2 ms·
What these guys just did here is actually a very clever idea in another way. Suppose that there exists a weakness in 1 in 2^30 curves, and each curve takes 2^10
by vbuterin 12y ago
What these guys just did here is actually a very clever idea in another way. Suppose that there exists a weakness in 1 in 2^30 curves, and each curve takes 2^10 steps to generate. If they picked seeds NIST style (or even using cos(1), exp(cos(1)), sin(sha3(5)) or other permutations) then they would be able to find a weak curve in 2^40 steps. Here, however, they're adding another trivial property, namely presence of BADA55EC at the start of B, which only 1 in 2^32 curves have. Hence, this increases the difficulty of finding a malicious curve to 2^72, which is actually pretty close to what many people consider a secure cryptographic safety margin.
My preference would be to not bother with such tricks and adopt a standard for nothing-up-my-sleeve numbers (eg. find the lowest N such that sha(N) results in desirable properties) to avoid people from end-running around the whole concept with prime square roots, cosines, exp and log and the like, but this is still an interesting concept.