Paper 2026/2312 Original: eprint.iacr.org/2026/2312 ↗

ECLIPSE: Strongly Unforgeable Isogeny Signatures from the Prime-Degree Variant of PRISM

Abstract

ECLIPSE is the prime-degree signature construction the PRISM authors describe beside their salted scheme, with that salt, implemented. It exists because a two-dimensional isogeny signature carries an auxiliary isogeny the hash does not bind: the SQIsign round-3 specification says SQIsign cannot be strongly unforgeable for that reason, and PRISM's prime-degree variant has no auxiliary isogeny but was published without parameters, code or a running verifier. This paper is the first implementation, on the SQIsign round-3 primes: a verifier that evaluates the paper's criterion through one isogeny chain and a pull-back, a canonical wire format whose strict decoder recovers one coefficient from two Weil pairings, randomisable keys, two independent implementations that accept each other's signatures, and one key in both roles: a MIKE key pair at the level I prime is an ECLIPSE key pair, the public curve re-encoded and the signing key derived from the MIKE secret alone, with MIKE's code untouched. The only post-quantum precedent is CSIDH with CSI-FiSh, a group action; this is the first shared key in the SQIsign family. Signatures are 206 bytes at NIST level I, within 15 bytes of SQIsign at every matched state. In one session against the SQIsign reference's assembly build, signing is 2.6 times faster and verification costs twice as much, 1.6 times with the public key prepared once. A formal strong-unforgeability (SUF-CMA) argument is left to future work.