Applications of Group Theory in Cryptography: Post-Quantum Group-based Cryptography
This book is intended as a comprehensive treatment of group-based cryptography accessible to both mathematicians and computer scientists, with emphasis on the most recent developments in the area. To make it accessible to a broad range of readers, the authors started with a treatment of elementary t...
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2024
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| Ausgabe: | 1st ed |
| Schriftenreihe: | Mathematical Surveys and Monographs
v.278 |
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| Online-Zugang: | DE-2070s |
| Zusammenfassung: | This book is intended as a comprehensive treatment of group-based cryptography accessible to both mathematicians and computer scientists, with emphasis on the most recent developments in the area. To make it accessible to a broad range of readers, the authors started with a treatment of elementary topics in group theory, combinatorics, and complexity theory, as well as providing an overview of classical public-key cryptography. Then some algorithmic problems arising in group theory are presented, and cryptosystems based on these problems and their respective cryptanalyses are described. The book also provides an introduction to ideas in quantum cryptanalysis, especially with respect to the goal of post-quantum group-based cryptography as a candidate for quantum-resistant cryptography.The final part of the book provides a description of various classes of groups and their suitability as platforms for group-based cryptography. The book is a monograph addressed to graduate students and researchers in both mathematics and computer science |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 Online-Ressource (162 Seiten) |
| ISBN: | 9781470476212 |
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| 505 | 8 | |a Cover -- Title page -- Contents -- Introduction -- Acknowledgments -- Notation -- Part 1. Background Information -- Chapter 1. Group Theory -- 1.1. Introduction -- 1.2. Basic definitions and examples -- 1.3. Examples of groups -- 1.4. Subgroups and order of elements -- 1.5. Normal subgroups and quotients -- 1.6. Group actions -- 1.7. Extensions -- 1.8. Nilpotent groups -- Chapter 2. Algorithmic Problems in Group Theory -- 2.1. Introduction -- 2.2. Combinatorial group theory -- 2.3. Decision problems in groups -- 2.4. Search problems -- 2.5. Algorithmic problems in graphs and groups -- 2.6. Other problems in groups -- Chapter 3. Classical Cryptography -- 3.1. Introduction -- 3.2. Digital signature schemes -- 3.3. Secret sharing schemes -- 3.4. Multilinear maps -- Part 2. Post-quantum Cryptography and Cryptanalysis -- Chapter 4. Noncommutative Cryptographic Protocols -- 4.1. Noncommutative key exchange protocols -- 4.2. Noncommutative digital signatures -- 4.3. Noncommutative secret sharing schemes -- Chapter 5. Attacks -- 5.1. Introduction -- 5.2. Length-based attack -- 5.3. Linear centralizer attack -- 5.4. Linear decomposition attack -- 5.5. Quotient attack -- Chapter 6. Quantum Cryptanalysis -- 6.1. Introduction -- 6.2. The hidden subgroup problem -- 6.3. Relation of HSP to other computational problems -- 6.4. Quantum cryptanalysis for group-based PQC -- Part 3. Cryptographic Platforms -- Chapter 7. Braid Groups -- 7.1. Introduction -- 7.2. Mathematical background -- 7.3. Algorithmic problems -- 7.4. Cryptographic protocols -- Chapter 8. Hyperbolic Groups -- 8.1. Introduction -- 8.2. Mathematical background -- 8.3. Algorithmic problems -- 8.4. Cryptographic protocols -- Chapter 9. Small Cancellation Groups -- 9.1. Introduction -- 9.2. Mathematical background -- 9.3. Algorithmic problems -- 9.4. Cryptographic protocols | |
