


@@ -1270,7 +1270,7 @@ It is  possible to build a  cryptographically secure PRNG based  on the previous
 algorithm (Algorithm~\ref{algo:gpu_kernel2}).   Due to Proposition~\ref{cryptopreuve},
 it simply consists  in replacing
 the  {\it  xor-like} PRNG  by  a  cryptographically  secure one.  
 algorithm (Algorithm~\ref{algo:gpu_kernel2}).   Due to Proposition~\ref{cryptopreuve},
 it simply consists  in replacing
 the  {\it  xor-like} PRNG  by  a  cryptographically  secure one.  

-We have chosen the Blum Blum Shum generator~\cite{BBS} (usually denoted by BBS) having the form:
+We have chosen the Blum Blum Shub generator~\cite{BBS} (usually denoted by BBS) having the form:

 $$x_{n+1}=x_n^2~ mod~ M$$  where $M$ is the product of  two prime numbers (these
 prime numbers  need to be congruent  to 3 modulus  4). BBS is known to be
 very slow and only usable for cryptographic applications. 
 $$x_{n+1}=x_n^2~ mod~ M$$  where $M$ is the product of  two prime numbers (these
 prime numbers  need to be congruent  to 3 modulus  4). BBS is known to be
 very slow and only usable for cryptographic applications. 


@@ -1471,10 +1471,10 @@ namely the BigCrush.
 Furthermore, we have shown that when the inputted generator is cryptographically
 secure, then it is the case too for the PRNG we propose, thus leading to
 the possibility to develop fast and secure PRNGs using the GPU architecture.
 Furthermore, we have shown that when the inputted generator is cryptographically
 secure, then it is the case too for the PRNG we propose, thus leading to
 the possibility to develop fast and secure PRNGs using the GPU architecture.

-Thoughts about an improvement of the Blum-Goldwasser cryptosystem, using the 
-proposed method, has been finally proposed.
+An improvement of the Blum-Goldwasser cryptosystem, making it 
+behaves chaotically, has finally been proposed.

 
 

-In future  work we plan to extend these researches, building a parallel PRNG for  clusters or
+In future  work we plan to extend this research, building a parallel PRNG for  clusters or

 grid computing. Topological properties of the various proposed generators will be investigated,
 and the use of other categories of PRNGs as input will be studied too. The improvement
 of Blum-Goldwasser will be deepened. Finally, we
 grid computing. Topological properties of the various proposed generators will be investigated,
 and the use of other categories of PRNGs as input will be studied too. The improvement
 of Blum-Goldwasser will be deepened. Finally, we