No. There's a bad reason though. Want to guess what? https://github.com/systemd/systemd/blob/master/src/basic/ran...
Yes, the old "draining entropy" fallacy.
No. There's a bad reason though. Want to guess what? https://github.com/systemd/systemd/blob/master/src/basic/ran...
Yes, the old "draining entropy" fallacy.
Why do you say draining entropy is a fallacy? It is certainly true that entropy recorded from I/O sources accumulates at a very limited rate.
There's no way to "use up" your entropy; this is a persistent myth that's been hanging around the Linux world for a very long time.
* https://www.2uo.de/myths-about-urandom/#what-about-entropy-r...
* https://www.mail-archive.com/cryptography@randombit.net/msg0...
Because after you gather ~256 bits of entropy from I/O sources (or rdrand^H^H^H rdseed [1]), using it to generate infinite output of /dev/urandom does not drain it. Adding more entropy only helps if the entropy pool inner state leaked, it is not needed to add more entropy because it drained through using it.
Proof:
1. Take 256 bits of entropy.
2. Use HKDF to generate 128 bit key and 64 bit nonce.
3. Use key and nonce for AES-CTR with all possible 2^64 counter values to produce 2^68 bytes of output.
4. goto 2.
If you can compute the inner state of the RNG (and thus predict future output) by just observing the output (not through side channels), using any amount of output, then all modern symmetric crypto is broken. If you can't, then using the entropy in an RNG does not drain the entropy pool.
And here is a CCC talk about it: https://www.youtube.com/watch?v=OSfmtRc4VsE
1 - https://software.intel.com/en-us/blogs/2012/11/17/the-differ...
EDIT: Thanks for 'dragontamer for pointing out difference between rdrand and rdseed.
> If you can compute the inner state of the RNG (and thus predict future output) by just observing the output (not through side channels), using any amount of output, then all modern symmetric crypto is broken. If you can't, then using the entropy in an RNG does not drain the entropy pool.
This seems wrong to me.
If you can predict #1 (the 256-bits of entropy in step 1), then you can break the system. This is highly likely, as Intel only assures 65-bits of entropy across two rdrand calls. (64-bits of entropy from the first call, +1 bit from the 2nd call, since RDRAND is generated from an internal random number generator. So there's going to be a correlation between the two values).
In effect, if #1 is created with four calls to RDRAND, you only have around 68-bits of entropy, which can be brute-forced faster than a true source of 256-bits of entropy. Therefore, your RNG is broken. https://software.intel.com/en-us/blogs/2012/11/17/the-differ...
RDSEED is the instruction that guarantees 64-bits of independent / multiplicative entropy, but executes slower as a result.
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In effect, you're "simplifying" the problem. #1, getting 256 bits of entropy, is the hard part of the problem. You cannot ignore this part of the problem.
In any case, it seems to me that a large number of people don't know how to properly use the RDRAND function, in this thread as well as in the Github thread. RDRAND has a chance of failure, AND it doesn't even hold multiplicative entropy guarantees.
So this seems like a case of EVERYONE hasn't read the docs yet. Please people, do NOT use RDRAND as a source of entropy. Use RDSEED as a source of entropy. RDRAND is only a random number generator with only 64-bits of entropy guaranteed at any given state, and probably additive entropy at that.
I can ignore "how to do #1" when discussing whether entropy is drained by using it or not.
You need to get 256 bits of high quality entropy. We assume there are ways to do that.
On a device that has no way to do that, you can't do crypto (unless you accept the entropy from outside, which is key escrow, but might be ok for an IoT device that communicates only to its mothership).
> I can ignore "how to do #1" when discussing whether entropy is drained by using it or not.
Ehhh... fair point. Still, the overall discussion is about RDRAND, so I feel like its very important to point out how RDSEED must be used to properly generate the 256 bits of entropy you require in step #1.
Each of these steps are tricky, and require thorough analysis to understand.
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EDIT: Its not so much that entropy is "used up". Its that RNG-sources of randomness gives "additive" entropy, while true entropy is "multiplicative".
Generating random numbers from a 256-bit RNG will give 256-bits of entropy from the first step, but be 100% predictable (and therefore "only" 256-bits on the 2nd step).
If the "next programmer" wants 512-bits of entropy, they will NEVER get 512-bits of entropy from your methodology, because you only started with 256-bits of entropy. Only by gathering "more" entropy will you be able to reach 512-bits of entropy.
