This is not the first RNG bug on Zen 2, I recall after I first got mine that some application or other would quit immediately at startup because rdrand always returned -1, i.e. all 1s. It was fixed with a microcode update.
Do we now learn that they fixed "always generate all 1s" with "never generate all 0s"??
EDIT: I've been unable to reproduce the problem on my CPU, FWIW. It's a Ryzen 5 3600.
EDIT2: OK, update, I can reproduce it with rdrand16, rdrand32 is fine but rdrand16 can never generate all 0s. So my CPU does have this problem!
But it looks like the rdrand16 instruction can produce zeros just fine, it just sets CF=0 erroneously (indicating an error and that the user program should retry).
So keep that in mind when you try to reproduce it too and use some abstraction that could implement retries internally.
No, CF=0 occurences seem to be happen frequently and uniformely distributed like valid results at ~1/65536, not clustered.
Under a minute-long all-core load CF=0 always produces zero, but that's to be expected according to the manual.
Here are some stats:
Rounds (N): 1000000000
Failed (F): 15312
Valid (V): 999984688
N/65536: 15258.789
V/65536: 15258.555
Failed, result was zero: 15312
Failed, result non-zero: 0
Bucket value for 0: 15312
Bucket value for 1: 15290
Bucket value for 65535: 15223
Min bucket value: 14670
Max bucket value: 15835
I used this C program to collect them:
#include <stdio.h>
#include <stdint.h>
#include <stdbool.h>
const size_t N = 1000000000; // 1e9
struct rdrand16_result {
uint16_t n;
bool ok;
};
static inline struct rdrand16_result rdrand16()
{
struct rdrand16_result result;
__asm__ __volatile__( "rdrand %0" : "=r" (result.n), "=@ccc" (result.ok) );
return result;
}
int main()
{
size_t buckets[0xFFFF + 1] = { 0 };
size_t notok = 0, notok_zero = 0, notok_nonz = 0;
for (size_t i = 0; i < N; ++i) {
struct rdrand16_result result = rdrand16();
++buckets[result.n];
if (! result.ok) {
++notok;
notok_zero += result.n == 0;
notok_nonz += result.n != 0;
}
}
size_t max = 0, min = N;
for (size_t i = 0; i <= 0xFFFF; ++i) {
size_t n = buckets[i];
min = n < min ? n : min;
max = n > max ? n : max;
}
printf("Rounds (N): %zu\n", N);
printf("Failed (F): %zu\n", notok);
printf("Valid (V): %zu\n", N - notok);
printf("N/65536: %.3f\n", (double)N / 65536);
printf("V/65536: %.3f\n", (double)(N - notok) / 65536);
printf("Failed, result was zero: %zu\n", notok_zero);
printf("Failed, result non-zero: %zu\n", notok_nonz);
printf("Bucket value for 0: %zu\n", buckets[0]);
printf("Bucket value for 1: %zu\n", buckets[1]);
printf("Bucket value for 65535: %zu\n", buckets[0xFFFF]);
printf("Min bucket value: %zu\n", min);
printf("Max bucket value: %zu\n", max);
return 0;
}
If I remember correctly, we had a setting in every Linux server we owned to remove CPU as a RNG seeder for the kernel because of those bugs with AMD CPUs.
I.e., we had `random.trust_cpu=off nordrand` in `GRUB_CMDLINE_LINUX`.
As far as I know that is correct; the kernel was written in a way such that one bad source doesn’t poison the pool. Still, if you know one source is bad, might as well take it out.
Yes it does. rdrand32()%65535 was my first attempt, and generated zeroes at about the expected rate, that's why I initially erroneously thought my CPU did not have this problem.
Really interesting and surprising article. As a workaround, if you're skeptical about an RNG you can implement an algorithm using AES-CTR and putting some entropy in by hand, like mashing on the keyboard a lot. (Like, a lot though.) You can then keep encrypting it, returning some of the ciphertext as the "random" values and rekeying with the rest. The Linux kernel does something similar in random.c, using ChaCha20, though it mixes in some more entropy from time to time.
In theory an encryption algorithm could be biased or not totally uniform in its output, but I think no one has come up with a statistical distinguisher between AES-CTR and pure random values so it should be as good as random.
Obviously you'll want to append the secret part to a keyused.txt file every few hours as once an rng has been running for a few months it's tedious to wait for it to catch up, this way you only have to wait a few hours after any sort of power loss etc.
This is why I use, in security critical contents of my software (where the numbers have to be computationally infeasible to produce), a type of random number generator called an XOF (extendable-output function).
It takes entropy from multiple different sources, makes it all input to the XOF, then the XOF uses cryptography to output a stream that has as much entropy as the combined entropy of all of its sources of randomness. So if an XOF, for example, takes 100 runs of rdrand16, along with the system time in microseconds and the number of milliseconds between receiving 100 packets over the network, the XOF will output a completely random stream without artifacts like never returning 0x0000, even if rdrand16 never outputs 0x0000.
Yes, /dev/(u)random is supposed to do that, but what if there’s a bug in a kernel (e.g. some embedded system which may not even be running Linux) which causes /dev/(u)ramdom to be less than secure? There’s also issues where, for example, it may no longer be possible to read /dev/(u)random after putting the process in a chroot() sandbox (chroot() isn’t defined in POSIX so its behavior is not guaranteed to be consistent across multiple operating systems).
getrandom() is often times suggested, but alas isn’t a standardized function, i.e. it’s not part of the POSIX specification. Considering how the C23 changes to the C specification caused a lot of perfectly good C code to no longer compile, I’m very anal about sticking to specs; I use '-std=C99' for my code these days (even though it can compile as C23 code) and stick to POSIX functions (except chroot() and setgroups(), but both of those predate POSIX, and even here I have a compile-time option to compile my code without those non-POSIX syscalls).
The code using a secure XOF (the algorithm was developed by the same team which later on made SHA-3, and includes people who helped make AES) has been around for nearly two decades (the code where I roll my own RNG to make secure random numbers has been around for over 25 years, but used AES before XOFs existed) and not one security problem has found with the RNG code has ever been found. [1] “Don’t roll your own RNG” is a suggestion, but it is possible to do so securely if one knows what they are doing (i.e. they have read Applied Cryptography and keep current with cryptographic developments).
For anything vibe coded (my code is 100% human written, for the record), rolling one’s own RNG is a really bad idea.
[1] There was a theoretical issue with cache timing attacks over two decades ago, so I put mitigations in place, and then chose to use an XOF for newer code.
[2] There was an issue where a separate implementation I made of this XOF would generate incorrect test vectors in clang, but only at some optimization levels. I now test the XOF in both GCC and clang at multiple optimization levels to make sure it acts correctly.
Black-and-white thinking like this is always inaccurate.
>untested
The automated tests includes tests that make sure the XOF is correctly implemented. [1]
>unlooked at
People have been looking at my code for security holes for well over 20 years, and I have been getting multiple AI assisted security reports over the last year, things like “there’s a buffer overflow in this code which is nay to impossible to exploit, using code which hasn’t even been able to compile since 2022”.
XOF correctly implemented doesn’t ensure you haven’t made other mistakes, such as using entropy sources correctly, doing needed math correctly to avoid any entropy bias, etc. etc….
You’re correct about black and white thinking. Then you invoke multiple straw men in this thread to defend that you’ll roll your own.
Disclaimer: I’ve been hired for multiple DoD projects to break hardware and software security systems, and I nearly always succeed, because so many people (and companies) roll their own.
The nice thing about a secure XOF is that it doesn’t matter if the entropy given to the XOF is less than perfect. If an XOF is given 10 different sources of entropy, and only one of them is secure, the XOF will remain secure. [1]
One reason why I don’t change the RNGs used in my code is because I know how dangerous playing with RNG code is. For example, one implemention I wrote of the XOF—not one I used in production code, mind you—generated incorrect vectors, but only in clang and only at some levels of optimization. Needless to say, I now have a test to make sure my XOF code generates correct vectors with both GCC and clang at multiple different optimization levels.
People have brought up CVE-2008-0166 in this thread, but the Coldcard incident from this year (where people literally lost millions of dollars) also comes to mind, so I’m aware how dangerous playing with RNG code is.
That’s why the code is basically the same code I had 18 years ago, and why I (as well as multiple people running AI-assisted security audits) have extensively tested that code.
