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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MDPI - Multidisciplinary Digital Publishing Institute
2021
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| _version_ | 1869531550321737728 |
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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. |
| format | Online |
| id | doab-20.500.12854ir-50457 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| 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 |