| 505 | 8 | |a Chapter 10. Polycyclic Groups -- 10.1. Introduction -- 10.2. Mathematical background -- 10.3. Algorithmic problems -- 10.4. Cryptographic protocols -- Chapter 11. Graph Groups -- 11.1. Introduction -- 11.2. Mathematical background -- 11.3. Algorithmic problems -- 11.4. Cryptographic protocols -- 11.5. Interesting problems -- Chapter 12. Arithmetic Groups -- 12.1. Introduction -- 12.2. Mathematical background -- 12.3. Algorithmic problems -- 12.4. The protocol -- Chapter 13. Engel Groups -- 13.1. Introduction -- 13.2. Mathematical background -- 13.3. Cryptographic protocols -- 13.4. Interesting problems -- Chapter 14. Self-Similar Groups -- 14.1. Introduction -- 14.2. Mathematical background -- 14.3. Algorithmic problems -- 14.4. Cryptographic protocols -- Bibliography -- Index -- Back Cover | |
| 520 | |a This book is intended as a comprehensive treatment of group-based cryptography accessible to both mathematicians and computer scientists, with emphasis on the most recent developments in the area. To make it accessible to a broad range of readers, the authors started with a treatment of elementary topics in group theory, combinatorics, and complexity theory, as well as providing an overview of classical public-key cryptography. Then some algorithmic problems arising in group theory are presented, and cryptosystems based on these problems and their respective cryptanalyses are described. The book also provides an introduction to ideas in quantum cryptanalysis, especially with respect to the goal of post-quantum group-based cryptography as a candidate for quantum-resistant cryptography.The final part of the book provides a description of various classes of groups and their suitability as platforms for group-based cryptography. The book is a monograph addressed to graduate students and researchers in both mathematics and computer science | ||
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| contents | Cover -- Title page -- Contents -- Introduction -- Acknowledgments -- Notation -- Part 1. Background Information -- Chapter 1. Group Theory -- 1.1. Introduction -- 1.2. Basic definitions and examples -- 1.3. Examples of groups -- 1.4. Subgroups and order of elements -- 1.5. Normal subgroups and quotients -- 1.6. Group actions -- 1.7. Extensions -- 1.8. Nilpotent groups -- Chapter 2. Algorithmic Problems in Group Theory -- 2.1. Introduction -- 2.2. Combinatorial group theory -- 2.3. Decision problems in groups -- 2.4. Search problems -- 2.5. Algorithmic problems in graphs and groups -- 2.6. Other problems in groups -- Chapter 3. Classical Cryptography -- 3.1. Introduction -- 3.2. Digital signature schemes -- 3.3. Secret sharing schemes -- 3.4. Multilinear maps -- Part 2. Post-quantum Cryptography and Cryptanalysis -- Chapter 4. Noncommutative Cryptographic Protocols -- 4.1. Noncommutative key exchange protocols -- 4.2. Noncommutative digital signatures -- 4.3. Noncommutative secret sharing schemes -- Chapter 5. Attacks -- 5.1. Introduction -- 5.2. Length-based attack -- 5.3. Linear centralizer attack -- 5.4. Linear decomposition attack -- 5.5. Quotient attack -- Chapter 6. Quantum Cryptanalysis -- 6.1. Introduction -- 6.2. The hidden subgroup problem -- 6.3. Relation of HSP to other computational problems -- 6.4. Quantum cryptanalysis for group-based PQC -- Part 3. Cryptographic Platforms -- Chapter 7. Braid Groups -- 7.1. Introduction -- 7.2. Mathematical background -- 7.3. Algorithmic problems -- 7.4. Cryptographic protocols -- Chapter 8. Hyperbolic Groups -- 8.1. Introduction -- 8.2. Mathematical background -- 8.3. Algorithmic problems -- 8.4. Cryptographic protocols -- Chapter 9. Small Cancellation Groups -- 9.1. Introduction -- 9.2. Mathematical background -- 9.3. Algorithmic problems -- 9.4. Cryptographic protocols Chapter 10. Polycyclic Groups -- 10.1. Introduction -- 10.2. Mathematical background -- 10.3. Algorithmic problems -- 10.4. Cryptographic protocols -- Chapter 11. Graph Groups -- 11.1. Introduction -- 11.2. Mathematical background -- 11.3. Algorithmic problems -- 11.4. Cryptographic protocols -- 11.5. Interesting problems -- Chapter 12. Arithmetic Groups -- 12.1. Introduction -- 12.2. Mathematical background -- 12.3. Algorithmic problems -- 12.4. The protocol -- Chapter 13. Engel Groups -- 13.1. Introduction -- 13.2. Mathematical background -- 13.3. Cryptographic protocols -- 13.4. Interesting problems -- Chapter 14. Self-Similar Groups -- 14.1. Introduction -- 14.2. Mathematical background -- 14.3. Algorithmic problems -- 14.4. Cryptographic protocols -- Bibliography -- Index -- Back Cover |
