Faster Cryptographic Hash Function from Supersingular Isogeny Graphs

We propose a variant of the CGL hash algorithm [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 \((5.7n + 110) / (13.5\log n + 46.4)\) . This gives an exponential speed up as the size of p increases. Assuming the best quantum preimage attack on the hash algorithm has complexity \(O(p^{\frac{1}{4}})\) , 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.