7 ms·
Cracking random number generators (xoroshiro128+)
- pbnjay 9y agoAuthor's title should be "Cracking PSEUDO-random number generators" - We should all basically assume that any PRNG will be easily cracked like this and not use them for anything important to security! Always use a cryptographic RNG for important code!
- anfractuosity 9y agoAren't cryptographic random number generators, still PRNGs. It sounds a fun problem, predicting the future random numbers, going to have to have a play later at trying it.
- hlieberman 9y agoYes. GP is mistaken here; this is novel work that is somewhat concerning -- mostly in how it might apply to other similarly state-based RNGs.
- pbnjay 9y agoI made no comment on the work done here, it is novel and concerning if you use the outputs for important things. My comment is that non-cryptographic random number generators should not be used for security-critical functions. These functions are specifically built for speed, not security.
- karanlyons 9y agoI wouldn’t say this work is novel in the general case of “PRNGs are not CSPRNGs”. You can throw a constraint solver at most any PRNG and given sufficient output determine the state fairly easily. As a datapoint, doing this for xoroshiro took me half an hour: https://gist.github.com/karanlyons/805dbcc9e898dbd17e06f2627d5f9111 https://gist.github.com/karanlyons/805dbcc9e898dbd17e06f2627...
- anfractuosity 9y agoHeh, that sounds cool. I'll save opening that link for later.
- karanlyons 9y agoDon’t worry, it’s safe: I didn’t put the actual solver, just proof that I solved it. Wouldn’t want to spoil the fun for anyone else :)
- DiThi 9y agoStrong crypto RNGs use PRNGs but combines sources of entropy, environmental noise from devices such as the number of CPU cycles between user keystrokes. T̶h̶a̶t̶'̶s̶ ̶t̶h̶e̶ ̶d̶i̶f̶f̶e̶r̶e̶n̶c̶e̶ ̶b̶e̶t̶w̶e̶e̶n̶ ̶/̶d̶e̶v̶/̶r̶a̶n̶d̶o̶m̶ ̶a̶n̶d̶ ̶/̶d̶e̶v̶/̶u̶r̶a̶n̶d̶o̶m̶ ̶i̶n̶ ̶L̶i̶n̶u̶x̶.̶
- Tomte 9y agoNo, that difference (between /dev/random and /dev/urandom) does not exist, has never existed and will never exist. Please don't spread those myths.
- andruby 9y agoAs I am uninformed on the subject, could you tell me the difference between /dev/random and /dev/urandom?
- filleokus 9y agoQuite a long read, but I think it explains the situation quite well: https://www.2uo.de/myths-about-urandom/ https://www.2uo.de/myths-about-urandom/
- snakeanus 9y agoAlso an interesting and related article https://sockpuppet.org/blog/2014/02/25/safely-generate-random-numbers/ https://sockpuppet.org/blog/2014/02/25/safely-generate-rando...
- Tomte 9y agoUnfortunately, the article isn't in the best shape right now. Back when it was written, things were clear: random and urandom are the same. Then came getrandom as a distraction. Now urandom is based on chacha. So it's different (but not worse – still, harder to explain). The article's structure couldn't easily accomodate those changes, and time was and is in short supply, and so it's not wrong, but much less forceful and clear than it used to be. I hope it shapes up soon, but don't promise anything! Still, I don't know a more up-to-date article. Maybe Thomas Pornin has something newer on StackOverflow?
- tptacek 9y agoThis shouldn't have been downvoted because it is exactly correct. Cryptographic generators don't work like PCG and xoroshiro and Mersenne Twister. They're generally built by taking a cryptographically secure cipher or hash core, "keying" it with secret entropy, and running it in a streaming configuration (like CTR mode). A properly designed CSPRNG can only be "cracked" in a few specific scenarios: 1. The primitive it's built on (or the streaming construction it's configured in) is broken, in which case the news for cryptography as a field is significantly bigger than the fact that an RNG has a flaw. 2. An attacker has exploited a systems flaw to directly disclose the contents of the memory the CSPRNG is operating out of, in which case you have bigger problems than your CSPRNG. 3. The secrets that key the generator have become predictable. This is in practice the only way CSPRNGs get broken (unintentionally), and, in practice, always means the CSPRNG wasn't initialized properly (the "cold start entropy problem"). You should use the getrandom() system call, or read from /dev/urandom, to the exclusion of all other mechanisms.
- baby 9y agoFWIW you rarely hear the term CSPRNG in crypto I find. I always call these PRNGs but I can see how having a naming distinction could help prevent misuse in the applied world. Edit: thinking a bit more about it. I guess it wouldn't make sense to call anything "crypto" in crypto. It's like calling fries "french fries" in France. There they're just fries. I know this is a bad example because french fries are probably not from France :o)
- gwbas1c 9y agoBut, it's important to make the decision because a "crypto" psudorandom number generator may be significantly slower than an insecure generator. This is critical for performance-sensitive operations. For example, certain audio and video codecs need to simulate noise. In these cases, high performance is much more important than cryptographic security.
- tptacek 9y agoIn the overwhelming majority of cases, cryptographic random bit generation performs perfectly adequately. Insecure random number generation is wildly overused in our industry. CSPRNGs should be the default application RNGs on most platforms, and should always be the default choice for developers. Which makes stuff like PCG even weirder! Because in most cases, what you want is a somewhat slower generator that has better failsafe behavior.
