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 (5.7n + 110)/(13.5 logn + 46.4). This gives an exponential speed up as the size of p increases. Assuming the best quantum preimage attack on the hash has complexity O(p 1 4 ), we attain a concrete speed-up for a 256-bit quantum preimage security level by a factor 33.5. For a 384-bit quantum preimage security level, the speed-up is by a factor 47.8.