| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910817177003321 |
|
|
Titolo |
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] |
|
©2004 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (186 p.) |
|
|
|
|
|
|
Collana |
|
Contemporary mathematics, , 0271-4132 ; ; 360 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Group theory |
Mathematical statistics |
Cryptography |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Description based upon print version of record. |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references. |
|
|
|
|
|
|
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"" |
|
|
|
|
|
| |