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

María Isabel González Vasco, Delaram Kahrobaei, Eilidh McKemmie

Research output: Contribution to journalReview articlepeer-review

1 Scopus citations

Abstract

The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modeling 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.

Original languageEnglish
Pages (from-to)588-603
Number of pages16
JournalMatematica
Volume3
Issue number2
DOIs
StatePublished - Jun 2024

Keywords

  • Encryption schemes
  • Hash functions
  • Post-quantum cryptography
  • Simple groups

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