The proof is in the pudding: No security issues have ever been found with the XOF PRNG, and it’s been nearly two decades.
(I also think “straw men” is being used incorrectly here; most likely the parent poster thinks I was implying that Linux’s /dev/urandom is insecure but the actual argument is that my code runs on a lot more than just Linux, and some of those systems could have an insecure /dev/urandom)
[1] As per https://blog.cr.yp.to/20140205-entropy.html as long as we’re not using a malicious source of entropy, but said malicious source will need to perform 2^n operations of the XOF to generate n bits of controlled output, and only in the case if said malicious entropy source can somehow know the output of the other entropy sources, especially since the XOF is seeded once then run indefinitely in my code.
No you see what we do, Is we ask Claude to make no mistakes in implementing the CSPRNG. This way we ensure there are no mistakes in the implementation or mathematics.
I know it’s a joke, but that code wouldn’t pass the DieHard tests. That’s actually one of the tests I did with the XOF I used, a test I ran over 16 years ago.
> getrandom() is often times suggested, but alas isn’t a standardized function
The POSIX standard function is getentropy(), which internally calls getrandom() on Linux.
> what if there’s a bug in the kernel which causes /dev/(u)ramdom to be less than secure?
It's often the other way around: the Linux kernel contains thousands of workarounds for buggy hardware, while the buggy hardware itself doesn't always get patched. Linux developers take this stuff very seriously. As a result it's often safer to rely on kernel APIs than to access the hardware directly.
The kernel code involving random number generation receives an exceptionally high amount of scrutiny because of its security implications, so I'd trust it to do the right thing over a naked call to RDRAND which nobody knows how exactly it's implemented in proprietary hardware or a handrolled solution to mix the RDRAND output with other entropy sources.
Remember the Debian openssl disaster from 2008? That happened exactly because someone had handrolled their entropy mixing solution, then someone else broke it.
“The intended use of this function is to create a seed for other pseudo-random number generators”
So, if I were to use genentropy() in a POSIX-compliant way, I would need to do what I already do: Use my own pseudo-random number generator.
The Debian openssl disaster (CVE 2008-0166, I remember it well) was caused because someone incorrectly patched secure code: Since the code used uninitialized memory as one of many entropy sources, which causes Valgrind to complain, they patched the code to not use uninitialized memory for entropy, but then accidentally disabled all other sources of entropy (except the 16-bit PID). It was caused because the person making the patch didn’t fully understand why it was a good idea to, in that context, use code which Valgrind complained about. [1]
As an aside, here’s how I deal with those Valgrind errors:
#ifdef VALGRIND_NOERRORS
/* Valgrind reports our intentional use of values of uncleared
* allocated memory as one source of entropy as an error, so we
* allow it to be disabled for Valgrind testing */
memset(noise,0,512);
#endif /* VALGRIND_NOERRORS */
I do believe the Linux Kernel does have secure RNG code, but I also write code which has run on a lot of different systems and environments, including embedded ones, and some of them might not have a secure /dev/urandom.
[1] Debian has a lot of inflexible policies like this which can cause problems. Another issue Debian has is they have a policy a given piece of code must always compile to the same binary on a given architecture. That isn’t true with the unpatched version of my code, because the hash compression routine uses a 32-bit random number generated at compile time to avoid hash collision attacks (it also uses another 32-bit random number at runtime, and I make sure the hash compression values are never visible). So the Debian version of my code was forced to be patched to be less secure.
i remember some linux kernel dev got ousted by the community because he/she wanted to not implement a backdoor that would compromise the results of /dev/urandom.
I have no idea about the claim of a backdoor. But here is the source:
Matt Mackall:
"It's worth noting that the maintainer of record (me) for the Linux RNG quit the project about two years ago precisely because Linus decided to include a patch from Intel to allow their unauditable RdRand to bypass the entropy pool over my strenuous objections. "
Yes, on any modern system you should use the kernel provided random number sources.
The only legitimate reason to roll your own is when you're developing for an embedded system or a bootloader or something like that where there is no kernel API available.
The code I wrote has been used by embedded developers in embedded spaces; I remember getting a bug report from someone in China because they used my code in an embedded system before the timestamp was correctly set on said system.
You can effectively achieve the same result with this simple operation:
hash = sha256(current_time());
for i := 0; i < n; i++ {
hash = sha256(hash.append(current_time()))
}
This is because the number of nanoseconds between hashes is actually itself variable, and this is true for physics reasons that are basically beyond the control of any attacker trying to manipulate your entropy. If your time() function has a resolution of nanoseconds, you only need your loop to iterate about 50 times to get a cryptographically secure amount of entropy. If your time() function has a resolution of milliseconds, you need to let this run for more like 20 milliseconds, and if your time() function has a resolution of seconds you need to let it run for more like 5 seconds.
The reason I like doing it this way is that it happens entirely in userspace, it's genuinely a secure method of generating entropy, and it has no dependencies on potentially buggy firmware or microcode outside of the time() call, which is both fairly narrow, fairly heavily used (meaning a bug is likely to be discovered during testing, as the implementation is likely heavily scrutinized), and also fairly easy to test independently - just look at the number of nanoseconds that elapse at each consecutive call to sha256(current_time()) and verify that there's some statistical variance. The above suggestions are assuming about 2.5 bits of variance between calls, meaning there should be a range of at least 20 nanoseconds between your slowest and fastest hash call. This has been true on every CPU I've ever measured, including microcontrollers.
I wouldn’t trust it as a sole source of entropy, but it can be one of multiple entropy sources to feed in to an XOF to get secure numbers.
The nice thing about using multiple entropy sources with a secure XOF is that the resulting entropy is at least as strong as the most secure entropy source given to the XOF.
TL;DR adding a compromised source of entropy to a pool of already secure sources of entropy can catastrophically compromise the final result.
It's better to source entropy from a smaller number of harder-to-compromise sources.
That's why I like the iterated hashes method; the security surface area is both very small and highly likely to be well tested.
>>>what I'm advocating here, for security reasons, is a sharp transition between
* before crypto: the whole system collecting enough entropy;
* after: the system using purely deterministic cryptography, never adding any more entropy.<<<
Which is exactly how a XOF should be used, and how I used the XOF in my code. A malicious source of entropy will need to perform 2^n operations to control n bits of the XOF’s output, and that’s assuming the malicious entropy source somehow perfectly knows the other entropy the XOF is using.
Yes but why introduce complexity and room for error when something that's extremely basic is also sufficient?
The point here is to eliminate surface area for mistakes, and an XOF has a much larger and more complex implementation than iterated hashing against a timer.
This comment demonstrates everything that's wrong with people trying to be clever and rolling their own crypto.
The security of your system depends on time() providing enough entropy, even though that's not what it's designed to do. It's built on top of the wrong primitive from the start.
> The reason I like doing it this way is that it happens entirely in userspace
On Linux this is often true, but there is no portable way to get the current time that is _guaranteed_ not to do any system calls.
> If your time() function has a resolution of nanoseconds, you only need your loop to iterate about 50 times to get a cryptographically secure amount of entropy.
You haven't proven that at all. It's easy to imagine that on a CPU running at a fixed frequency the interval between reads is constant, so if anyone knows (or can guess) the start time the resulting seed is entirely predictable.
This is completely independent of timer resolution. You seem to realize that as you were writing that:
> just look at the number of nanoseconds that elapse at each consecutive call to sha256(current_time()) and verify that there's some statistical variance
Oh yes, because evaluating the quality of a random number generator is such a trivial thing to do, it's not like there is decades of research behind it or anything.
And assuming you are able to verify the statistical variance: are you going to put that logic in the loop, making it significantly more complex?
Or are you going to do this test on your machine and then ship your code on the assumption that if it works on your machine, it will work everywhere else, too?
> if your time() function has a resolution of seconds you need to let it run for more like 5 seconds.
So not only is it insecure, it's agonizingly slow by design. Why do a system call that takes milliseconds at best, when we can run a loop in userspace for 5 seconds?
All this just so you can avoid writing the obviously correct oneliner:
if (getentropy(&seed, sizeof(seed)) != 0) abort();
Depends in what trust do you have over your hardware/OS. If you assume the hardware is potentially backdoored, and the OS is proprietary, or even if open could have malware/rootkits that can thinker around the random number generator, the solution of using a sole implementation inside the program (assuming the sha256 function is inside the program itself) maybe better.
