03754nam 2200625 450 991078866780332120170814182155.00-8218-7950-2(CKB)3240000000069886(EBL)3113281(SSID)ssj0000712524(PQKBManifestationID)11407519(PQKBTitleCode)TC0000712524(PQKBWorkID)10644608(PQKB)10248295(MiAaPQ)EBC3113281(WaSeSS)Ind00039627(RPAM)13597089(PPN)197106870(EXLCZ)99324000000006988620040518h20042004 uy| 0engur|n|---|||||txtccrGroup theory, statistics, and cryptography AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University /Alexei G. Myasnikov, Vladimir Shpilrain, editorsProvidence, Rhode Island :American Mathematical Society,[2004]©20041 online resource (186 p.)Contemporary mathematics,0271-4132 ;360Description based upon print version of record.0-8218-3444-4 Includes bibliographical references.""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. Encipheringâ€?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""Contemporary mathematics (American Mathematical Society) ;360.Group theoryCongressesMathematical statisticsCongressesCryptographyCongressesGroup theoryMathematical statisticsCryptography512/.2Myasnikov Alexei G.1955-Shpilrain Vladimir1960-MiAaPQMiAaPQMiAaPQBOOK9910788667803321Group theory statistics and cryptography752450UNINA