TY - JOUR
T1 - Applications of Finite Non-Abelian Simple Groups to Cryptography in the Quantum Era
AU - Vasco, María Isabel González
AU - Kahrobaei, Delaram
AU - McKemmie, Eilidh
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/6
Y1 - 2024/6
N2 - 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.
AB - 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.
KW - Encryption schemes
KW - Hash functions
KW - Post-quantum cryptography
KW - Simple groups
UR - http://www.scopus.com/inward/record.url?scp=85195369322&partnerID=8YFLogxK
U2 - 10.1007/s44007-024-00096-z
DO - 10.1007/s44007-024-00096-z
M3 - Review article
AN - SCOPUS:85195369322
SN - 2730-9657
VL - 3
SP - 588
EP - 603
JO - Matematica
JF - Matematica
IS - 2
ER -