LEADER 03754nam 2200625 450 001 9910817177003321 005 20170814182155.0 010 $a0-8218-7950-2 035 $a(CKB)3240000000069886 035 $a(EBL)3113281 035 $a(SSID)ssj0000712524 035 $a(PQKBManifestationID)11407519 035 $a(PQKBTitleCode)TC0000712524 035 $a(PQKBWorkID)10644608 035 $a(PQKB)10248295 035 $a(MiAaPQ)EBC3113281 035 $a(WaSeSS)Ind00039627 035 $a(RPAM)13597089 035 $a(PPN)197106870 035 $a(EXLCZ)993240000000069886 100 $a20040518h20042004 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGroup theory, statistics, and cryptography $eAMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University /$fAlexei G. Myasnikov, Vladimir Shpilrain, editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2004] 210 4$dİ2004 215 $a1 online resource (186 p.) 225 1 $aContemporary mathematics,$x0271-4132 ;$v360 300 $aDescription based upon print version of record. 311 $a0-8218-3444-4 320 $aIncludes bibliographical references. 327 $a""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. Encipheringa???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"" 327 $a""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"" 327 $a""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"" 327 $a""Assessing security of some group based cryptosystems"" 410 0$aContemporary mathematics (American Mathematical Society) ;$v360. 606 $aGroup theory$vCongresses 606 $aMathematical statistics$vCongresses 606 $aCryptography$vCongresses 615 0$aGroup theory 615 0$aMathematical statistics 615 0$aCryptography 676 $a512/.2 702 $aMyasnikov$b Alexei G.$f1955- 702 $aShpilrain$b Vladimir$f1960- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817177003321 996 $aGroup theory statistics and cryptography$9752450 997 $aUNINA