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Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University
- Author / Creator
- Conferences
- AMS Special Session Combinatorial and Statistical Group Theory (2003 : New York University)
- Available as
- Online
Details
- Creator
- Alexei G. Myasnikov, Vladimir Shpilrain, editors
- Format
- Books
- Language
- English
- Publication
-
- Providence, Rhode Island : American Mathematical Society, [2004]
- ©2004
- Physical Details
-
- 1 online resource (186 p.)
- ISBNs
- 9780821856956, 0821879502, 9780821879504, 0821856952, 0821834444, 9780821834442
- OCLC
- ocn774694976
- Description based upon print version of record.
- Includes bibliographical references.
- English
- ""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""