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Leonardo Errati

Cryptography PhD student @ PoliTo, Italy.

LESS: Linear Equivalence Signature Scheme

first made 20 June 2025, last modified 26 August 2025

Abstract

LESS (Linear Equivalence Signature Scheme) is a digital signature scheme relying on the hardness of the Linear Code Equivalence Problem, perhaps the first code-based scheme not relying on a variant of the Syndrome Decoding Problem.

We will explore the foundations, construction, and security of LESS. We also discuss upgrades such as LESS-F, LESS-M, and CF-LESS, and how group actions provide a unifying language to describe its functionality.

Notes

The target is an advanced audience familiar with the notion of digital signatures.

This talk was part of the course Post-Quantum Cryptography by Prof. Daniele Friolo (Università La Sapienza, Roma), whom I thank for the great occasion and interesting course.

Material

Much of the content builds on papers and preprints published between 2020 and 2025. All references are on the respective slides. For a quick introduction, see the LESS technical report (v2).