Sure an infected system may as well fake time values, but that is much more difficult and it's possible to detect from a userspace program. For example you mention to use getentroy, but on a compromised system you know how easy it is to change something that is implemented in a system library (e.g. libc) or even if you read /dev/random directly without passing from the libc how easy it's to make it read whatever you want?
To me that is not that bad implementation, in fact it's an implementation that is used in a lot of security software (including GPG, not as the sole source of course but as one of many).
If you cannot trust the platform you're running on, all bets are off. There is a reason so much effort is put in TPM and remote attestation and so on.
A compromised kernel doesn't even have to fake any data. It can just read the generated seed directly from user space without the program ever knowing about it.
> Sure an infected system may as well fake time values, but that is much more difficult
clock_gettime() just reads a value that the kernel has set, so that's not particularly difficult to fake.
If you're thinking of using RDTSC instructions directly, that's of course not portable, and at that point you might as well call RDRAND directly, which is at least designed to provide random data.
> it's possible to detect from a userspace program.
There is no detection that is guaranteed to work on a compromised system.
And whatever detection you have in mind to make the algorithm resistant to tampering was _not_ part of the original for-loop. You cannot claim the for-loop is superior to just calling getentropy() because it "can detect" clock tampering, while handwaving away the actual code to detect this clock tampering.
> it's an implementation that is used in a lot of security software (including GPG, not as the sole source of course but as one of many).
It's fine if you use it as a strictly additional source of entropy, but then the whole argument that it is superior because it avoids syscalls goes out of the window, because you're doing strictly _more_ work.
The strength in this method is that it has the littlest possible surface area for upstream bugs to compromise your final entropy. Because, in the applied world, upstream bugs in "secure" system RNGs have been the cause of stolen crypto and other critical security compromises on numerous occasions.
And, I agree that if the system is compromised to the level that the attacker can control the output of the timer, it's probably compromised to the level that the attacker can just read your generated entropy straight from memory.
The point here is not to be fast, it's to be protected against implementation bugs on systems that weren't designed by security professionals.
The reason I roll entropy in userspace is because there's a very long history of "cryptographic" libraries getting it wrong (see the parent article for an example). Crypto tokens stolen because the underlying call to the web browser entropy only had 32 bits of actual randomness. Crypto tokens stolen because the underlying embedded system (like cold card) turned off some security critical features to improve performance and power.
Pretty much the only thing you can control when shipping software to many devices is that it runs on a physical CPU and has a timer. Every other RNG assumption over the decades has shown that sometimes someone upstream gets something catastrophically incorrect.
Any good crypto library will have a solid secure random source that usually combines entropy from multiple sources with a provably secure hash based mixing scheme.
Hardware RNGs can be one source, but no single source is trusted, and they're all combined in a way where even an intentionally malicious source is lost in noise and cannot actually determine output.
That's exactly the challenge though: "any good crypto library" - there is a long history of meaningful security breached (like stolen crypto tokens) due to bugs in an upstream library, especially when using things like embedded code, alternative operating systems, newer programming languages, etc.
The value of the iterated hashing method is that it is dead simple and has little dependency on potentially buggy upstream code; it works even in very lightweight environments designed by engineers with no experience in security.
Yeah, this comes off as a “they already are on the wrong side of the secure hatch” kind of attack. A malicious hardware device with physical access to a victim’s computer can do a lot more than generate malicious entropy.
It’s like the attacks I occasionally see which are like “once we have administrator, we can attack the process because of this insecurity”. Well, yeah, but once we have administrator, we can read the entire memory of the “vulnerable” process and completely control its output too.
I’ve seen in the real world attacks where things were insecure because the PRNG wasn’t given enough entropy (CVE 2008-0166, Coldcard, etc.). I’ve never seen real world attacks where a PRNG was insecure from getting too much entropy.
Hold on I have to go edit the rest of my responses because I just assumed you wrote the code correctly; you did not.
You are not hashing between calls to the timer. The sha256 hash itself is responsible for doing physical things to the chip (heating up some parts unevenly during the hashing computation) which introduces meaningful entropy between calls to the current time.
You can't just do calls to clock_gettime(), you have do an actual sequential sha256() call between them. Please run this code again and tell me what results you get.
You don't need 256 bits of entropy, you only need 128.
I have tested this method on over 100 different CPUs and I have never seen such consistent output. I'm genuinely surprised to see that you only hit 92 bits of entropy, but that can trivially be fixed by doing 10x the iterations. 500 iterations is still going to put you under a millisecond of cost.
And, for what it's worth, code I've actually shipped has combined the above technique with Fortuna, and has typically targeted 2000 bits of entropy rather than 128 (for security buffer).
EDIT: I reviewed his code, and he's not hashing between calls to check the clock; the hash call itself causes the CPU to heat up in arbitrary ways which changes the timing between hashes and introduces more entropy; removing that call basically entirely defeats the idea behind the technique, these results are fully invalid.
The point is this: Getting micro-timing won’t give us as much entropy as we want, but it will still give us entropy. So it’s a perfectly good yet-another-source of entropy to feed in to an entropy pool (such as the input to a XOF).
If those Coldcard devices had used this code as one source of entropy, and this source of entropy was the only entropy still working, they never would had been compromised.
(I won’t update my 18-year-old PRNG to use this code, of course, since that code is now 18 years old and there are no known weaknesses in said code)
Actually, it gives you as much entropy as you need, just increase the iterations. That guy's output is shockingly consistent, so to be conservative maybe we say 0.2 bits of entropy per iteration. So just do 1000 iterations. That's still only going to take a few milliseconds even on embedded hardware.
EDIT: I reviewed his code, and he's not hashing between calls to check the clock; the hash call itself causes the CPU to heat up in arbitrary ways which changes the timing between hashes and introduces more entropy; removing that call basically entirely defeats the idea behind the technique, these results are fully invalid.
Nifty! Out of curiosity, how much different is that from taking several partly-random streams and XORing them together? I always assumed what was going on was essentially a fancier version of that.
Oh, I guess you have to ensure the inputs aren’t correlated, or they’ll cancel out?
The advantage of a secure XOF is that a malicious source of entropy needs to do a good deal more work than a simple XOR to generate controlled PRNG output (the attacker needs to do 2^n XOF operations to generate n bits of PRNG output).
The sources of entropy can be correlated and won’t cancel out with a well designed secure XOF. SHAKE-256 is an example of a secure XOF.
Yikes at this: "I am so glad I resisted pressure from engineers working at Intel to let /dev/random in Linux rely blindly on the output of the RDRAND instructure." -Theodore Ts'o (2013)
According to Theodore Ts there was pressure from Intel engineers to let /dev/random rely only on the RDRAND instruction.
"
I am so glad I resisted pressure from Intel engineers to let /dev/random rely only on the RDRAND instruction. To quote from the article below:
"By this year, the Sigint Enabling Project had found ways inside some of the encryption chips that scramble information for businesses and governments, either by working with chipmakers to insert back doors...."
Relying solely on the hardware random number generator which is using an implementation sealed inside a chip which is impossible to audit is a BAD idea.
"
Putting a backdoor into CSPRNG is a favored way to break crypto, for example Dual_EC_DRBG.
"
Weaknesses in the cryptographic security of the algorithm were known and publicly criticised well before the algorithm became part of a formal standard endorsed by the ANSI, ISO, and formerly by the National Institute of Standards and Technology (NIST). One of the weaknesses publicly identified was the potential of the algorithm to harbour a cryptographic backdoor advantageous to those who know about it—the United States government's National Security Agency (NSA)—and no one else. In 2013, The New York Times reported that documents in their possession but never released to the public "appear to confirm" that the backdoor was real, and had been deliberately inserted by the NSA as part of its Bullrun decryption program. In December 2013, a Reuters news article alleged that in 2004, before NIST standardized Dual_EC_DRBG, NSA paid RSA Security $10 million in a secret deal to use Dual_EC_DRBG as the default in the RSA BSAFE cryptography library, which resulted in RSA Security becoming the most important distributor of the insecure algorithm. RSA responded that they "categorically deny" that they had ever knowingly colluded with the NSA to adopt an algorithm that was known to be flawed, but also stated, "We have never kept this relationship [with the NSA] a secret and in fact have openly publicized it."
