Applications of Finite non-Abelian Simple Groups to Cryptography in the Quantum Era

María Isabel González Vasco; Delaram Kahrobaei; Eilidh McKemmie

Paper 2023/1293

Applications of Finite non-Abelian Simple Groups to Cryptography in the Quantum Era

María Isabel González Vasco, Universidad Carlos III de Madrid

Delaram Kahrobaei, Queens College, CUNY, University of York, New York University

Eilidh McKemmie, Rutgers, The State University of New Jersey

Abstract

The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian simple groups to cryptography and discuss different scenarios in which this theory is clearly central, providing the relevant definitions to make the material accessible to both cryptographers and group theorists, in the hope of stimulating further interaction between these two (non-disjoint) communities. In particular, we look at constructions based on various group-theoretic factorization problems, review group theoretical hash functions, and discuss fully homomorphic encryption using simple groups. The Hidden Subgroup Problem is also briefly discussed in this context.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Finite Simple Groups Hash Function PQC DSS KEM FHE
Contact author(s): mariaigo @ math uc3m es
delaram kahrobaei @ qc cuny edu
eilidh mckemmie @ gmail com
History: 2023-09-02: approved; 2023-08-29: received; See all versions
Short URL: https://ia.cr/2023/1293
License: CC BY-NC-ND

BibTeX

@misc{cryptoeprint:2023/1293,
      author = {María Isabel González Vasco and Delaram Kahrobaei and Eilidh McKemmie},
      title = {Applications of Finite non-Abelian Simple Groups to Cryptography in the Quantum Era},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/1293},
      year = {2023},
      url = {https://eprint.iacr.org/2023/1293}
}