TY - BOOK
ID - 46039
TI - Interactions between Group Theory, Symmetry and Cryptology
AU - González Vasco, María Isabel
PB - MDPI - Multidisciplinary Digital Publishing Institute
PY - 2020
KW - cryptography
KW - non-commutative cryptography
KW - one-way functions
KW - NP-Completeness
KW - key agreement protocol
KW - group theory
KW - symmetry
KW - Engel words
KW - alternating group
KW - WalnutDSA
KW - digital signatures
KW - post-quantum cryptography
KW - cryptanalysis
KW - braid groups
KW - algorithms in groups
KW - group-based cryptography
KW - Reed–Solomon codes
KW - key equation
KW - Berlekamp–Massey algorithm
KW - Sugiyama et al. algorithm
KW - euclidean algorithm
KW - numerical semigroup
KW - Weierstrass semigroup
KW - semigroup ideal
KW - error-correcting code
KW - algebraic-geometry code
KW - lightweight cryptography
KW - permutation group
KW - block cipher
KW - generalized self-shrinking generator
KW - t-modified self-shrinking generator
KW - pseudo-random number generator
KW - statistical randomness tests
KW - cryptography
KW - pseudorandom permutation
KW - block cipher
KW - ideal cipher model
KW - beyond birthday bound
KW - provable security
KW - group key establishment
KW - group theory
KW - provable security
KW - protocol compiler
SN - 9783039288021 / 9783039288038
AB - 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 algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.
ER -