The argument would go "who needs more than 256-bits of entropy", which is a fine point. But... that's how the math checks out.
It all comes back to the RDRAND vs RDSEED question. If the user just wants "unpredictable random numbers", then RDRAND and /dev/urandom is sufficient. But if you're creating independent random number generators (ex: If you're creating a service like random.org, and are guaranteeing certain amount of entropy per call to everyone), then you need to be using RDSEED.
Does 10 calls of your RNG produce 256-bits of randomness, or 2560-bits of randomness? What are your requirements? What are the requirements of the end user? For most people, having a RNG that "only" provides 256-bits of randomness across 10,000 calls is perfectly fine and sufficient. But there are plenty of cryptographic cases where that's not enough (and "true" 256-bits of entropy are needed in every call).
True about no way to deterministically get more than 256 bits of entropy out of 256 bits of initial entropy, but the requirements are to run wireguard, ssh, tls, generate web app session cookies. All those, I believe, would be satisfied by using a urandom which is implemented the way I described. What real use case has a requirement of more than 256 bits of "real" entropy?
Note that the real linux urandom is not as simple as I described, and djb's proposed key erasure RNG [1] is not as simple as I described. My design was just to talk about "draining" of the entropy.
1 - https://blog.cr.yp.to/20170723-random.html
> All those, I believe, would be satisfied by using a urandom which is implemented the way I described.
Do you want all of your AES Keys to be generated from one 256-bit random number generator? Or would you feel more comfortable for each AES Key to be independent sources of entropy? Assume all AES Keys are 256-bits for the rest of this post, to keep all encryption targets at 256-bits of security.
If an attacker breaks urandom, they effectively gain the key-generation for all keys that were based on that entropy pool (at least, until its 'entropy fills back up').
So if you're a server handling say, 100-connections per second... and for round-numbers sake, lets say that /dev/urandom generates 256-bits of entropy every second. If you break /dev/urandom for a 1-second interval (ie: you figure out /dev/urandom's 256-bit key for that 1-second interval), you now know all keys to all 100-connections that happened within that second.
If all 100-connections grabbed their own independent sources of entropy (/dev/random), then it wouldn't be possible. Probably because 100-connections per second would block and your hardware wouldn't support it. :-)
But yeah, its a question of "what do you want your server to do when it runs out of entropy". Do you want to just use pseudo-randomness to "fill in the blanks", which increases your attack surface. (All AES-keys you generate within that time period will have weakened security from an entropy perspective). Or would you rather BLOCK, and simply not support that case? (waiting on /dev/random will cause the server to slow down)
Since 256-bits of entropy is such a huge amount of security (if done properly), I think I'm inclined to agree with you. But still, its an engineering choice that has to be made.
I would be comfortable using AES keys generated by my algorithm, even though I would prefer djb's proposed key erasure RNG I linked above.
If the attacker managed to read the inner state of your RNG, you need to rotate all keys. There is no defense. The key erasure RNG only limits the damage.
There is no "entropy fills back up", because it is not drained. There is "adding/replacing non-deterministic entropy", to mitigate how many keys are known to attacker if attacker had access to RNG inner state for limited amount of time.
The entropy in /dev/random it not any better than the entropy in /dev/urandom, after the entropy pool has been initialized (step 1 in my algo) they are the same. /dev/random blocks until step 1 is complete. Step #1 is not complete in two cases: very early boot before the entropy pool has been read from storage and boot with no entropy pool stored, so need to gather entropy from I/O or hardware RNG like rdseed.
For ssh, tls, wireguard etc, use urandom.
For embedded devices: inject entropy pool value at manufacturing time.
For VMs: inject entropy pool from host at first start / VM clone.
The server never "runs out of entropy".
Please watch the CCC presentation I linked above.
> If the attacker managed to read the inner state of your RNG, you need to rotate all keys.
That's not the attack I'm talking about. The inner-state of your RNG can be brute-forced with an attack of size 2^256 (assuming 256-bits of internal state to your RNG).
If your 256-bit RNG creates 100x 256-bit AES-keys, the "common thread" is to attack the RNG. That's the most efficient way to get all 100x AES keys.
Case in point:
1. Try state X
2. Did it generate the RNG Sequence you're attacking? If so, you're done.
3. If not, X = X+1. Go back to step #1 and loop.
Simple brute-force attack against the state. That is to say, a 256-bit RNG only has "256-bits" of protection. Or to put it another way: the 100x AES Keys you've generated all have 256-bits of protection, max.
