03759nam 2200757z- 450 991040408670332120231214133644.03-03928-803-2(CKB)4100000011302271(oapen)https://directory.doabooks.org/handle/20.500.12854/50457(EXLCZ)99410000001130227120202102d2020 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierInteractions between Group Theory, Symmetry and CryptologyMDPI - Multidisciplinary Digital Publishing Institute20201 electronic resource (164 p.)3-03928-802-4 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.NP-Completenessprotocol compilerpost-quantum cryptographyReed–Solomon codeskey equationeuclidean algorithmpermutation groupt-modified self-shrinking generatorideal cipher modelalgorithms in groupslightweight cryptographygeneralized self-shrinking generatornumerical semigrouppseudo-random number generatorsymmetrypseudorandom permutationBerlekamp–Massey algorithmsemigroup idealalgebraic-geometry codenon-commutative cryptographyprovable securityEngel wordsblock ciphercryptographybeyond birthday boundWeierstrass semigroupgroup theorybraid groupsstatistical randomness testsgroup-based cryptographyalternating groupWalnutDSASugiyama et al. algorithmcryptanalysisdigital signaturesone-way functionskey agreement protocolerror-correcting codegroup key establishmentGonzález Vasco María Isabelauth1246436BOOK9910404086703321Interactions between Group Theory, Symmetry and Cryptology3032109UNINA