I'm getting 16-bit zeros on my Zen 3 chip (+1:3821, 0:3893, -1:3895), I will wait to get some statistically significant samples for the 32-bit values and update the forum thread. Maybe it was fixed after Zen 2?
Does anyone have access to an HPC cluster with thousands of Zen2 chips? We might want to check 64-bit ones with that - should take just a couple years depending on the size of the machine.
Anyone from the High-Performance Computing Center Stuttgart willing to play on the 720,320 Zen2 cores?
I always wonder how hardware bugs like this happen with the sheer amount of hardware validation that's done. It'd be fascinating to know how it slipped through the cracks, though I know almost nothing about this side of the industry sadly
Validation can't be better than the quality of the specification. Humans don't create comprehensive, unambiguous specifications for the same reasons that we don't write bug-free code, and need formal validation.
Brooks talks about this in _Mythical_Man-Month_... if you really could "just implement the specification", then the specification itself would be complete enough to serve as your code. There will always be bugs in both.
That "sheer amount of hardware validation" is always less-than-perfectly spread across a whole lotta billions of transistors, and combinatorics is a harsh mistress.
Looks like they tried 16-bit numbers. Does the odd behavior happen also on 32 and 64 (might take a long time to check - I'd start scratching my head after a couple hundred years of no zeroes) ones? Is the zero masking as some other fixed number, increasing its output count? Is RDRAND implemented as multiple reads of an internal state so that a larger random number takes longer?
So what? The point is to be non predictable not to pick all the numbers in the range with exactly the same probability. Would it be a problem if it never generated 16542?
By your argument, it would not be a problem if the RNG never generated 0. So, it must follow that it would also not be a problem if it never generated {1, 2, 3, ..., 253}.
That means that our RNG now only generates the values 254 and 255. Which of the values is generated is unpredictable on any given call. However, 7 of the 8 output bits are now always fixed and so completely predictable. Can you imagine how an attacker could exploit that?
Failing to generate only the number 0 is a weaker version of the same class of flaw.
We're talking about whether a modification of the expected probabilities changes the dynamics of the game. The example I gave was deliberately extreme, because that makes it easier to reason about.
If you want a casino example, then consider a roulette wheel that always lands on 36 but still pays out as usual. I think you'd want to play on it. Now consider one that always lands somewhere between 30 and 36. Still worth it, right? With careful bets and a good starting float you're still coming away from the table up (with a very high probability).
In fact for a roulette wheel you only need two dead pockets for the player to get an edge. Bias is exploitable.
Sure, but you’re pressing on the truth that a small modification taken to an extreme is a large modification.
When the original point was that a tiny fractional loss in an RNG is not going to make a practical difference. Which I believe is also true. And it is also true that a large loss in an RNG is catastrophic.
They can both be true.
And roulette is 2 out of 38, 5.2%. That’s 17 times more than the 1/256 here, which was already a simplification of the (I think) 1/65536 in question.
It is absolutely untrue that a biased RNG has "zero practical impact." Modern cryptography has plenty of examples of relatively small biases leading to breaks. Check out Bleichenbacher's attack, for instance.
You could be correct that the very small bias here is not enough to be exploitable. But, given the history around this, it would be wrong to handwave it away as trivial.
“Pick all the numbers in the range with exactly the same probability” is a very important property of RNGs. Yes, skipping 16542 would be equally bad.
You can frame it around being “non predictable”, but then you need to define those words. It’s not, for example, a poker game where it’s trying to bluff you, right? It’s also not about just making predictions < 100% reliable and declaring victory. It must specifically make all predictions no better than random guessing, and that entails picking any number in range with equal probability, otherwise predictions like “it will be {hot spot}” or “it won’t be {cold spot}” do better than random chance. In this case, specifically, I can predict with 100% accuracy that the result won’t be 0, and that’s a flaw in its unpredictability. I can also predict a bunch of other things with slightly higher accuracy than random guessing, like that it will be odd or greater than max ÷ 2.
It's not a 2^16-sided weighted die. But a 2^16 - 1 sided fair die.
I am not saying there is no bug. I am saying the bug has no practical impact.
Sure if you are that one guy that is getting these values raw from the instruction and comparing to zero for some purpose then you are in trouble. But I am pretty sure no one is doing that, especially given that the bug surfaced after 6 years of millions of users.
Usually you do "rdrand % <some-number>" anyways, and in that case you will still get zeroes. True, your result might be skewed by 1/(maxint/some-number) but I guess that's not a big problem in practice
If you want uniformly-distributed random numbers, computing the remainder works only when the modulus is a power of two.
Otherwise, a slightly more complicated algorithm is necessary, where you reject a range of numbers either before computing the remainder (to make the set of possible values a multiple of the modulus) or after computing the value modulo some power of two (to reject values greater than your target).
Besides these 2 variants based on the remainder of division of integers, there are also 2 corresponding algorithms using multiplication of the input interpreted as a fraction, followed by taking the integer part of the result.
Because each number is equally as likely as every other number. If you know you're more likely to get certain numbers, or in this case have no chance of getting certain other numbers, it is by definition _less random_.
So you think a weighted die is more random than a fair die? A uniform distribution means each outcome has equal probability; it doesn’t mean the outcome is predictable.
It is just possible they decided crypto code that uses it was safer to skip zeros. (Whist mathematically it should be no more likely; it is vastly more likely someone will actually try that key).
It is also possible that their code was generating too many zeros and the easiest fix was to discard them all.
Can you clarify what you mean by "it is vastly more likely someone will actually try that key"?
I'm guessing you don't think there are people calling rdrand in a loop and throwing away the output with high probability except when it is 0, but I can't see how else you imagine people would be vastly more likely to use the output when it is 0?
In lots of scenarios I know the software used to generate the key; the only unknown is the random numbers used. If I am searching for weaknesses it is highly likely I would try keys with different seeds; zero, one, are going to me much more likely choices here then hoping I can guess the right values.
If someone was using RDRAND16 to seed a PRNG, choosing to omit one single value (a zero) from the return value would not significantly improve the generated values, if at all.
This is not the first RNG bug on Zen 2, I recall after I first got mine that some application or other would quit immediately at startup because rdrand always returned -1, i.e. all 1s. It was fixed with a microcode update.
Do we now learn that they fixed "always generate all 1s" with "never generate all 0s"??
EDIT: I've been unable to reproduce the problem on my CPU, FWIW. It's a Ryzen 5 3600.
EDIT2: OK, update, I can reproduce it with rdrand16, rdrand32 is fine but rdrand16 can never generate all 0s. So my CPU does have this problem!
I can reproduce it too with rdrand16 on Zen2.
But it looks like the rdrand16 instruction can produce zeros just fine, it just sets CF=0 erroneously (indicating an error and that the user program should retry).
So keep that in mind when you try to reproduce it too and use some abstraction that could implement retries internally.
Good observation, that seems like the most likely explanation. Do you ever see "true" CF=0 (with nonzero arg) or did they just take the lazy approach?
No, CF=0 occurences seem to be happen frequently and uniformely distributed like valid results at ~1/65536, not clustered. Under a minute-long all-core load CF=0 always produces zero, but that's to be expected according to the manual.
Here are some stats:
I used this C program to collect them:I always think of https://www.reddit.com/r/ProgrammerHumor/comments/5yhl93/ran...
https://xkcd.com/221/ for those not in the know
And for the full fail story behind it, fail0verflow hacking the PS3 presentation is great and covers the bug: https://youtu.be/DUGGJpn2_zY
Most of the console hacking talks are great, both informative and entertaining.
This comic predates that presentation, in fact they use it in their slide deck at 39:00 in your linked video.
That presentation is awesome though, worth a watch either way!
https://i.imgur.com/bwFWMqQ.png
CVE-2008-0166 (Debian OpenSSL Predictable PRNG Vulnerability) inspired xkcd/221 but this sort of thing happens a lot :)
Zen 4 reporting in. I'm unable to reproduce it (7840U).
I used the GCC intrinsic ( _rdrand16_step ),If I remember correctly, we had a setting in every Linux server we owned to remove CPU as a RNG seeder for the kernel because of those bugs with AMD CPUs.
I.e., we had `random.trust_cpu=off nordrand` in `GRUB_CMDLINE_LINUX`.
Adding bad randomness can't degrade good randomness, can it?
I thought the kernel would not replace anything just because it adds a potentially bad source.