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Stick a TRUE Hardware random number generator with entropy guarantees (such as RDSEED) as your generator, and you're immune to this brute force attack. In theory, its a non-trivial difference. In practice, 256-bits of entropy is enough for most people, and no one is going to accomplish this brute force attack.
Its not about "draining" entropy. Its about asking yourself how much entropy your application needs. I can IMAGINE people needing more than 256-bits of entropy in higher-security contexts.
What? No, brute forcing 2^256 is not an option. We assume brute forcing 2^128 is not an option. If brute forcing 2^256 were an option, why would anyone use AES-256?
No. Its not an option in practice. But its the starting point for a research problem.
* 100x different AES-256 keys generated by /dev/random would have 25,600 bits of entropy. (All 100x keys are independent, and would require an attack effort per key).
* 100x different AES-256 keys generated by /dev/urandom would "only" have 256-bits of entropy. (/dev/urandom would be attacked, assuming /dev/urandom started with 256-bits of entropy in its pool, assuming /dev/urandom never got extra entropy in the 100x calls)
You can't pretend that the two solutions to the problem are the same. At best, you can suggest that 256-bits of entropy is enough for practical purposes.
No, brute forcing 2^256 is not the starting point of anything.
Again, after seeding with initial entropy, /dev/random and /dev/urandom are the same, /dev/random is not better entropy.
Attacking a single 256 bit key is exactly as equally impossible as attacking a 256 bit RNG pool used to generate 100 keys.
There is no actual scenario in which using hardware RNG to generate 100 keys would keep me safe while using a hardware RNG to initialize a deterministic RNG to generate 100 keys would lead to compromise.
If your attacker model includes brute forcing 2^256, I can't help you. If you're trying to prove that Aleph-one is greater than Aleph-0, perhaps, but the number of atoms in the universe is less than Aleph-0, so it's irrelevant to cryptography or to information security.
People who say "maybe an advance in math will break 2048 bit DHE" are at least theoretically correct. But no advance in math is going to break that RNG. If you can't trust that RNG, you can't send secrets using CTR, GCM, CHACHA, etc. because they will all break using that method.
> Attacking a single 256 bit key is exactly as equally impossible as attacking a 256 bit RNG pool used to generate 100 keys.
But both are strictly easier than attacking 100x independently created 256-bit keys. The /dev/random case.
> If you're trying to prove that Aleph-one is greater than Aleph-0
I mean, yeah, that's basically the argument I have. 256-bits of entropy are probably enough for your application, but you cannot under any circumstances tell me that its the same as 25,600 bits of entropy. That's what /dev/random vs /dev/urandom comes down to. For most people in most situations, its almost inconceivable to imagine an application that needs more than 256-bits of true high quality entropy.
EDIT: A POTENTIAL case, which I admit I haven't though too much about... is a 2048-bit RSA key. I assume the RSA key needs to be generated with 2048-bits of true entropy (please correct me if I'm wrong), but the bits-of-security are far less than that, because RSA doesn't scale like other encryption schemes. So your 2048-bits of entropy RSA-key only scales to 128-bits of security.
If your 2048-bits of entropy RSA-key ended up to only have 256-bits of entropy generating it, you're possibly in bad luck (only 16-bits of entropy assuming a similar scaling factor). I'm not a specialist in the math, but... not all cryptographic primitives scale 1-to-1 with the input entropy source.
> > Attacking a single 256 bit key is exactly as equally impossible as attacking a 256 bit RNG pool used to generate 100 keys.
> But both are strictly easier than attacking 100x independently created 256-bit keys. The /dev/random case.
Both are impossible. Like, 'Solar System turned into thermodynamically optimal computronium fails' impossible. (seriously - '((mass of solar system * (speed of light)^2) / 0.0172 electronvolts ) / (2^256)' for calculations performed at 20C [0], and that evaluates to 5*10^-10. Drop the assumed temperature to 2.75K - the cosmic background temperature - and the energy per computation drops by a factor of several hundred, but that's still not nearly enough)
Or, put another way - if you can bruteforce 2^256, you can do that 100 times. (Even if you encrypt an object 100 times, you'll still only need to do ~2^264 work - not 2^25600)
0: https://en.wikipedia.org/wiki/Landauer%27s_principle
RSA-2048 is only about 112 bits of security because index calculus methods of breaking RSA-2048 (and DHE-2048) have an algorithm with ~2^112 steps to break it, not because of the amount of entropy used to generate the key [4].
