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Book
Interactions between Group Theory, Symmetry and Cryptology
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ISBN: 3039288032 3039288024 Year: 2020 Publisher: MDPI - Multidisciplinary Digital Publishing Institute

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Abstract

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.


Book
Theoretical Computer Science and Discrete Mathematics
Authors: ---
Year: 2022 Publisher: Basel MDPI - Multidisciplinary Digital Publishing Institute

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Abstract

This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity.

Keywords

Research & information: general --- Mathematics & science --- fuzzy set --- n-Pythagorean --- n-PFS algebra --- triangular norms --- outer-independent Roman domination --- Roman domination --- vertex cover --- rooted product graph --- total domination --- domination --- secure domination --- secure Italian domination --- weak roman domination --- w-domination --- cryptanalysis --- group key establishment --- topology optimization --- optimization --- filtering --- method --- penalization --- weight factor --- FEM --- MATLAB --- SIMP --- estimated prime factor --- integer factorisation problem --- continued fraction --- Fermat’s Factoring Algorithm --- genetic algorithm --- AES(t) --- heuristics --- microaggregation --- statistical disclosure control --- graph theory --- traveling salesman problem --- data privacy --- location privacy --- differentials in graphs --- strong differential --- quasi-total strong differential --- quasi-total Italian domination number --- numerical semigroup --- forest --- ordinarization transform --- quasi-ordinarization transform --- load redistribution --- leveling power consumption per phase --- three-phase asymmetric distribution networks --- ideal power consumption --- mixed-integer convex optimization --- strongly total Roman domination --- total Roman domination --- lexicographic product graph --- improved crow search algorithm --- normal Gaussian distribution --- phase swapping problem --- power losses --- asymmetric distribution grids --- vortex search algorithm --- nonidentical parallel production lines --- axle housing machining --- mixed model production --- eligibility constraint --- fuzzy due date --- grey wolf optimizer --- n/a --- Fermat's Factoring Algorithm


Book
Theoretical Computer Science and Discrete Mathematics
Authors: ---
Year: 2022 Publisher: Basel MDPI - Multidisciplinary Digital Publishing Institute

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Abstract

This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity.

Keywords

fuzzy set --- n-Pythagorean --- n-PFS algebra --- triangular norms --- outer-independent Roman domination --- Roman domination --- vertex cover --- rooted product graph --- total domination --- domination --- secure domination --- secure Italian domination --- weak roman domination --- w-domination --- cryptanalysis --- group key establishment --- topology optimization --- optimization --- filtering --- method --- penalization --- weight factor --- FEM --- MATLAB --- SIMP --- estimated prime factor --- integer factorisation problem --- continued fraction --- Fermat’s Factoring Algorithm --- genetic algorithm --- AES(t) --- heuristics --- microaggregation --- statistical disclosure control --- graph theory --- traveling salesman problem --- data privacy --- location privacy --- differentials in graphs --- strong differential --- quasi-total strong differential --- quasi-total Italian domination number --- numerical semigroup --- forest --- ordinarization transform --- quasi-ordinarization transform --- load redistribution --- leveling power consumption per phase --- three-phase asymmetric distribution networks --- ideal power consumption --- mixed-integer convex optimization --- strongly total Roman domination --- total Roman domination --- lexicographic product graph --- improved crow search algorithm --- normal Gaussian distribution --- phase swapping problem --- power losses --- asymmetric distribution grids --- vortex search algorithm --- nonidentical parallel production lines --- axle housing machining --- mixed model production --- eligibility constraint --- fuzzy due date --- grey wolf optimizer --- n/a --- Fermat's Factoring Algorithm


Book
Theoretical Computer Science and Discrete Mathematics
Authors: ---
Year: 2022 Publisher: Basel MDPI - Multidisciplinary Digital Publishing Institute

Loading...
Export citation

Choose an application

Bookmark

Abstract

This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity.

Keywords

Research & information: general --- Mathematics & science --- fuzzy set --- n-Pythagorean --- n-PFS algebra --- triangular norms --- outer-independent Roman domination --- Roman domination --- vertex cover --- rooted product graph --- total domination --- domination --- secure domination --- secure Italian domination --- weak roman domination --- w-domination --- cryptanalysis --- group key establishment --- topology optimization --- optimization --- filtering --- method --- penalization --- weight factor --- FEM --- MATLAB --- SIMP --- estimated prime factor --- integer factorisation problem --- continued fraction --- Fermat's Factoring Algorithm --- genetic algorithm --- AES(t) --- heuristics --- microaggregation --- statistical disclosure control --- graph theory --- traveling salesman problem --- data privacy --- location privacy --- differentials in graphs --- strong differential --- quasi-total strong differential --- quasi-total Italian domination number --- numerical semigroup --- forest --- ordinarization transform --- quasi-ordinarization transform --- load redistribution --- leveling power consumption per phase --- three-phase asymmetric distribution networks --- ideal power consumption --- mixed-integer convex optimization --- strongly total Roman domination --- total Roman domination --- lexicographic product graph --- improved crow search algorithm --- normal Gaussian distribution --- phase swapping problem --- power losses --- asymmetric distribution grids --- vortex search algorithm --- nonidentical parallel production lines --- axle housing machining --- mixed model production --- eligibility constraint --- fuzzy due date --- grey wolf optimizer

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