LEAST: Linear Equivalence Action Threshold Signature

"Preview Talk" (by Team LEAST) @ MPTS 2026, in reply to the NIST Threshold Call

Abstract. Group actions are fundamental mathematical tools, with a long history of use in cryptography. In this presentation we show that isomorphism problems which stem from non-abelian cryptographic group actions can be viable building blocks for threshold signature schemes. In particular we focus on the Linear Code Equivalence group action and show how to obtain a threshold signature for it, that we call LEAST. The signature is compatible with LESS digital signature, that is currently in the Round 2 Additional Signatures standardization effort. We also present a distributed key generation for it and a more efficient but centralized key generation obtained by the Vandermonde Secret Sharing. The results presented in this talk will be included in a future submission to the NIST Threshold Call.

Joint work: Michele Battagliola, Marco Baldi, Giacomo Borin, Giovanni Di Crescenzo, Rahmi El Mechri, Alessio Meneghetti, Edoardo Persichetti, Paolo Santini, Floyd Zweydinger.

[Slides] Suggested reading:

• Preview Writeup: LEAST: Linear Equivalence Action Threshold Signature
• Enhancing Threshold Group Action Signature Schemes: Adaptive Security and Scalability Improvements (ia.cr/2025/085)