Failing to hash into supersingular isogeny graphs

arXiv:2205.00135v3 Announce Type: replace-cross
Abstract: An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equations for supersingular curves for which computing the endomorphism ring is as difficult as it is for random supersingular curves. A related open problem is to produce a hash function to the vertices of the supersingular $\ell$-isogeny graph which does not reveal the endomorphism ring, or a path to a curve of …

arxiv authority computing concrete cryptography cs.cr examples graphs hard hash important math.nt problem random ring