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| spelling | Kahrobaei, Delaram Verfasser aut Applications of Group Theory in Cryptography Post-Quantum Group-based Cryptography 1st ed Providence American Mathematical Society 2024 ©2024 1 Online-Ressource (162 Seiten) txt rdacontent c rdamedia cr rdacarrier Mathematical Surveys and Monographs v.278 Description based on publisher supplied metadata and other sources Cover -- Title page -- Contents -- Introduction -- Acknowledgments -- Notation -- Part 1. Background Information -- Chapter 1. Group Theory -- 1.1. Introduction -- 1.2. Basic definitions and examples -- 1.3. Examples of groups -- 1.4. Subgroups and order of elements -- 1.5. Normal subgroups and quotients -- 1.6. Group actions -- 1.7. Extensions -- 1.8. Nilpotent groups -- Chapter 2. Algorithmic Problems in Group Theory -- 2.1. Introduction -- 2.2. Combinatorial group theory -- 2.3. Decision problems in groups -- 2.4. Search problems -- 2.5. Algorithmic problems in graphs and groups -- 2.6. Other problems in groups -- Chapter 3. Classical Cryptography -- 3.1. Introduction -- 3.2. Digital signature schemes -- 3.3. Secret sharing schemes -- 3.4. Multilinear maps -- Part 2. Post-quantum Cryptography and Cryptanalysis -- Chapter 4. Noncommutative Cryptographic Protocols -- 4.1. Noncommutative key exchange protocols -- 4.2. Noncommutative digital signatures -- 4.3. Noncommutative secret sharing schemes -- Chapter 5. Attacks -- 5.1. Introduction -- 5.2. Length-based attack -- 5.3. Linear centralizer attack -- 5.4. Linear decomposition attack -- 5.5. Quotient attack -- Chapter 6. Quantum Cryptanalysis -- 6.1. Introduction -- 6.2. The hidden subgroup problem -- 6.3. Relation of HSP to other computational problems -- 6.4. Quantum cryptanalysis for group-based PQC -- Part 3. Cryptographic Platforms -- Chapter 7. Braid Groups -- 7.1. Introduction -- 7.2. Mathematical background -- 7.3. Algorithmic problems -- 7.4. Cryptographic protocols -- Chapter 8. Hyperbolic Groups -- 8.1. Introduction -- 8.2. Mathematical background -- 8.3. Algorithmic problems -- 8.4. Cryptographic protocols -- Chapter 9. Small Cancellation Groups -- 9.1. Introduction -- 9.2. Mathematical background -- 9.3. Algorithmic problems -- 9.4. Cryptographic protocols Chapter 10. Polycyclic Groups -- 10.1. Introduction -- 10.2. Mathematical background -- 10.3. Algorithmic problems -- 10.4. Cryptographic protocols -- Chapter 11. Graph Groups -- 11.1. Introduction -- 11.2. Mathematical background -- 11.3. Algorithmic problems -- 11.4. Cryptographic protocols -- 11.5. Interesting problems -- Chapter 12. Arithmetic Groups -- 12.1. Introduction -- 12.2. Mathematical background -- 12.3. Algorithmic problems -- 12.4. The protocol -- Chapter 13. Engel Groups -- 13.1. Introduction -- 13.2. Mathematical background -- 13.3. Cryptographic protocols -- 13.4. Interesting problems -- Chapter 14. Self-Similar Groups -- 14.1. Introduction -- 14.2. Mathematical background -- 14.3. Algorithmic problems -- 14.4. Cryptographic protocols -- Bibliography -- Index -- Back Cover This book is intended as a comprehensive treatment of group-based cryptography accessible to both mathematicians and computer scientists, with emphasis on the most recent developments in the area. To make it accessible to a broad range of readers, the authors started with a treatment of elementary topics in group theory, combinatorics, and complexity theory, as well as providing an overview of classical public-key cryptography. Then some algorithmic problems arising in group theory are presented, and cryptosystems based on these problems and their respective cryptanalyses are described. The book also provides an introduction to ideas in quantum cryptanalysis, especially with respect to the goal of post-quantum group-based cryptography as a candidate for quantum-resistant cryptography.The final part of the book provides a description of various classes of groups and their suitability as platforms for group-based cryptography. The book is a monograph addressed to graduate students and researchers in both mathematics and computer science Group theory Cryptography Flores, Ramón Sonstige oth Noce, Marialaura Sonstige oth Erscheint auch als Druck-Ausgabe Kahrobaei, Delaram Applications of Group Theory in Cryptography Providence : American Mathematical Society,c2024 9781470474690 |
