Faster Cryptographic Hash Function From Supersingular Isogeny Graphs

We propose a variant of the CGL hash [5] that is significantly faster than the original algorithm, and prove that it is preimage and collision resistant. For n = log p where p is the characteristic of the finite field, the performance ratio between CGL and the new proposal is (2n + 104.8)/(1.8 logn + 12.6). Assuming the best quantum preimage attack on the hash has complexityO(p 1 4 ), we attain a concrete speed-up for a 256-bit quantum preimage security level by a factor 70.35. For a 384-bit quantum preimage security level, the speed-up is by a factor 100.36.