O'Neill recently mentioned the crypto aspects of PCG in an comment on another post by John D. Cook. I'll just quote it below. But it looks to me like she thought that any analysis she did on the prediction difficulty of PCG wouldn't be well regarded.
Also, I notice that lots of people seem to think her paper was too long, but they also claim that it doesn't say enough about their favorite topic. That seems to be happening with you.
Direct quote from O'Neill's comment here https://www.johndcook.com/blog/2017/07/07/testing-the-pcg-ra...
John, in your post, you said that PCG has “excellent statistical and cryptographic properties”. I’ve learn it best never to say “cryptographic security” or “cryptographic properties” when trying to place something on a spectrum of prediction difficulty. Too many misunderstandings. Saying “prediction difficulty” still causes some crossed wires, but it’s about as good as we can go.
Dan & Dmitriy, just to be 100% clear, I HAVE NEVER RECOMMENDED PCG FOR CRYPTOGRAPHY. I do however, care about prediction difficulty, and I don’t like trivially predictable generators. Because my viewpoint is often misunderstood, I have some more blog posts in the pipeline about these issues, but the key thing is that general-purpose PRNGs get used for almost anything, from using the low-order bit to toss a coin, to supporting randomized algorithms. If someone can predict your generator, they can mount an algorithmic complexity attack on your randomized algorithm, tanking its performance. If predicting the generator is more costly than the algorithmic complexity attack itself, people will try their attacks on easier targets. But if the generator spends to much time being trying hard to be unpredictable, we also tank our performance, thus we have to try to strike a balance in a different place than we do for traditional cryptographic applications. We already live in a world where hash table implementations in scripting languages need to be hardened because of algorithmic complexity attacks; this is the next logical step.
All that said, there are members of the pcg family (not pcg32 and especially not pcg32_fast!) that I personally think would be really challenging to predict. I also find it frustrating that people don’t compare like with like. If you want to compare the prediction difficulty of PCG against a cryptographically secure PRNG, you need to compare a PCG variant at least broadly similar in size. Say, for example, we wanted to contrast PCG against the ChaCha PRNG from Orson Peters (perhaps with four rounds rather than the full 20), that PRNG is 104 bytes in size, so it’s fairest to compare it to pcg64_c8, which is 80 bytes, or pcg64_c16, which is 144 bytes.
Regarding prediction difficulty, I’m very well aware of Bruce Schneier’s law, “Anyone, from the most clueless amateur to the best cryptographer, can create an algorithm that he himself can’t break. It’s not even hard. What is hard is creating an algorithm that no one else can break, even after years of analysis. And the only way to prove that is to subject the algorithm to years of analysis by the best cryptographers around.”, and his subsequent elaboration “Anyone can invent a security system that he himself cannot break. I’ve said this so often that Cory Doctorow has named it “Schneier’s Law”: When someone hands you a security system and says, “I believe this is secure,” the first thing you have to ask is, “Who the hell are you?” Show me what you’ve broken to demonstrate that your assertion of the system’s security means something.” Thus my personal thoughts on how difficult it is mean NOTHING in a cryptography context. I also can’t expect cryptographers to spend their time on my education, but if someone out does know a simple and efficient algorithm that can reliably break pcg64_c8, I really would love to see how. (Also, hey Bruce, gender-neutral language, it’s a thing.)
I can do at least one thing that adds a tiny tiny tiny bit of credibility in the eyes of folks like Bruce Schneier , I can show other PRNGs I have broken that might have seemed hard to predict to a casual observer. Mostly that won’t actually help though, because a cryptographer would say “Ha! That’s toddler level stuff!” and a mathematician might say “I can’t understand why you care about prediction at all”. Sometimes I feel there should be more people trying to occupy the middle ground. Meh.
But, let’s be clear, DO NOT USE PCG FOR CRYPTOGRAPHY. DO NOT USE PCG FOR CRYPTOGRAPHY. DO NOT USE PCG FOR CRYPTOGRAPHY. Clear?