- imaginenore 9y agoCan you crack this PRNG without knowing the seed? f(1) = 1 // seed f(n) = sha512(f(n-1) . f(1))
- sdevlin 9y agoI guess it depends what you mean by “crack”. Given f(1), which I assume is public, you can predict all future outputs.
- IshKebab 9y agoThat is not what we mean by "crack". Read the article.
- imaginenore 9y agoI said without knowing the seed, so f(1) is not public, only f(n) formula is.
- benchaney 9y agof(1) is the first batch of output.
- mdpopescu 9y agoThis is similar to Yarrow / Fortuna (internal state is a counter, output is the hash of the state) so I'm guessing it's not breakable, at least not trivially.
- VikingCoder 9y ago"Always use a cryptographic PSUEDO-RNG for important code!" Just because it's "cryptographic" doesn't mean it's not pseudo-random.
- TACIXAT 9y agoHey, author of the SMT attack here. There is probably a clever way to go after XorShift128+ as well, symbolic execution using an SMT solver is basically a brute-force solution. I'll have to give this challenge a shot later.
- aj7 9y agoHa ha! By going to your predictions page I can crack you! Great post.
- xoroshiro 9y agoAs someone who first learned how to program by implementing PRNGs but never really digging deeper into it, I found this post very interesting to read. I do have an idea about some (small portion) of the things behind it, but I have no background in cryptography. Looking at the other posts, it seems like most PRNGs are fine for non-cryptographic applications, but what are other ways to make PRNG's though? Everything I've learned (mostly simple stuff; Linear Congruential, Midsquare, etc.) seem to need to store a state to work, because otherwise, wouldn't you just output the same thing over and over again? I know there's stuff like /dev/random (though I'm unsure how that works), but that doesn't seem like a good idea for getting a lot of numbers.
- andrewla 9y agoProfessor O'Neill (mentioned in the article) has written a PRNG [1]. The jury is still out on how powerful it is in general. There continue to be fights between what it means to be random for cryptographic purposes vs. numerical analysis purposes. That said, the PDF on that site that serves as a writeup for PCG contains a nice discussion of the links between the size of the state held and the strength of the algorithm, including a discussion of the state of the art for crypto- and non-crypto- PRNGs. [1] http://www.pcg-random.org/ http://www.pcg-random.org/
- tptacek 9y agoThere is in fact no real debate about what's required for an RNG to be suitable for security purpose. The standard for security is cryptographic. To design a new secure RNG, you effectively need to design a new cryptographic primitive (most likely, a new native stream cipher). There may indeed be some debate about the requirements for non-security numerical analysis applications. Most development platforms should be defaulting to secure random number generators, and most developers should be reaching for secure random number generators as their default choice. Neither PCG nor xorshiro128 are examples of these.
- fpgaminer 9y ago> Most development platforms should be defaulting to secure random number generators, and most developers should be reaching for secure random number generators as their default choice. I was curious about this statement. So I did some research. This page (http://vigna.di.unimi.it/xorshift/ http://vigna.di.unimi.it/xorshift/) indicates that xoroshiro128+ generates 64-bits in 0.81ns on a modern 3.6GHz CPU. If I'm reading this page correctly (https://bench.cr.yp.to/results-stream.html https://bench.cr.yp.to/results-stream.html) ChaCha20 gets about 0.8 cycles per byte these days on modern CPUs. Running the math we get 9.88 GB/s for Xoroshiro128+ and 5.14 GB/s for ChaCha20 (assuming a 3.6GHz modern CPU for both). Actually a _lot_ closer than I thought. It never occurred to me that a CSPRNG could compete, performance wise, with a non-CS PRNG. I'm sure there's variation here. Sometimes CSPRNGs will have re-keying cycles, and probably most implementations aren't going to use the highly optimized version we see in the benchmark. I'm not sure if the Xoroshiro128+ benchmark I found used a version utilizing all the SIMD functionality of the CPU (like the ChaCha20 benchmark does). I'm also not sure if Xoroshiro128+ is the fastest PRNG or not. But I have to say, if these numbers are accurate ... you're just plain right. There's no reason to default to a non-CSPRNG. CSPRNG is a safer default, and in the rare scenario that a developer needs more performance they can go seek out a specific PRNG for their needs.
- nolemurs 9y agoThe article is a serious waste of time. It can be summarized as "Non cryptographic PRNGs can be predicted! Look, I cracked this one! I'm not going to tell you how I did it though." There's no exposition describing non cryptographic PRNGs, nor any evidence given for why they're not sound beyond the author's assertion that he cracked one. To be clear, non cryptographic PRNGs are often predictable, and shouldn't be used if that's a problem, but if you're interested in learning more about that, this article isn't going to help you much. Skip the read.
- zb3 9y agoThis problem can be solved using Z3: https://gist.github.com/zb3/c59cf596ce80c501db5ca16c31a1c3a7 https://gist.github.com/zb3/c59cf596ce80c501db5ca16c31a1c3a7 I don't know whether autor used solver or some other magic method... Solutions should be available to those who want to see them.
- edflsafoiewq 9y agoDoes anyone know how the constants in xoroshiro128+ were chosen?