Paper 2026/443

PRISM with a pinch of salt: Simple, Efficient and Strongly Unforgeable Signatures from 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. The most efficient variant of our signature schemes features a signing which is $1.4\times$ to $1.6\times$ faster than the most recent implementaion of SQIsign, whereas verification ranges from $1.2\times$ slower to $1.01\times$ faster depending on the security level. The sizes of public key and signature are comparable to existing schemes.