Year: 2026
Type: article
Abstract: Cryptographic group actions have gained significant attention in recent years for their application on post-quantum Sigma protocols and digital signatures. In NIST’s recent additional call for post-quantum signatures, three relevant proposals are based on group actions: LESS, MEDS, and ALTEQ. This work explores signature optimisations leveraging a group’s factorisation. We show that if the group admits a factorisation as a semidirect product of subgroups, the group action can be restricted on a quotient space under the equivalence relation induced by the factorisation. If the relation is efficiently decidable, we show that it is possible to construct an equivalent Sigma protocol for a relationship that depends only on one of the subgroups. Moreover, if a special class of representative of the quotient space is efficiently computable via a canonical form, the restricted action is effective and does not incur in security loss. Finally, we apply these techniques to the group actions underlying LESS and MEDS, showing how they will affect the length of signatures and public keys.
Source: Designs Codes and Cryptography
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Politecnico di Torino, European Commission, Università degli Studi di Trento, Universita degli Studi di Bari Aldo Moro, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, HORIZON EUROPE Framework Programme
OpenAlex ID: W7127159668