E.g. if you have rand source A, and xor it with rand source B, then you get, at worst, the best of A and B,
As far as I know that is correct; the kernel was written in a way such that one bad source doesn’t poison the pool. Still, if you know one source is bad, might as well take it out.
Does rdrand32 and then taking the lowest 16 bits of its result yield any zeroes?
Basically I'm wondering if it's a bug in the version of the instruction that writes to a 16-bit reg, or a bug in the underlying RNG
Yes it does. rdrand32()%65535 was my first attempt, and generated zeroes at about the expected rate, that's why I initially erroneously thought my CPU did not have this problem.
You should be using &0xFFFF for masking. Your mod is off by 1 too.
You're right, the code was correct but my comment above is wrong.
How about* rdrand32()%65536? Taking the remainder by 65535 doesn't take the lowest 16 bits after all
*: missed a word the first time around
You probably recall https://news.ycombinator.com/item?id=19848953 .
Even if you reproduce the issue, it is not a proof it can't generate a zero - just that it's very unlikely.
To prove it, we'd need to examine the chip and its microcode.
Really interesting and surprising article. As a workaround, if you're skeptical about an RNG you can implement an algorithm using AES-CTR and putting some entropy in by hand, like mashing on the keyboard a lot. (Like, a lot though.) You can then keep encrypting it, returning some of the ciphertext as the "random" values and rekeying with the rest. The Linux kernel does something similar in random.c, using ChaCha20, though it mixes in some more entropy from time to time.
In theory an encryption algorithm could be biased or not totally uniform in its output, but I think no one has come up with a statistical distinguisher between AES-CTR and pure random values so it should be as good as random.
Obviously you'll want to append the secret part to a keyused.txt file every few hours as once an rng has been running for a few months it's tedious to wait for it to catch up, this way you only have to wait a few hours after any sort of power loss etc.
This is why I use, in security critical contents of my software (where the numbers have to be computationally infeasible to produce), a type of random number generator called an XOF (extendable-output function).
It takes entropy from multiple different sources, makes it all input to the XOF, then the XOF uses cryptography to output a stream that has as much entropy as the combined entropy of all of its sources of randomness. So if an XOF, for example, takes 100 runs of rdrand16, along with the system time in microseconds and the number of milliseconds between receiving 100 packets over the network, the XOF will output a completely random stream without artifacts like never returning 0x0000, even if rdrand16 never outputs 0x0000.
Isn’t this effectively what systems like /dev/(u)rand do? Pool multiple random sources together to hedge against these things?
I fail to see why one should either rely on a single random source nor roll their own.
Yes, /dev/(u)random is supposed to do that, but what if there’s a bug in a kernel (e.g. some embedded system which may not even be running Linux) which causes /dev/(u)ramdom to be less than secure? There’s also issues where, for example, it may no longer be possible to read /dev/(u)random after putting the process in a chroot() sandbox (chroot() isn’t defined in POSIX so its behavior is not guaranteed to be consistent across multiple operating systems).
getrandom() is often times suggested, but alas isn’t a standardized function, i.e. it’s not part of the POSIX specification. Considering how the C23 changes to the C specification caused a lot of perfectly good C code to no longer compile, I’m very anal about sticking to specs; I use '-std=C99' for my code these days (even though it can compile as C23 code) and stick to POSIX functions (except chroot() and setgroups(), but both of those predate POSIX, and even here I have a compile-time option to compile my code without those non-POSIX syscalls).
The code using a secure XOF (the algorithm was developed by the same team which later on made SHA-3, and includes people who helped make AES) has been around for nearly two decades (the code where I roll my own RNG to make secure random numbers has been around for over 25 years, but used AES before XOFs existed) and not one security problem has found with the RNG code has ever been found. [1] “Don’t roll your own RNG” is a suggestion, but it is possible to do so securely if one knows what they are doing (i.e. they have read Applied Cryptography and keep current with cryptographic developments).
For anything vibe coded (my code is 100% human written, for the record), rolling one’s own RNG is a really bad idea.
[1] There was a theoretical issue with cache timing attacks over two decades ago, so I put mitigations in place, and then chose to use an XOF for newer code.
[2] There was an issue where a separate implementation I made of this XOF would generate incorrect test vectors in clang, but only at some optimization levels. I now test the XOF in both GCC and clang at multiple optimization levels to make sure it acts correctly.
> but what if there’s a bug in the kernel which causes /dev/(u)ramdom to be less than secure?
so instead you suggest trusting your own untested unlooked at implementation more?
Black-and-white thinking like this is always inaccurate.
>untested
The automated tests includes tests that make sure the XOF is correctly implemented. [1]
>unlooked at
People have been looking at my code for security holes for well over 20 years, and I have been getting multiple AI assisted security reports over the last year, things like “there’s a buffer overflow in this code which is nay to impossible to exploit, using code which hasn’t even been able to compile since 2022”.
[1] https://github.com/samboy/MaraDNS/tree/master/deadwood-githu... and https://github.com/samboy/MaraDNS/tree/master/deadwood-githu...
XOF correctly implemented doesn’t ensure you haven’t made other mistakes, such as using entropy sources correctly, doing needed math correctly to avoid any entropy bias, etc. etc….
You’re correct about black and white thinking. Then you invoke multiple straw men in this thread to defend that you’ll roll your own.
Disclaimer: I’ve been hired for multiple DoD projects to break hardware and software security systems, and I nearly always succeed, because so many people (and companies) roll their own.
The nice thing about a secure XOF is that it doesn’t matter if the entropy given to the XOF is less than perfect. If an XOF is given 10 different sources of entropy, and only one of them is secure, the XOF will remain secure. [1]
One reason why I don’t change the RNGs used in my code is because I know how dangerous playing with RNG code is. For example, one implemention I wrote of the XOF—not one I used in production code, mind you—generated incorrect vectors, but only in clang and only at some levels of optimization. Needless to say, I now have a test to make sure my XOF code generates correct vectors with both GCC and clang at multiple different optimization levels.
People have brought up CVE-2008-0166 in this thread, but the Coldcard incident from this year (where people literally lost millions of dollars) also comes to mind, so I’m aware how dangerous playing with RNG code is.
That’s why the code is basically the same code I had 18 years ago, and why I (as well as multiple people running AI-assisted security audits) have extensively tested that code.
The proof is in the pudding: No security issues have ever been found with the XOF PRNG, and it’s been nearly two decades.
(I also think “straw men” is being used incorrectly here; most likely the parent poster thinks I was implying that Linux’s /dev/urandom is insecure but the actual argument is that my code runs on a lot more than just Linux, and some of those systems could have an insecure /dev/urandom)
[1] As per https://blog.cr.yp.to/20140205-entropy.html as long as we’re not using a malicious source of entropy, but said malicious source will need to perform 2^n operations of the XOF to generate n bits of controlled output, and only in the case if said malicious entropy source can somehow know the output of the other entropy sources, especially since the XOF is seeded once then run indefinitely in my code.
No you see what we do, Is we ask Claude to make no mistakes in implementing the CSPRNG. This way we ensure there are no mistakes in the implementation or mathematics.
https://xkcd.com/221/
I know it’s a joke, but that code wouldn’t pass the DieHard tests. That’s actually one of the tests I did with the XOF I used, a test I ran over 16 years ago.
https://maradns.blogspot.com/2010/07/radiogatun32-passes-all...
> getrandom() is often times suggested, but alas isn’t a standardized function
The POSIX standard function is getentropy(), which internally calls getrandom() on Linux.
> what if there’s a bug in the kernel which causes /dev/(u)ramdom to be less than secure?
It's often the other way around: the Linux kernel contains thousands of workarounds for buggy hardware, while the buggy hardware itself doesn't always get patched. Linux developers take this stuff very seriously. As a result it's often safer to rely on kernel APIs than to access the hardware directly.
The kernel code involving random number generation receives an exceptionally high amount of scrutiny because of its security implications, so I'd trust it to do the right thing over a naked call to RDRAND which nobody knows how exactly it's implemented in proprietary hardware or a handrolled solution to mix the RDRAND output with other entropy sources.
Remember the Debian openssl disaster from 2008? That happened exactly because someone had handrolled their entropy mixing solution, then someone else broke it.
From https://pubs.opengroup.org/onlinepubs/9799919799/functions/g...
“The intended use of this function is to create a seed for other pseudo-random number generators”
So, if I were to use genentropy() in a POSIX-compliant way, I would need to do what I already do: Use my own pseudo-random number generator.
