Paper 2025/135 Original: eprint.iacr.org/2025/135 ↗

PRISM: Simple And Compact Identification and Signatures From Large Prime Degree Isogenies

Abstract

The problem of computing an isogeny of large prime degree from a supersingular elliptic curve of unknown endomorphism ring is assumed to be hard both for classical as well as quantum computers. In this work, we first build a two-round identification protocol whose security reduces to this problem. The challenge consists of a random large prime $q$ and the prover simply replies with an efficient representation of an isogeny of degree $q$ from its public key. Using the hash-and-sign paradigm, we then derive a signature scheme with a very simple and flexible signing procedure and prove its security in the standard model. Our optimized C implementation of the signature scheme shows that signing is roughly $1.8\times$ faster than all SQIsign variants, whereas verification is $1.4\times$ times slower. The sizes of the public key and signature are comparable to existing schemes. Latest version: PRISM with a pinch of salt: Simple, Efficient and Strongly Unforgeable Signatures from Isogenies, from the same authors, is an extended and updated version of the present article. It is available at https://eprint.iacr.org/2026/443.