\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 (namely, the Section 9.2) has been added to measure practically the security of the generator.
+A new section (namely, the Section 8.2) and a discussion at the end of Section 9.1 have been added to measure practically the security of the generator.
\bigskip
\textit{In the conclusion:
\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
+A large section (Section 5) has been added, using and extending some previous works. It explains with more detail why topological chaos
is useful to pass statistical tests. This new section contains both qualitative explanations and quantitative (experimental) evaluations.
Using several examples, this section illustrates that defective PRNGs are always improved, according
to the NIST, DieHARD, and TestU01 batteries.
\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}
+We agree with the reviewer in the fact that using coprimes here will improve
+the period of the resulted PRNG. Nevertheless the goal of this section was to
+pass the Big Crush battery, and we achieve that with proposed combination of
+the three XORshifts.
\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.}
cryptographically secure, but whatever the size of the keys, a brute force attack always
achieve to break it. It is only a question of time: with sufficiently large primes,
the time required to break it is astronomically large, making this attack completely
-impracticable in practice. To sum up, being cryptographically secure is not a
+impracticable: being cryptographically secure is not a
question of key size.
\begin{color}{green}
keys/seeds are large enough.
\end{color}
+Nevertheless, new arguments have been added in several places of the revision of our paper,
+concerning more concrete and practical aspects of security, like the
+$(T,\varepsilon)-$security notion of Section 8.2. Such a practical evaluation
+has not yet been performed for the GPU version of our PRNG, and the reviewer
+has true when thinking that these aspects are fundamentals to determine whether
+the proposed PRNG can face or not attacks in practice. A formula similar to what
+has been computed for the BBS (as in Section 8.2) must be found in future work,
+to measure how much time an attacker must have to break the proposed generator
+when considering the parameters we have chosen (this computation is a difficult
+task).
+Sentenses have been added in several places (like at the end of Section 9.1)
+summarizing this.
+
\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.}
-We hope now that, with the new sections added to the document, we have convinced the reviewers that to add chaotic properties in
+We hope now that, with the new sections added to the document (like the Section 5), we have convinced the reviewers that to add chaotic properties in
existing generators can be of interest.
\bigskip
