A Guide to the Design of Digital Signatures based on Cryptographic Group Actions

Giacomo Borin; Edoardo Persichetti; Paolo Santini; Federico Pintore; Krijn Reijnders

Paper 2023/718

A Guide to the Design of Digital Signatures based on Cryptographic Group Actions

Giacomo Borin

, University of Zurich, IBM Research - Zurich

Edoardo Persichetti

, Florida Atlantic University, Sapienza University of Rome

Paolo Santini

, Marche Polytechnic University

Federico Pintore, University of Trento

Krijn Reijnders, Radboud University Nijmegen

Abstract

Cryptography based on group actions has been studied since 1990. In recent years, however, the area has seen a revival, partially due to its role in post-quantum cryptography. For instance, several works have proposed signature schemes based on group actions, as well as a variety of techniques aimed at improving their performance and efficiency. Most of these techniques can be explained as transforming one Sigma protocol into another, while essentially preserving security. In this work, we present a unified taxonomy of such techniques. In particular, we describe all techniques in a single fashion, show how they impact the performance of the resulting protocols and analyse in detail how different techniques can be combined for optimal performance. Furthermore, to provide a tangible perspective, we apply the results of our analysis to the (group action-based) candidates in the current NIST call for digital signatures. This gives a full overview of the state of the art of signatures based on group actions, as well as a flexible tool which is easy to adapt and employ in the design of future schemes.

Note: In the revised version results from previous versions are improved, reorganised in a general framework and compared in details.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Group Actions Zero-Knowledge Code Equivalence Digital Signatures
Contact author(s): giacomo borin @ ibm com
edopers @ gmail com
p santini @ staff univpm it
federico pintore @ unitn it
krijn @ cs ru nl
History: 2024-03-11: last of 2 revisions; 2023-05-18: received; See all versions
Short URL: https://ia.cr/2023/718
License: CC BY

BibTeX

@misc{cryptoeprint:2023/718,
      author = {Giacomo Borin and Edoardo Persichetti and Paolo Santini and Federico Pintore and Krijn Reijnders},
      title = {A Guide to the Design of Digital Signatures based on Cryptographic Group Actions},
      howpublished = {Cryptology ePrint Archive, Paper 2023/718},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/718}},
      url = {https://eprint.iacr.org/2023/718}
}