The Debian openssl disaster (CVE 2008-0166, I remember it well) was caused because someone incorrectly patched secure code: Since the code used uninitialized memory as one of many entropy sources, which causes Valgrind to complain, they patched the code to not use uninitialized memory for entropy, but then accidentally disabled all other sources of entropy (except the 16-bit PID). It was caused because the person making the patch didn’t fully understand why it was a good idea to, in that context, use code which Valgrind complained about. [1]
As an aside, here’s how I deal with those Valgrind errors:
I do believe the Linux Kernel does have secure RNG code, but I also write code which has run on a lot of different systems and environments, including embedded ones, and some of them might not have a secure /dev/urandom.[1] Debian has a lot of inflexible policies like this which can cause problems. Another issue Debian has is they have a policy a given piece of code must always compile to the same binary on a given architecture. That isn’t true with the unpatched version of my code, because the hash compression routine uses a 32-bit random number generated at compile time to avoid hash collision attacks (it also uses another 32-bit random number at runtime, and I make sure the hash compression values are never visible). So the Debian version of my code was forced to be patched to be less secure.
i remember some linux kernel dev got ousted by the community because he/she wanted to not implement a backdoor that would compromise the results of /dev/urandom.
Who?
I have no idea about the claim of a backdoor. But here is the source:
Matt Mackall: "It's worth noting that the maintainer of record (me) for the Linux RNG quit the project about two years ago precisely because Linus decided to include a patch from Intel to allow their unauditable RdRand to bypass the entropy pool over my strenuous objections. "
https://cryptome.wikileaks.org/2013/07/intel-bed-nsa.htm?utm...
That doesn’t read like a backdoor or like the community pushing somebody out.
Yes, on any modern system you should use the kernel provided random number sources.
The only legitimate reason to roll your own is when you're developing for an embedded system or a bootloader or something like that where there is no kernel API available.
The code I wrote has been used by embedded developers in embedded spaces; I remember getting a bug report from someone in China because they used my code in an embedded system before the timestamp was correctly set on said system.
You can effectively achieve the same result with this simple operation:
This is because the number of nanoseconds between hashes is actually itself variable, and this is true for physics reasons that are basically beyond the control of any attacker trying to manipulate your entropy. If your time() function has a resolution of nanoseconds, you only need your loop to iterate about 50 times to get a cryptographically secure amount of entropy. If your time() function has a resolution of milliseconds, you need to let this run for more like 20 milliseconds, and if your time() function has a resolution of seconds you need to let it run for more like 5 seconds.The reason I like doing it this way is that it happens entirely in userspace, it's genuinely a secure method of generating entropy, and it has no dependencies on potentially buggy firmware or microcode outside of the time() call, which is both fairly narrow, fairly heavily used (meaning a bug is likely to be discovered during testing, as the implementation is likely heavily scrutinized), and also fairly easy to test independently - just look at the number of nanoseconds that elapse at each consecutive call to sha256(current_time()) and verify that there's some statistical variance. The above suggestions are assuming about 2.5 bits of variance between calls, meaning there should be a range of at least 20 nanoseconds between your slowest and fastest hash call. This has been true on every CPU I've ever measured, including microcontrollers.
I wouldn’t trust it as a sole source of entropy, but it can be one of multiple entropy sources to feed in to an XOF to get secure numbers.
The nice thing about using multiple entropy sources with a secure XOF is that the resulting entropy is at least as strong as the most secure entropy source given to the XOF.
Unfortunately you are not correct, and djb explains it quite well here:
https://blog.cr.yp.to/20140205-entropy.html
TL;DR adding a compromised source of entropy to a pool of already secure sources of entropy can catastrophically compromise the final result.
It's better to source entropy from a smaller number of harder-to-compromise sources. That's why I like the iterated hashes method; the security surface area is both very small and highly likely to be well tested.
Indeed, that’s a real attack.
From that page:
>>>what I'm advocating here, for security reasons, is a sharp transition between
* before crypto: the whole system collecting enough entropy;
* after: the system using purely deterministic cryptography, never adding any more entropy.<<<
Which is exactly how a XOF should be used, and how I used the XOF in my code. A malicious source of entropy will need to perform 2^n operations to control n bits of the XOF’s output, and that’s assuming the malicious entropy source somehow perfectly knows the other entropy the XOF is using.
Yes but why introduce complexity and room for error when something that's extremely basic is also sufficient?
The point here is to eliminate surface area for mistakes, and an XOF has a much larger and more complex implementation than iterated hashing against a timer.
This comment demonstrates everything that's wrong with people trying to be clever and rolling their own crypto.
The security of your system depends on time() providing enough entropy, even though that's not what it's designed to do. It's built on top of the wrong primitive from the start.
> The reason I like doing it this way is that it happens entirely in userspace
On Linux this is often true, but there is no portable way to get the current time that is _guaranteed_ not to do any system calls.
> If your time() function has a resolution of nanoseconds, you only need your loop to iterate about 50 times to get a cryptographically secure amount of entropy.
You haven't proven that at all. It's easy to imagine that on a CPU running at a fixed frequency the interval between reads is constant, so if anyone knows (or can guess) the start time the resulting seed is entirely predictable.
This is completely independent of timer resolution. You seem to realize that as you were writing that:
> just look at the number of nanoseconds that elapse at each consecutive call to sha256(current_time()) and verify that there's some statistical variance
Oh yes, because evaluating the quality of a random number generator is such a trivial thing to do, it's not like there is decades of research behind it or anything.
And assuming you are able to verify the statistical variance: are you going to put that logic in the loop, making it significantly more complex?
Or are you going to do this test on your machine and then ship your code on the assumption that if it works on your machine, it will work everywhere else, too?
> if your time() function has a resolution of seconds you need to let it run for more like 5 seconds.
So not only is it insecure, it's agonizingly slow by design. Why do a system call that takes milliseconds at best, when we can run a loop in userspace for 5 seconds?
All this just so you can avoid writing the obviously correct oneliner:
Depends in what trust do you have over your hardware/OS. If you assume the hardware is potentially backdoored, and the OS is proprietary, or even if open could have malware/rootkits that can thinker around the random number generator, the solution of using a sole implementation inside the program (assuming the sha256 function is inside the program itself) maybe better.
Sure an infected system may as well fake time values, but that is much more difficult and it's possible to detect from a userspace program. For example you mention to use getentroy, but on a compromised system you know how easy it is to change something that is implemented in a system library (e.g. libc) or even if you read /dev/random directly without passing from the libc how easy it's to make it read whatever you want?
To me that is not that bad implementation, in fact it's an implementation that is used in a lot of security software (including GPG, not as the sole source of course but as one of many).
If you cannot trust the platform you're running on, all bets are off. There is a reason so much effort is put in TPM and remote attestation and so on.
A compromised kernel doesn't even have to fake any data. It can just read the generated seed directly from user space without the program ever knowing about it.
> Sure an infected system may as well fake time values, but that is much more difficult
clock_gettime() just reads a value that the kernel has set, so that's not particularly difficult to fake.
If you're thinking of using RDTSC instructions directly, that's of course not portable, and at that point you might as well call RDRAND directly, which is at least designed to provide random data.
> it's possible to detect from a userspace program.
There is no detection that is guaranteed to work on a compromised system.
And whatever detection you have in mind to make the algorithm resistant to tampering was _not_ part of the original for-loop. You cannot claim the for-loop is superior to just calling getentropy() because it "can detect" clock tampering, while handwaving away the actual code to detect this clock tampering.
> it's an implementation that is used in a lot of security software (including GPG, not as the sole source of course but as one of many).
It's fine if you use it as a strictly additional source of entropy, but then the whole argument that it is superior because it avoids syscalls goes out of the window, because you're doing strictly _more_ work.
The strength in this method is that it has the littlest possible surface area for upstream bugs to compromise your final entropy. Because, in the applied world, upstream bugs in "secure" system RNGs have been the cause of stolen crypto and other critical security compromises on numerous occasions.
And, I agree that if the system is compromised to the level that the attacker can control the output of the timer, it's probably compromised to the level that the attacker can just read your generated entropy straight from memory.
The point here is not to be fast, it's to be protected against implementation bugs on systems that weren't designed by security professionals.
