Paper 2023/1293
Applications of Finite non-Abelian Simple Groups to Cryptography in the Quantum Era
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 GroupsHash FunctionPQCDSSKEMFHE
- 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},
note = {\url{https://eprint.iacr.org/2023/1293}},
url = {https://eprint.iacr.org/2023/1293}
}