| spellingShingle | Kahrobaei, Delaram Applications of Group Theory in Cryptography Post-Quantum Group-based Cryptography Cover -- Title page -- Contents -- Introduction -- Acknowledgments -- Notation -- Part 1. Background Information -- Chapter 1. Group Theory -- 1.1. Introduction -- 1.2. Basic definitions and examples -- 1.3. Examples of groups -- 1.4. Subgroups and order of elements -- 1.5. Normal subgroups and quotients -- 1.6. Group actions -- 1.7. Extensions -- 1.8. Nilpotent groups -- Chapter 2. Algorithmic Problems in Group Theory -- 2.1. Introduction -- 2.2. Combinatorial group theory -- 2.3. Decision problems in groups -- 2.4. Search problems -- 2.5. Algorithmic problems in graphs and groups -- 2.6. Other problems in groups -- Chapter 3. Classical Cryptography -- 3.1. Introduction -- 3.2. Digital signature schemes -- 3.3. Secret sharing schemes -- 3.4. Multilinear maps -- Part 2. Post-quantum Cryptography and Cryptanalysis -- Chapter 4. Noncommutative Cryptographic Protocols -- 4.1. Noncommutative key exchange protocols -- 4.2. Noncommutative digital signatures -- 4.3. Noncommutative secret sharing schemes -- Chapter 5. Attacks -- 5.1. Introduction -- 5.2. Length-based attack -- 5.3. Linear centralizer attack -- 5.4. Linear decomposition attack -- 5.5. Quotient attack -- Chapter 6. Quantum Cryptanalysis -- 6.1. Introduction -- 6.2. The hidden subgroup problem -- 6.3. Relation of HSP to other computational problems -- 6.4. Quantum cryptanalysis for group-based PQC -- Part 3. Cryptographic Platforms -- Chapter 7. Braid Groups -- 7.1. Introduction -- 7.2. Mathematical background -- 7.3. Algorithmic problems -- 7.4. Cryptographic protocols -- Chapter 8. Hyperbolic Groups -- 8.1. Introduction -- 8.2. Mathematical background -- 8.3. Algorithmic problems -- 8.4. Cryptographic protocols -- Chapter 9. Small Cancellation Groups -- 9.1. Introduction -- 9.2. Mathematical background -- 9.3. Algorithmic problems -- 9.4. Cryptographic protocols Chapter 10. Polycyclic Groups -- 10.1. Introduction -- 10.2. Mathematical background -- 10.3. Algorithmic problems -- 10.4. Cryptographic protocols -- Chapter 11. Graph Groups -- 11.1. Introduction -- 11.2. Mathematical background -- 11.3. Algorithmic problems -- 11.4. Cryptographic protocols -- 11.5. Interesting problems -- Chapter 12. Arithmetic Groups -- 12.1. Introduction -- 12.2. Mathematical background -- 12.3. Algorithmic problems -- 12.4. The protocol -- Chapter 13. Engel Groups -- 13.1. Introduction -- 13.2. Mathematical background -- 13.3. Cryptographic protocols -- 13.4. Interesting problems -- Chapter 14. Self-Similar Groups -- 14.1. Introduction -- 14.2. Mathematical background -- 14.3. Algorithmic problems -- 14.4. Cryptographic protocols -- Bibliography -- Index -- Back Cover Group theory Cryptography |
| title | Applications of Group Theory in Cryptography Post-Quantum Group-based Cryptography |
| title_auth | Applications of Group Theory in Cryptography Post-Quantum Group-based Cryptography |
| title_exact_search | Applications of Group Theory in Cryptography Post-Quantum Group-based Cryptography |
| title_full | Applications of Group Theory in Cryptography Post-Quantum Group-based Cryptography |
| title_fullStr | Applications of Group Theory in Cryptography Post-Quantum Group-based Cryptography |
| title_full_unstemmed | Applications of Group Theory in Cryptography Post-Quantum Group-based Cryptography |
| title_short | Applications of Group Theory in Cryptography |
| title_sort | applications of group theory in cryptography post quantum group based cryptography |
| title_sub | Post-Quantum Group-based Cryptography |
| topic | Group theory Cryptography |
| topic_facet | Group theory Cryptography |
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