Implementation Aspects of Supersingular Isogeny-Based Cryptographic Hash Function.

Supersingular isogeny-based cryptosystems are considered an attractive candidate for the post-quantum cryptographic world due to their smaller key sizes. Based on the traversal in a supersingular isogeny graph (expander graph), Charles, Goren, and Lauter proposed a cryptographic hash function also known as CGL hash. In this paper, we present our study on the implementation-related aspects of the compact variation of the standard CGL hash function using different forms of elliptic curves (Weierstrass, Montgomery, and Legendre). Moreover, we show that some redundant computations in the original propositions of the CGL hash function can be avoided by utilizing the unique characteristics of the different forms of the elliptic curve. We also compared the running time and the total number of collisions through the experiments with the implemented algorithms.