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If you mean that “I (Daniel Lemire) make a fuss”, then I have to disagree with you. If you mean that O’Neill is making a fuss, then please be specific. Here is what I wrote: I should point out that the same is true of most random number generators in widespread use today.
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Cryptographic random number generators should probably be used if you want to open a casino. I trust that you are in agreement with this statement?
You write: “the generator produces all possible distinct k-tuples it can actually generate, given its state space Which of course implies that after any k outputs you can predict the generator.” I am trying to parse this statement and I am having difficulties. What is the value of k in this instance (xoroshiro128+)?
Hey, Daniel, I said “this lady”. Clearly I’m not referring to you! I completely agree with your statement. But your title is “Cracking random number generators (xoroshiro128+)”, not “Cracking the Mersenne Twister”. And “cracking” the Mersenne Twister is even easier.
So I think that the way you are presenting the material is very misleading. But, hey, it’s your blog. Do you agree with me that renaming “equidistributed” (20 years of history) with “crackable” is a bit of a stretch? Xoroshiro128+ is not maximally equidistributed in its maximal dimension: it emits all values the same number of times, but not all pairs of values (it is 1-equidistributed, but not 2-equidistributed).
For instance, the Mersenne Twister is: it’s actually stated in the title of the paper: “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator.” So after 623 inputs you can predict, and it’s impossible to do it before due to state space size (every 622-tuple is followed by all possible values). I’m not a big fan of equidistribution: I argued in my paper on TOMS that’s vastly overestimated as a feature of a PRNG. I got through.four. rounds of refereeing in two years to get my ideas through.
But they were discussed with expert in the fields before being published, as it should happen. I completely agree with your statement. But your title is “Cracking random number generators (xoroshiro128+)”, not “Cracking the Mersenne Twister”. And “cracking” the Mersenne Twister is even easier.
So I think that the way you are presenting the material is very misleading. But, hey, it’s your blog. It is less interesting to crack SplitMix or the Mersenne Twister because it is obvious how if you have some working knowledge of computer arithmetic. (And see James Roper’s post about.) Do you agree with me that renaming “equidistributed” (20 years of history) with “crackable” is a bit of a stretch? I’m sorry if you are offended by the terminology, that was not my intention. So you are saying that “equidistributed” is synonymous with being computationally easy to invert?
No, but maximally equidistributed in the output dimension implies predictability, and all examples I’ve seen so far for generators with large state space involve some kind of equidistribution. I think it’s very dangerous to make people believe that there are “easily predictable”, “less easy to predict” and “secure” generators. There are secure and non-secure generators, period. The difficulty of predicting a generator, given that it can predicted feasibly, is irrelevant. You want secure? Use Fortuna, or something like that.
Making people believe that a.slight less predictable. generator (like PCG) will solve their security problems will meet harsh comments from people working on security. It feels to me like there is no significant disagreement between us that I can see. I take it that you might feel that using the term “cracking” might be pejorative.
But xoroshiro128+ is not secure (by your own admission, surely), so it is reasonable to talk about “cracking it”. You object that the same can be said of many other functions, but my posts says so, explicitly. Let me recopy my statement once more: I should point out that the same is true of most random number generators in widespread use today.
Cryptographic random number generators should probably be used if you want to open a casino. You would prefer, it seems that I give as a title to my post “xoroshiro128+ is maximally equidistributed”. But I don’t think it is correct. That’s not what I illustrate. And I think you agree. You write: “You want secure?
Use Fortuna, or something like that.” Again, please go back to what I wrote: “Cryptographic random number generators should probably be used if you want to open a casino.” We are saying the same thing! L’Ecuyer, Handbook of Computational Statistics, J. Haerdle, and Y. Mori, eds., Second Edition, Springer-Verlag, 2012, 35-71.
Relevant quote: Generators Based on a Deterministic Recurrence RNGs with short periods or bad structures are usually easy to crack You find other instances by other authors such as J. Reeds, Cracking a random number generator, cryptologia, 1977 He goes on to explain how to “crack” simple generators (that have not been claimed to be cryptographically strong). James Roper has a whole series. He shows how to crack the among other things. I believe that it is a very reasonable term.
You could, in fact, define a non-cryptographically secured generator as being easily cracked. Note that people will definitively use such non-cryptographically strong generators for applications where a cryptographically strong generator is needed, precisely because they do not understand that they can get cracked. What I illustrated in this blog post is not entirely trivial.
Many engineers could very reasonably expect it to be difficult to infer the seed from the outputs of xoroshiro128+. We need to educate people, and if the term “cracking” sounds a bit scary, then I say “good!”. I submit to you that cryptographers will approve of my message. What they would criticize, if this would go through formal peer review is the triviality of it all They would say “oh!
But of course it is easy to crack” They would point me to Reeds (1977) and say “we were cracking simple generators decades ago”. Dear Daniel, Do you think I’m stupid? Or I can’t read? The complete quote from the paper is “are usually easy to crack by standard statistical tests” Of course, “crack” here has nothing to do with what you mean. L’Ecuyer has decades of experience and would never use words so carelessly.
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The other quotation is another nice trick, but short lived: it is a famous paper, and the actual title is “Cracking” a random number generator. Notice the quotes. The author know what’s taking about. This is not a scientific discussion, and I’m out of it. You can of course delete this comment (as you disabled replies in the other thread). Of course, “crack” here has nothing to do with what you mean. L’Ecuyer has decades of experience and would never use words so carelessly.
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Ok, so if I find that a generator fails at a statistical test, I can say that I cracked it and you will find the term acceptable? I personally prefer my own use of the word “crack”. Notice the quotes. The author know what’s taking about.
It is true that he uses quotes whereas I did not except in my first use the term, but Reeds (who is famous, of course) uses the term with exactly the same meaning as I do here. I’ll revise my blog post so that there are quotes around the word “crack” on every single use of the term. This will put me on par with Reeds. This is not a scientific discussion, and I’m out of it. I’m sorry if you are offended.
“We had a 20-minute solo that Marshall Allen from the Sun Ra Arkestra did for us. “The album is full of friends of ours just soloing and improvising,” Daniel says. He was playing an EVI—basically, it’s a breath-controlled oscillator. 
That was not my intention. You can of course delete this comment (as you disabled replies in the other thread). I did no such thing as disabling replies in any thread regarding this post.
We know that the piracy enablers are at the top of the software piracy distribution process. The software 'crackers” are individuals and groups who love to crack DRM and software licensing schemes.
While many crackers are well-hidden, some are surprisingly visible on the Web and have established their own blogs to announce their crack releases. The crack group Team SolidSQUAD (SSQ) is one such piracy group. They have been very active in the last few years and have routinely targeted high value software in CAD, CAM, simulation and other engineering industries. From our own experience we know these groups do quality assurance (QA) on their work and have built up a following of users based on their success producing high quality crack software. This in turn contributes to a high number of organizations adopting their specific releases – something else we know by looking at our customers’ aggregated infringement data. We recently dug into this a bit further, leveraging the SSQ blog to do some analysis on their followers.