3 ms·
The issue with the NIST curves is that they were generated from a PRNG with some kind of completely random seed. The conspiracy theory there is that the seed wa
by dfox 3y ago
The issue with the NIST curves is that they were generated from a PRNG with some kind of completely random seed. The conspiracy theory there is that the seed was selected such as to make the curve exploitable for NSA and NSA only. Choosing such a seed is somewhat harder than complete break of the hash function (IIRC SHA-2) used in the PRNG that was used to derive the curve.
On the other hand, there is a lot of reasons to use elliptic curve that was intentionally designed, so, DJB's designs. And well, in 2009 I would not imagine that the kinds of stuff that DJB publishes will end up being TLS1.3.
- tptacek 3y agoIt's very unlikely the seeds were random, and they weren't even ostensibly generated from a PRNG, as I understand it. Rather, they were passed through SHA1 (remember: this is the 1990s), as a means to destroy any possible structure in the original seed. The actual seeds themselves aren't my story to tell, but are a story that other people are talking about. For my part, I'll just point again to Koblitz and Menenzes on the actual cryptographic problems with the NIST P-curve seed conspiracy: https://eprint.iacr.org/2015/1018.pdf https://eprint.iacr.org/2015/1018.pdf
- f33d5173 3y agoA hash function is a (CS)PRNG. It has the key property, namely of being indistinguishable from randomness while being generated deterministically.
- tptacek 3y agoIn fact, `echo "This is my seed" | openssl sha -sha256` is not really a CSPRNG. Hash functions are the bases of many PRNGs. But I think you're abusing an ambiguity with the word "random" here. At any rate: we should be clear now on the point being made about the P-curve seeds.
- Ar-Curunir 3y agoThat is not true. There is no such requirement for a hash function.
- ethbr1 3y agoThread is talking about cryptographic hash functions, given the context
- Ar-Curunir 3y agoYes, they don’t output random looking things necessarily. For example a hash function could be collision resistant but not pre image resistant, or vice versa. There’s much more nuance in these definitions.
- wolf550e 3y agoThis seems to be all that is publicly known about the seeds: https://saweis.net/posts/nist-curve-seed-origins.html https://saweis.net/posts/nist-curve-seed-origins.html