The reason I roll entropy in userspace is because there's a very long history of "cryptographic" libraries getting it wrong (see the parent article for an example). Crypto tokens stolen because the underlying call to the web browser entropy only had 32 bits of actual randomness. Crypto tokens stolen because the underlying embedded system (like cold card) turned off some security critical features to improve performance and power.
Pretty much the only thing you can control when shipping software to many devices is that it runs on a physical CPU and has a timer. Every other RNG assumption over the decades has shown that sometimes someone upstream gets something catastrophically incorrect.
Any good crypto library will have a solid secure random source that usually combines entropy from multiple sources with a provably secure hash based mixing scheme.
Hardware RNGs can be one source, but no single source is trusted, and they're all combined in a way where even an intentionally malicious source is lost in noise and cannot actually determine output.
That's exactly the challenge though: "any good crypto library" - there is a long history of meaningful security breached (like stolen crypto tokens) due to bugs in an upstream library, especially when using things like embedded code, alternative operating systems, newer programming languages, etc.
The value of the iterated hashing method is that it is dead simple and has little dependency on potentially buggy upstream code; it works even in very lightweight environments designed by engineers with no experience in security.
There are theoretical issues where a malicious source of entropy could control the PRNG output, but it’s not a very practical attack.
https://blog.cr.yp.to/20140205-entropy.html
Intel could much more easily compromise and attack systems than make an implementation of RdRand which is malicious in this manner.
Oh yeah, if your hardware is malicious you are pretty much F'd.
Yeah, this comes off as a “they already are on the wrong side of the secure hatch” kind of attack. A malicious hardware device with physical access to a victim’s computer can do a lot more than generate malicious entropy.
It’s like the attacks I occasionally see which are like “once we have administrator, we can attack the process because of this insecurity”. Well, yeah, but once we have administrator, we can read the entire memory of the “vulnerable” process and completely control its output too.
I’ve seen in the real world attacks where things were insecure because the PRNG wasn’t given enough entropy (CVE 2008-0166, Coldcard, etc.). I’ve never seen real world attacks where a PRNG was insecure from getting too much entropy.
And to show my objections are not just theoretical I wrote a little program to check:
On my system this prints: So no, 50 iterations of that loop does not provide 256 bits of entropy due to random fluctuations in nanontime between calls.Hold on I have to go edit the rest of my responses because I just assumed you wrote the code correctly; you did not.
You are not hashing between calls to the timer. The sha256 hash itself is responsible for doing physical things to the chip (heating up some parts unevenly during the hashing computation) which introduces meaningful entropy between calls to the current time.
You can't just do calls to clock_gettime(), you have do an actual sequential sha256() call between them. Please run this code again and tell me what results you get.
You don't need 256 bits of entropy, you only need 128.
I have tested this method on over 100 different CPUs and I have never seen such consistent output. I'm genuinely surprised to see that you only hit 92 bits of entropy, but that can trivially be fixed by doing 10x the iterations. 500 iterations is still going to put you under a millisecond of cost.
And, for what it's worth, code I've actually shipped has combined the above technique with Fortuna, and has typically targeted 2000 bits of entropy rather than 128 (for security buffer).
EDIT: I reviewed his code, and he's not hashing between calls to check the clock; the hash call itself causes the CPU to heat up in arbitrary ways which changes the timing between hashes and introduces more entropy; removing that call basically entirely defeats the idea behind the technique, these results are fully invalid.
Thanks for writing that code!
The point is this: Getting micro-timing won’t give us as much entropy as we want, but it will still give us entropy. So it’s a perfectly good yet-another-source of entropy to feed in to an entropy pool (such as the input to a XOF).
If those Coldcard devices had used this code as one source of entropy, and this source of entropy was the only entropy still working, they never would had been compromised.
(I won’t update my 18-year-old PRNG to use this code, of course, since that code is now 18 years old and there are no known weaknesses in said code)
Actually, it gives you as much entropy as you need, just increase the iterations. That guy's output is shockingly consistent, so to be conservative maybe we say 0.2 bits of entropy per iteration. So just do 1000 iterations. That's still only going to take a few milliseconds even on embedded hardware.
EDIT: I reviewed his code, and he's not hashing between calls to check the clock; the hash call itself causes the CPU to heat up in arbitrary ways which changes the timing between hashes and introduces more entropy; removing that call basically entirely defeats the idea behind the technique, these results are fully invalid.
Nifty! Out of curiosity, how much different is that from taking several partly-random streams and XORing them together? I always assumed what was going on was essentially a fancier version of that.
Oh, I guess you have to ensure the inputs aren’t correlated, or they’ll cancel out?
The advantage of a secure XOF is that a malicious source of entropy needs to do a good deal more work than a simple XOR to generate controlled PRNG output (the attacker needs to do 2^n XOF operations to generate n bits of PRNG output).
The sources of entropy can be correlated and won’t cancel out with a well designed secure XOF. SHAKE-256 is an example of a secure XOF.
https://www.amd.com/en/resources/product-security/bulletin/a...
The OP says they discovered this on a Zen 2, which is not covered by that bulletin (?)
[edit to add]: Also, the bulletin is solely about RDSEED zeros, whereas the OP is also reporting RDRAND zeroes.
Older AMD processors had issues as well:
https://github.com/systemd/systemd/pull/12536/commits/1c53d4...
Why does systemd use architecture-specific instructions rather than using the kernel-provided random interface in the first place?
It was removed later https://github.com/systemd/systemd/commit/ffa047a03e4c5f6bd3...
That one's insidious!
I found the thread about it,
https://news.ycombinator.com/item?id=19848953
Yikes at this: "I am so glad I resisted pressure from engineers working at Intel to let /dev/random in Linux rely blindly on the output of the RDRAND instructure." -Theodore Ts'o (2013)
Embarrassing, but probably little practical impact, since these hardware random numbers are typically not used directly and instead seed a CSPRNG.
According to Theodore Ts there was pressure from Intel engineers to let /dev/random rely only on the RDRAND instruction.
" I am so glad I resisted pressure from Intel engineers to let /dev/random rely only on the RDRAND instruction. To quote from the article below:
"By this year, the Sigint Enabling Project had found ways inside some of the encryption chips that scramble information for businesses and governments, either by working with chipmakers to insert back doors...."
Relying solely on the hardware random number generator which is using an implementation sealed inside a chip which is impossible to audit is a BAD idea. "
https://web.archive.org/web/20180611180213/https://plus.goog...
Putting a backdoor into CSPRNG is a favored way to break crypto, for example Dual_EC_DRBG.
"
Weaknesses in the cryptographic security of the algorithm were known and publicly criticised well before the algorithm became part of a formal standard endorsed by the ANSI, ISO, and formerly by the National Institute of Standards and Technology (NIST). One of the weaknesses publicly identified was the potential of the algorithm to harbour a cryptographic backdoor advantageous to those who know about it—the United States government's National Security Agency (NSA)—and no one else. In 2013, The New York Times reported that documents in their possession but never released to the public "appear to confirm" that the backdoor was real, and had been deliberately inserted by the NSA as part of its Bullrun decryption program. In December 2013, a Reuters news article alleged that in 2004, before NIST standardized Dual_EC_DRBG, NSA paid RSA Security $10 million in a secret deal to use Dual_EC_DRBG as the default in the RSA BSAFE cryptography library, which resulted in RSA Security becoming the most important distributor of the insecure algorithm. RSA responded that they "categorically deny" that they had ever knowingly colluded with the NSA to adopt an algorithm that was known to be flawed, but also stated, "We have never kept this relationship [with the NSA] a secret and in fact have openly publicized it."
"
https://en.wikipedia.org/wiki/Dual_EC_DRBG
I'm getting 16-bit zeros on my Zen 3 chip (+1:3821, 0:3893, -1:3895), I will wait to get some statistically significant samples for the 32-bit values and update the forum thread. Maybe it was fixed after Zen 2?
Does anyone have access to an HPC cluster with thousands of Zen2 chips? We might want to check 64-bit ones with that - should take just a couple years depending on the size of the machine.
Anyone from the High-Performance Computing Center Stuttgart willing to play on the 720,320 Zen2 cores?
I always wonder how hardware bugs like this happen with the sheer amount of hardware validation that's done. It'd be fascinating to know how it slipped through the cracks, though I know almost nothing about this side of the industry sadly
Validation can't be better than the quality of the specification. Humans don't create comprehensive, unambiguous specifications for the same reasons that we don't write bug-free code, and need formal validation.
