Comment by dragontamer
7 years ago
> 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
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