Interactions between Group Theory, Symmetry and Cryptology

• Main Author: González Vasco, María Isabel (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: NP-Completeness; protocol compiler; post-quantum cryptography; Reed-Solomon codes; key equation; euclidean algorithm; permutation group; t-modified self-shrinking generator; ideal cipher model; algorithms in groups; lightweight cryptography; generalized self-shrinking generator; numerical semigroup; pseudo-random number generator; symmetry; pseudorandom permutation; Berlekamp-Massey algorithm; semigroup ideal; algebraic-geometry code; non-commutative cryptography; provable security; Engel words; block cipher; cryptography; beyond birthday bound; Weierstrass semigroup; group theory; braid groups; statistical randomness tests; group-based cryptography; alternating group; WalnutDSA; Sugiyama et al. algorithm; cryptanalysis; digital signatures; one-way functions; key agreement protocol; error-correcting code; group key establishment
• Online Access: DOAB: download the publication; DOAB: description of the publication

Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebra...