Group-based cryptography/ (Record no. 179837)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 00353nam a2200145Ia 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 3764388269 |
| 040 ## - CATALOGING SOURCE | |
| Transcribing agency | CUS |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.2 |
| Item number | MYA/G |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Myasnikov, Alexei |
| 245 #0 - TITLE STATEMENT | |
| Title | Group-based cryptography/ |
| Statement of responsibility, etc. | Alexei Myasnikov |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2008 |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | Boston: |
| Name of publisher, distributor, etc. | Birkhäuser, |
| Date of publication, distribution, etc. | 2008. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 183 p. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | I Background on Groups, Complexity, and Cryptography 1<br/>1 Background on Public Key Cryptography 3<br/>1.1 Prom key establishment to encryption 4<br/>1.2 The DifFIe-Hellman key establishment 5<br/>1.3 The ElGamal cryptosystem 6<br/>1.4 Authentication 7<br/>2 Background on Combinatorial Group Theory 9<br/>2.1 Basic definitions and notation 9<br/>2.2 Presentations of groups by generators and relators 11<br/>2.3 Algorithmic problems of group theory 11<br/>2.3.1 The word problem 11<br/>2.3.2 The conjugacy problem 12<br/>2.3.3 The decomposition and factorization problems 12<br/>2.3.4 The membership problem 13<br/>2.3.5 The isomorphism problem 14<br/>2.4 Nielsen's and Schreier's methods 14<br/>2.5 Tietze's method 16<br/>2.6<br/>Normal forms 17<br/>3 Background On Computational Complexity 19<br/>3.1 Algorithms 19<br/>3.1.1 Deterministic Turing machines •: • • • 19<br/>3.1.2 Non-deterministic Turing machines 20<br/>3.1.3 Probabilistic Turing machines 21<br/>3.2 Computational problems 21<br/>3.2.1 Decision and search computational problems 21<br/>3.3<br/>3.2.2<br/>Size functions<br/>3.2.3<br/>Stratification<br/>3.2.4<br/>Reductions and complete problems<br/>3.2.5<br/>Many-one reductions<br/>3.2.6<br/>Turing reductions<br/>The worst case complexity<br/>3.3.1<br/>Complexity classes<br/>3.3.2<br/>Class NP<br/>3.3.3<br/>Polynomial-time many-one reductions and class NP<br/>3.3.4<br/>NP-complete problems<br/>3.3.5<br/>Deficiency of the worst case complexity<br/>II Non-commutative Cryptography 35<br/>4 Canonical Non-commutative Cryptography .37<br/>4.1 Protocols based on the conjugacy search problem 37<br/>4.2 Protocols based on the decomposition problem 39<br/>4.2.1 "Twisted" protocol 40<br/>4.2.2 Hiding one of the subgroups 41<br/>4.2.3 Using the triple decomposition problem 42<br/>4.3 A protocol based on the factorization search problem 43<br/>4.4 Stickel's key exchange protocol 43<br/>4.4.1 Linear algebra<br/>attack 45<br/>4.5 The Anshel-Anshel-Goldfeld protocol 47<br/>4.6 Authentication protocols based on the conjugacy problem 49<br/>4.6.1 A Diffie-Hellman-like scheme 49<br/>4.6.2 A Fiat-Shamir-like scheme 50<br/>4.6.3 An authentication scheme based on the twisted conjugacy<br/>problem 5I<br/>4.7 Relations between different problems 52<br/>5 Platform Groups 55<br/>5.1 Braid groups 55<br/>5.1.1 A group of braids and its presentation 56<br/>5.1.2 Dehornoy handle free form 59<br/>5.1.3 Garside normal form 50<br/>5.2<br/>Thompson's group 61<br/>5.3 Groups of matrices 65<br/>5.4 Small cancellation groups 67<br/>5.4.1 Dehn's algorithm 67<br/>5.5 Solvable groups 68<br/>5.5.1 Normal forms in free metabelian groups 68<br/>5.6 Artin groups 71<br/>Contents<br/>.Grigorchuk group 72<br/>6 Using Decision Problems in Public Key Cryptography 77<br/>6.1 The Shpilrain-Zapata scheme 78<br/>6.1.1<br/>The protocol 78<br/>6.1.2 Pool of<br/>group presentations 81<br/>6.1.3 Tietze transformations: elementary isomorphisms 82<br/>6.1.4 Generating random elements in finitely presented groups . . 84<br/>6.1.5 Isomorphism attack 87<br/>6.1.6 Quotient attack 88<br/>6.2 Public key encryption and encryption emulation attacks 89<br/>III Generic Complexity and Cryptanalysis 95<br/>7 Distributional Problems and the Average Case Complexity 99<br/>7.1 Distributional computational problems 99<br/>7.1.1 Distributions and computational problems 99<br/>7.1.2 Stratified problems with ensembles of distributions 101<br/>7.1.3 Randomized many-one reductions 102<br/>7.2 Average case complexity 103<br/>7.2.1 Polynomial on average functions 103<br/>7.2.2 Average case behavior of functions 109<br/>7.2.3 Average case complexity of algorithms 109<br/>7.2.4 Average case vs worst case 110<br/>7.2.5 Average case behavior as a trade-off Ill<br/>7.2.6 Deficiency of average case complexity 114<br/>8 Generic Case Complexity 117<br/>8.1 Generic Complexity 117<br/>8.1.1 Generic sets 117<br/>8.1.2 Asymptotic density 118<br/>8.1.3 Convergence rates 120<br/>8.1.4 Generic complexity of algorithms and algorithmic problems 121<br/>8.1.5 Deficiency of<br/>the generic complexity 122<br/>8.2 Generic- versus average case complexity 123<br/>8.2.1 Comparing generic and average case complexities ....... 123<br/>8.2.2 When average polynomial time implies generic polynomial<br/>time 124<br/>8.2.3 When generically easy implies easy on average 125<br/>Generic Complexity of NP-complete Problems 129<br/>9.1 The linear generic time complexity of subset sum problem 129<br/>9.2 A practical algorithm for subset sum problem 131<br/>9.3 3-Satisfiability 131<br/>IV Asymptotically Dominant Properties and Cryptanalysis 135<br/>10 Asymptotically Dominant Properties 139<br/>10.1 A brief description 139<br/>10.2 Random subgroups and generating tuples 141<br/>10.3 Asymptotic properties of subgroups 142<br/>10.4 Groups with generic free basis property 143<br/>10.5 Quasi-isometrically<br/>embedded subgroups 145<br/>11<br/>Length-Based and Quotient Attacks 149<br/>11.1 Anshel-Anshel-Goldfeld scheme 149<br/>11.1.1 Description of the Anshel-Anshel-Goldfeld scheme 149<br/>11.1.2 Security assumptions of the AAG scheme 150<br/>11.2 Length-based attacks 152<br/>11.2.1 A general description 152<br/>11.2.2 LBA in free groups 155<br/>11.2.3 LBA in groups from J^Bexp 156<br/>11.3 Computing the geodesic length in a subgroup 157<br/>11.3.1 Related algorithmic problems 158<br/>11.3.2 Geodesic<br/>length in braid groups 159<br/>11.4<br/>Quotient attacks 161<br/>11.4.1 Membership problems in free groups 162<br/>11.4.2 Conjugacy problems in free groups 164<br/>11.4.3 The MSP and SCSP* problems in groups with "good" quo<br/>tients 167<br/> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | General Books |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Date acquired | Full call number | Accession number | Date last seen | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 29/08/2016 | 512.2 MYA/G | P34848 | 29/08/2016 | General Books |