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Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors
| Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (186 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory
Mathematical statistics Cryptography |
| ISBN | 0-8218-7950-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""On power- and commutation transitive, power commutative, and restricted Gromov groups""; ""Braid-based cryptography""; ""1. Background on braids""; ""1.1. Braid groups""; ""1.2. The greedy normal form""; ""1.3. Implementation of braids""; ""2. Braid-based schemes""; ""2.1. Key exchange""; ""2.2. Enciphering�deciphering""; ""2.3. Authentication""; ""2.4. Signature""; ""3. Attacks against the braid schemes""; ""3.1. Solutions to the Conjugacy Problem""; ""3.2. Attacks based on length""; ""3.3. Attacks based on linear representations""
""3.4. Are these attacks dangerous?""""4. Clues for further research""; ""4.1. Key generation""; ""4.2. Random drawing and security proofs""; ""4.3. Using braid words and braid reduction""; ""4.4. Hash functions""; ""4.5. Resorting to other braid problems""; ""5. Conclusion""; ""Discriminating and squarelike groups I: Axiomatics""; ""The density of small words in a free group is 0""; ""Braid groups and Aut(F2) are not rigid""; ""On varieties of groups in which all periodic groups are abelian""; ""Subgroups of fully residually free groups: algorithmic problems""; ""1. Introduction"" ""2. Preliminaries""""3. Intersection of two finitely generated subgroups of FZ[t]""; ""4. Properties of intersections of finitely generated subgroups of FZ[t]""; ""5. Centralizers in finitely generated fully residually free groups""; ""6. Conjugacy problem in finitely generated subgroups of FZ[t]""; ""References""; ""Weak hyperbolicity and free constructions""; ""Some properties of the conjugacy class growth function""; ""Boundary test elements""; ""Geodesics in the braid group on three strands""; ""Remarks on the growth of inverse semigroups"" ""Assessing security of some group based cryptosystems"" |
| Record Nr. | UNINA-9910788667803321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors
| Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (186 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory
Mathematical statistics Cryptography |
| ISBN | 0-8218-7950-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""On power- and commutation transitive, power commutative, and restricted Gromov groups""; ""Braid-based cryptography""; ""1. Background on braids""; ""1.1. Braid groups""; ""1.2. The greedy normal form""; ""1.3. Implementation of braids""; ""2. Braid-based schemes""; ""2.1. Key exchange""; ""2.2. Enciphering�deciphering""; ""2.3. Authentication""; ""2.4. Signature""; ""3. Attacks against the braid schemes""; ""3.1. Solutions to the Conjugacy Problem""; ""3.2. Attacks based on length""; ""3.3. Attacks based on linear representations""
""3.4. Are these attacks dangerous?""""4. Clues for further research""; ""4.1. Key generation""; ""4.2. Random drawing and security proofs""; ""4.3. Using braid words and braid reduction""; ""4.4. Hash functions""; ""4.5. Resorting to other braid problems""; ""5. Conclusion""; ""Discriminating and squarelike groups I: Axiomatics""; ""The density of small words in a free group is 0""; ""Braid groups and Aut(F2) are not rigid""; ""On varieties of groups in which all periodic groups are abelian""; ""Subgroups of fully residually free groups: algorithmic problems""; ""1. Introduction"" ""2. Preliminaries""""3. Intersection of two finitely generated subgroups of FZ[t]""; ""4. Properties of intersections of finitely generated subgroups of FZ[t]""; ""5. Centralizers in finitely generated fully residually free groups""; ""6. Conjugacy problem in finitely generated subgroups of FZ[t]""; ""References""; ""Weak hyperbolicity and free constructions""; ""Some properties of the conjugacy class growth function""; ""Boundary test elements""; ""Geodesics in the braid group on three strands""; ""Remarks on the growth of inverse semigroups"" ""Assessing security of some group based cryptosystems"" |
| Record Nr. | UNINA-9910817177003321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
