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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| Format: | Book Chapter |
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MDPI - Multidisciplinary Digital Publishing Institute
2020
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| Online Access: | Get Fullteks DOAB: description of the publication |
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| LEADER | 03811naaaa2200709uu 4500 | ||
|---|---|---|---|
| 001 | doab_20_500_12854_50457 | ||
| 005 | 20210211 | ||
| 020 | |a books978-3-03928-803-8 | ||
| 020 | |a 9783039288038 | ||
| 020 | |a 9783039288021 | ||
| 024 | 7 | |a 10.3390/books978-3-03928-803-8 |c doi | |
| 041 | 0 | |a English | |
| 042 | |a dc | ||
| 100 | 1 | |a González Vasco, María Isabel |4 auth | |
| 245 | 1 | 0 | |a Interactions between Group Theory, Symmetry and Cryptology |
| 260 | |b MDPI - Multidisciplinary Digital Publishing Institute |c 2020 | ||
| 300 | |a 1 electronic resource (164 p.) | ||
| 506 | 0 | |a Open Access |2 star |f Unrestricted online access | |
| 520 | |a 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. | ||
| 540 | |a Creative Commons |f https://creativecommons.org/licenses/by-nc-nd/4.0/ |2 cc |4 https://creativecommons.org/licenses/by-nc-nd/4.0/ | ||
| 546 | |a English | ||
| 653 | |a NP-Completeness | ||
| 653 | |a protocol compiler | ||
| 653 | |a post-quantum cryptography | ||
| 653 | |a Reed-Solomon codes | ||
| 653 | |a key equation | ||
| 653 | |a euclidean algorithm | ||
| 653 | |a permutation group | ||
| 653 | |a t-modified self-shrinking generator | ||
| 653 | |a ideal cipher model | ||
| 653 | |a algorithms in groups | ||
| 653 | |a lightweight cryptography | ||
| 653 | |a generalized self-shrinking generator | ||
| 653 | |a numerical semigroup | ||
| 653 | |a pseudo-random number generator | ||
| 653 | |a symmetry | ||
| 653 | |a pseudorandom permutation | ||
| 653 | |a Berlekamp-Massey algorithm | ||
| 653 | |a semigroup ideal | ||
| 653 | |a algebraic-geometry code | ||
| 653 | |a non-commutative cryptography | ||
| 653 | |a provable security | ||
| 653 | |a Engel words | ||
| 653 | |a block cipher | ||
| 653 | |a cryptography | ||
| 653 | |a beyond birthday bound | ||
| 653 | |a Weierstrass semigroup | ||
| 653 | |a group theory | ||
| 653 | |a braid groups | ||
| 653 | |a statistical randomness tests | ||
| 653 | |a group-based cryptography | ||
| 653 | |a alternating group | ||
| 653 | |a WalnutDSA | ||
| 653 | |a Sugiyama et al. algorithm | ||
| 653 | |a cryptanalysis | ||
| 653 | |a digital signatures | ||
| 653 | |a one-way functions | ||
| 653 | |a key agreement protocol | ||
| 653 | |a error-correcting code | ||
| 653 | |a group key establishment | ||
| 856 | 4 | 0 | |a www.oapen.org |u https://mdpi.com/books/pdfview/book/2232 |7 0 |z Get Fullteks |
| 856 | 4 | 0 | |a www.oapen.org |u https://directory.doabooks.org/handle/20.500.12854/50457 |7 0 |z DOAB: description of the publication |