Interactions between Group Theory, Symmetry and Cryptology

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...

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Մատենագիտական մանրամասներ
Հիմնական հեղինակ: González Vasco, María Isabel
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Հրապարակվել է: MDPI - Multidisciplinary Digital Publishing Institute 2021
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Առցանց հասանելիություն:46039
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author González Vasco, María Isabel
author_browse González Vasco, María Isabel
author_facet González Vasco, María Isabel
author_sort González Vasco, María Isabel
collection Directory of Open Access Books
description 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.
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language eng
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publisherStr MDPI - Multidisciplinary Digital Publishing Institute
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spelling doab-20.500.12854ir-504572023-12-20T18:40:40Z Interactions between Group Theory, Symmetry and Cryptology González Vasco, María Isabel QA1-939 Q1-390 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 bic Book Industry Communication::P Mathematics & science 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. 2021-02-11T16:27:51Z 2021-02-11T16:27:51Z 2020-06-09 16:38:57 2020 book 46039 9783039288038 9783039288021 https://directory.doabooks.org/handle/20.500.12854/50457 eng application/octet-stream Attribution-NonCommercial-NoDerivatives 4.0 International https://mdpi.com/books/pdfview/book/2232 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03928-803-8 10.3390/books978-3-03928-803-8 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783039288038 9783039288021 164 open access
spellingShingle QA1-939
Q1-390
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
bic Book Industry Communication::P Mathematics & science
González Vasco, María Isabel
Interactions between Group Theory, Symmetry and Cryptology
title Interactions between Group Theory, Symmetry and Cryptology
title_full Interactions between Group Theory, Symmetry and Cryptology
title_fullStr Interactions between Group Theory, Symmetry and Cryptology
title_full_unstemmed Interactions between Group Theory, Symmetry and Cryptology
title_short Interactions between Group Theory, Symmetry and Cryptology
title_sort interactions between group theory symmetry and cryptology
topic QA1-939
Q1-390
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
bic Book Industry Communication::P Mathematics & science
topic_facet QA1-939
Q1-390
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
bic Book Industry Communication::P Mathematics & science
url 46039
work_keys_str_mv AT gonzalezvascomariaisabel interactionsbetweengrouptheorysymmetryandcryptology