Supersingular Isogeny-Based Single Compression Cryptographic Hash Function

In this paper, we propose a novel single compression cryptographic hash function based on traversal in the super-singular isogeny (2-isogeny) graph and point mapping under the isogeny. Unlike existing supersingular isogeny-based hash functions, our proposed function outputs the X-coordinate of a point on a supersingular elliptic curve without revealing the j-invariant of the traversed curve. This makes our hash function more secure, as an attacker faces two hard problems: finding the curve from its X-coordinate and the supersingular isogeny problem. Hence, our hash function offers improved preimage resistance. The pure randomness of mapping two different points over an isogeny (or two different isogenies) to the same point ensures the collision-free property of the proposed hash function. The compression function of the hash function processes bits from multiple blocks of the message in a single step, giving it an advantage in terms of computational complexity compared to other supersingular isogeny-based hash functions. Additionally, the compression function organically modifies the message to ensure resilience to parallelization attempts. We analyze the computational complexity of the proposed hash function and compare it with CGL and CGL-like hash functions.