-Comments:
-The paper is, overall, well written and clear, with appropriate references to the relevant concepts and prior work. The motivation of the work, however, is not quite clear: the authors present (provable) chaotic properties of a PRNG as a security improvement, but provide no convincing argument beyond opinion (or hope). 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.
+\bigskip
+\textit{The paper is, overall, well written and clear, with appropriate references to the relevant concepts and prior work. The motivation of the work, however, is not quite clear: the authors present (provable) chaotic properties of a PRNG as a security improvement, but provide no convincing argument beyond opinion (or hope).}
+
+
+\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.}
+
+\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]).}
+
+\bigskip
+\textit{Secondly, the periods of the 3 xorshift generators are not coprime --- this reduces the useful period of combining the sequences.}
+
+\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.}
+
+\bigskip
+\textit{The BBS-based generator of section 9 is anything but cryptographically secure.}
+
+This claim is surprising, as this result is mathematically proven in the article:
+either there is something wrong in the proof, or the generator is cryptographically
+secure. Indeed, there is probably a misunderstanding of this notion, which does
+not deal with the practical aspects of security. For instance, BBS is
+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
+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.}
