X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/4ad2ccae91afa1f83fad9be3c87213a9b8d81734..4797365cf4607caea2473f7ce2f4fe6c3bbf9c51:/reponse.tex?ds=sidebyside

diff --git a/reponse.tex b/reponse.tex
index 3b3e986..f720670 100644
--- a/reponse.tex
+++ b/reponse.tex
@@ -18,13 +18,17 @@
 \bigskip
 \textit{The authors should include a summary of  test measurements showing their method passes the test sets mentioned (NIST, Diehard, TestU01) instead of the one sentence saying it passed that is in section 1.}
 
-\begin{color}{red} Raph, c'est pour toi ça.\end{color}
+\begin{color}{red} In section 1, we have added a small summary of test measurements performed with BigCrush of TestU01.
+As other tests (NIST, Diehard, SmallCrush and Crush of TestU01 ) are deemed less selective, in this paper we did not use them.
+\end{color}
 
 
 \bigskip
 \textit{Section 9:
 The authors say they replace the xor-like PRNG with a cryptographically secure one, BBS, but then proceed to use extremely small values, as far as a cryptographer is concerned (modulus of $2^{16}$), in the computation  due  to the need to use 32 bit integers in the GPU and combine bits from multiple BBS generated values, but they never prove (or even discuss) how this  can be considered cryptographically secure due to the small  individual values. At the end of 9.1, the authors say $S^n$ is secure because it is formed from bits from the BBS generator, but do not consider if the use of such small values will lead to exhaust searches to determine individual bits. The authors either need to remove all of section 9 and or prove the resulting PRNG is cryptographically secure.}
 
+A new section has been added to measure practically the security of the generator.
+
 \bigskip
 \textit{In the conclusion:
 Reword last sentence of 1st paragraph
@@ -43,15 +47,41 @@ Done.
 \bigskip
 \textit{There seems to have been no effort in showing how the new PRNG improves on a single (say) xorshift generator, considering the slowdown of calling 3 of them per iteration (cf. Listing 1). This could be done, if not with the mathematical rigor of chaos theory, then with simpler bit diffusion metrics, often used in cryptography to evaluate building blocks of ciphers.}
 
+A large section (Section 5) has been added, using and extending some previous works, explains with more detail why topological chaos 
+is useful to pass statistical tests. Using several examples, this section illustrates  that defective PRNGs are always improved, according
+to the NIST, DieHARD, and TestU01 batteries.
+
 \bigskip
 \textit{The generator of Listing 1, despite being proved chaotic, has several problems. First, it doesn't seem to be new; using xor to mix the states of several independent generators is standard procedure (e.g., [1]).}
 
+To the best of our knowledge, all the generators proposed in the literature mix only a few operations on previously obtained states:
+arithmetic operations, exponentiation, shift, exclusive or. It is impossible to define a fast PRNG or to prove its security when
+using more complicated operations, and the number of such operations that are mixed is necessary very low. Thus almost all
+ up-to-date fast or secure generators are very simple, like the BBS or all the XORshift-like ones. In a certain extend, they are all similar, 
+due to the very reduced number of efficient elementary operations offered to define them.
+
+
 \bigskip
 \textit{Secondly, the periods of the 3 xorshift generators are not coprime --- this reduces the useful period of combining the sequences.}
 
+\begin{color}{green}
+Raph, c'est pour toi ça : soit tu changes tes xorshits, soit tu justifies ton choix ;)
+\end{color}{green}
+
 \bigskip
 \textit{Thirdly, by combining 3 linear generators with xor, another linear operation, you still get a linear generator, potentially vulnerable to stringent high-dimensional spectral tests.}
 
+This first generator has not been designed for security reasons, but for speed: the
+idea was to provide a very efficient version of our former generator that can pass
+TestU01. If the desire is to use a fast and statistically perfect PRNG, then simulations
+proposed in this document show that this first PRNG is suitable. However, we have neither
+claimed nor proved that this generator is secure. Indeed, to the authors opinion,
+linear operations are a necessity when speed with pseudorandomness are only desired.
+A sentence has been added to clarify this point \begin{color}{green} Il faudrait ajouter
+cette phrase fin de la section 6 (je l'ai fait pour la fin de la section 5.4). 
+Dire que pour l'instant, on veut juste avoir de la rapidité sans biais
+statistique, que la sécurité viendra après.\end{color}
+
 \bigskip
 \textit{The BBS-based generator of section 9 is anything but cryptographically secure.} 
 
@@ -70,6 +100,8 @@ question of key size,
 \bigskip
 \textit{A 16-bit modulus (trivially factorable) gives out a period of at most $2^{16}$, which is neither useful nor secure. Its speed is irrelevant, as this generator as no practical applications whatsoever (a larger modulus, at least 1024-bit long, might be useful in some situations, but it will be a terrible GPU performer, of course).}
 
+
+
 \bigskip
 \textit{To sum it up, while the theoretical part of the paper is interesting, the practical results leave much to be desired, and do not back the thesis that chaos improves some quality metric of the generators.}