Brooks talks about this in _Mythical_Man-Month_... if you really could "just implement the specification", then the specification itself would be complete enough to serve as your code. There will always be bugs in both.
The verification plan did not make 0 a bin to cover.
Me too. Hardware bugs that arise out of unanticipated module interactions are understandable. But this is a "you had one job" moment.
Almost definitely an off by one bug.
That "sheer amount of hardware validation" is always less-than-perfectly spread across a whole lotta billions of transistors, and combinatorics is a harsh mistress.
Chased a similar bug in a KDF once and only caught it by histogramming the 16 bit draws, statistical suites never flagged it.
Your suites didn't even do a https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_tes... which is what you did?
I have a couple questions:
Looks like they tried 16-bit numbers. Does the odd behavior happen also on 32 and 64 (might take a long time to check - I'd start scratching my head after a couple hundred years of no zeroes) ones? Is the zero masking as some other fixed number, increasing its output count? Is RDRAND implemented as multiple reads of an internal state so that a larger random number takes longer?
I would be very concerned if an RNG simply produced a natural 0.
I would be very concerned if an RNG simply produced a natural 1.
I would be very concerned if an RNG simply produced a natural 0xf379aa46d1086bca.
So what? The point is to be non predictable not to pick all the numbers in the range with exactly the same probability. Would it be a problem if it never generated 16542?
Consider an 8-bit RNG.
By your argument, it would not be a problem if the RNG never generated 0. So, it must follow that it would also not be a problem if it never generated {1, 2, 3, ..., 253}.
That means that our RNG now only generates the values 254 and 255. Which of the values is generated is unpredictable on any given call. However, 7 of the 8 output bits are now always fixed and so completely predictable. Can you imagine how an attacker could exploit that?
Failing to generate only the number 0 is a weaker version of the same class of flaw.
This is the “what’s the big deal if I lost $100k in a casino, it’s really the same thing as if I had lost $5” argument.
I don’t think you can rebut “you only lose one of many values” with “it’s the same as only having one left”.
We're talking about whether a modification of the expected probabilities changes the dynamics of the game. The example I gave was deliberately extreme, because that makes it easier to reason about.
If you want a casino example, then consider a roulette wheel that always lands on 36 but still pays out as usual. I think you'd want to play on it. Now consider one that always lands somewhere between 30 and 36. Still worth it, right? With careful bets and a good starting float you're still coming away from the table up (with a very high probability).
In fact for a roulette wheel you only need two dead pockets for the player to get an edge. Bias is exploitable.
Sure, but you’re pressing on the truth that a small modification taken to an extreme is a large modification.
When the original point was that a tiny fractional loss in an RNG is not going to make a practical difference. Which I believe is also true. And it is also true that a large loss in an RNG is catastrophic.
They can both be true.
And roulette is 2 out of 38, 5.2%. That’s 17 times more than the 1/256 here, which was already a simplification of the (I think) 1/65536 in question.
> So, it must follow
It certainly does not.
A never-zero RNG is something one should know about, so that it can be mitigated if necessary, but it's not inherently a dealbreaker.
The value space goes from 2^16, 2^32, 2^64 to 2^16 - 1, 2^32 - 1, and 2^64 - 1 respectively.
The bug has zero practical impact.
It is absolutely untrue that a biased RNG has "zero practical impact." Modern cryptography has plenty of examples of relatively small biases leading to breaks. Check out Bleichenbacher's attack, for instance.
You could be correct that the very small bias here is not enough to be exploitable. But, given the history around this, it would be wrong to handwave it away as trivial.
“Pick all the numbers in the range with exactly the same probability” is a very important property of RNGs. Yes, skipping 16542 would be equally bad.
You can frame it around being “non predictable”, but then you need to define those words. It’s not, for example, a poker game where it’s trying to bluff you, right? It’s also not about just making predictions < 100% reliable and declaring victory. It must specifically make all predictions no better than random guessing, and that entails picking any number in range with equal probability, otherwise predictions like “it will be {hot spot}” or “it won’t be {cold spot}” do better than random chance. In this case, specifically, I can predict with 100% accuracy that the result won’t be 0, and that’s a flaw in its unpredictability. I can also predict a bunch of other things with slightly higher accuracy than random guessing, like that it will be odd or greater than max ÷ 2.
What are you talking about? The point is in fact to pick all the numbers in the range with exactly the same probability.
See section 7.3.17 of the Intel SDM, and how NIST SP800-90A (which the SDM refers to) defines "random number".
"Random" is used by most people to mean "random with an even distribution".
A weighted die is still random, but with an uneven distribution. This is effectively a 2^16-sided, weighted die.
My argument to follow your analogy is.
It's not a 2^16-sided weighted die. But a 2^16 - 1 sided fair die.
I am not saying there is no bug. I am saying the bug has no practical impact.
Sure if you are that one guy that is getting these values raw from the instruction and comparing to zero for some purpose then you are in trouble. But I am pretty sure no one is doing that, especially given that the bug surfaced after 6 years of millions of users.
I can imagine someone doing a
where these are not equally likely anymore (I may have an off-by-one anyway ;)).Betty from accounting will have words.
What does Betty from accounting care about RNGs?
There's an edge case somewhere that will affect a real user when you can't get a zero. Forecasting simulations perhaps?
That may well be a problem, yes.
“Predictable” and “not pick all numbers in range with exactly the same probability” are synonyms here.
Usually you do "rdrand % <some-number>" anyways, and in that case you will still get zeroes. True, your result might be skewed by 1/(maxint/some-number) but I guess that's not a big problem in practice
If you want uniformly-distributed random numbers, computing the remainder works only when the modulus is a power of two.
Otherwise, a slightly more complicated algorithm is necessary, where you reject a range of numbers either before computing the remainder (to make the set of possible values a multiple of the modulus) or after computing the value modulo some power of two (to reject values greater than your target).
Besides these 2 variants based on the remainder of division of integers, there are also 2 corresponding algorithms using multiplication of the input interpreted as a fraction, followed by taking the integer part of the result.
The probability of generating a zero is incredibly low if you use the normal distribution curve.
So it is not necessarily that it doesn't generate zero, they did not run enough times to increase the probability of actually generating a zero.
From what I can see they were trying to generate 16bit integers, so the probability is 1 in 65536 and they were running the test for 11 hours.
You definitely would expect a roughly equal number of 0s as any other of those numbers since it's uniformly distributed. And definitely not 0
> You definitely would expect a roughly equal number of 0s as any other of those numbers since it's uniformly distributed.
How would random numbers be uniformly distributed?
Because each number is equally as likely as every other number. If you know you're more likely to get certain numbers, or in this case have no chance of getting certain other numbers, it is by definition _less random_.
With enough repetitions.
With a few (say 10, so 655360 runs), you will not get a uniform distribution, and some numbers (like 0) might not appear.
So you think a weighted die is more random than a fair die? A uniform distribution means each outcome has equal probability; it doesn’t mean the outcome is predictable.
https://en.wikipedia.org/wiki/Discrete_uniform_distribution
This also seems to happen for 16 and 32 bit numbers, so you should be able to see zeros easily.
They also write:
> Running the same programs on an Intel processor, and the 0's are there with no problem.
Why would it be a normal distribution?
should be a discrete uniform distribution right?
0 is not a number, it's undefined
the what?
That's a thing some people used to believe, I guess some of them still do.
It is just possible they decided crypto code that uses it was safer to skip zeros. (Whist mathematically it should be no more likely; it is vastly more likely someone will actually try that key).
It is also possible that their code was generating too many zeros and the easiest fix was to discard them all.
Can you clarify what you mean by "it is vastly more likely someone will actually try that key"?
I'm guessing you don't think there are people calling rdrand in a loop and throwing away the output with high probability except when it is 0, but I can't see how else you imagine people would be vastly more likely to use the output when it is 0?
In lots of scenarios I know the software used to generate the key; the only unknown is the random numbers used. If I am searching for weaknesses it is highly likely I would try keys with different seeds; zero, one, are going to me much more likely choices here then hoping I can guess the right values.
If someone was using RDRAND16 to seed a PRNG, choosing to omit one single value (a zero) from the return value would not significantly improve the generated values, if at all.
If the keys are selected uniformly at random why are 0 and 1 more likely than other values?
this is not how crypto works