An RSA-2048 keypair is generated by taking a CSPRNG like the one I proposed, generating 1024 bit numbers, checking them for being a prime number using Miller Rabin [1] until the chance of the number not being prime is below 2^-128 (generating new candidate primes if the current one turns out to be not prime), and then doing it all over again for the other prime. The two 1024 bit probably-primes "p" and "q" are the private key, their product "n" (with the public exponent e=65537) is the public key. Most systems precalculate some derived values used to speed up operations and store them with p and q, but you don't have to [2][3].
The RNG I proposed is absolutely good enough to generate RSA key pairs. There is no benefit to using "true hardware randomness" for generating candidate primes, after the initial pool of 256 bits of entropy has been generated.
1 - https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality...
2 - https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Key_generat...
3 - https://tools.ietf.org/html/rfc8017#section-3.2
4 - https://crypto.stackexchange.com/a/8692/24949
What are you talking about? This is not an "in practice" detail.
Let's put the time involved in perspective.
``` int main() { for (unsigned long long i = 0; i < (((unsigned long long)1) << 35ull); i++) { __asm__ __volatile__ (""); } } ```
this is large enough to remove the relevance of any start up time, and make noise somewhat meaningless.
On my laptop this takes 9 seconds. That's just counting to 2^35. Now let's imagine we're just counting to 2^256. Not even doing the work to break the rng. How long does it take?
2^221 * 9seconds.
Which is approximately 1.397 * 10 ^ 50 times the age of the universe (I think a billion billion billion billion billion times the age of the universe).
That's just counting from 0 to 2^256, not doing anything else at all.
Understand that if you can break a CSPRNG with 2^256 bits of state, you can break:
* The entire WebPKI system, because all you're doing is brute forcing an very high speed 256 bit hash function.
* TLS connections: you're just brute forcing 256bit keys here as well, in the worst case. Fortunately most are still just aes128. That's 6471949087173059816 times faster, so that's only a billion billion billion times the age of the universe.
Note that the numbers involved mean that "making computers faster" and "adding more computers" doesn't making a meaningful difference, because you run into an energy wall - literally more power than a star emits ends up being necessary.
So, please don't just regurgitate nonsense: brute forcing a current 256 bit CSPRNG is not possible, at all. because physics.
So to break it, you have to break the csprng algorithm. But if you can do that, then you can break any of the places the an RNG is used in practice. Eg. you could have a "true" rng seeding crypto, but it doesn't matter because the attacker can just use your algorithm to break the result of your crypto.
Note also the "true" random you get on a computer is fairly restricted - it has both little variance, and also significant bias, so the output has to be merged (hash function that you've broken) and whitened (again, hash function that you've broken). So even if you were trying to rely on "true" random, you're not getting as much "entropy" as you seem to think you are, and you've invented an algorithm that breaks all the massaging used to make it seem more random.
So after reading this thread my understanding of the "draining is a fallacy" view is
(1) yes genuine non-programmatic entropy bits accumulate at a slow rate and can be drained
(2) in practise no one should care about (1) because once you have ~256 bits to initialise a CSPRNG you can use the output of that CSPRNG until the Earth is swallowed up by the sun; thats what the S of Cryptographically Secure Programmatic Random Number Generator promises.
(3) the linked systemd code is silly to even provide a function genuine_random_bytes that tries to get additional genuine non-programmatic entropy as every possible use case is covered by (2)
(4) The real fallacy is when people think that it might be possible to discover the seed of a CSRNG or predict its next outputs by examining a long enough run of its previous output. In practise such an attack should not be possible.
If I've got the summary right, the only point I would disagree on principle is (3). I can imagine that someone might rationally want "genuine" entropy independent of a kernel CSPRNG, for example for seeding their own CSPRNG.
re your (1), the bits cannot be drained. The only thing that can happen to them is that there is an attacker with root on your computer, and they see the CSPRNG inner state, and the attacker loses their access but they can still predict output of CSPRNG because it's deterministic, so you want to inject new entropy into it so the attacker will lose ability to predict CSPRNG output. djb says this is nonse. https://blog.cr.yp.to/20140205-entropy.html
Which one of these statements is false:
1. When secure your TLS 1.2 connection with a 128 bit AES key, you can transmit a small amount of data (on the order of ~128 bits) before the entropy is drained from your CSPRNG state.
2. When you generate at least ~128 bits of entropy in your kernel's CSPRNG state, you can generate a very large amount of random bits before the entropy is drained from your CSPRNG state.