LEADER 06300nam 22007695 450 001 9910144154003321 005 20200702165759.0 010 $a3-540-24847-1 024 7 $a10.1007/b98210 035 $a(CKB)1000000000212427 035 $a(DE-He213)978-3-540-24847-7 035 $a(SSID)ssj0000101083 035 $a(PQKBManifestationID)11122006 035 $a(PQKBTitleCode)TC0000101083 035 $a(PQKBWorkID)10037371 035 $a(PQKB)10305078 035 $a(MiAaPQ)EBC3088003 035 $a(PPN)155192108 035 $a(EXLCZ)991000000000212427 100 $a20121227d2004 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgorithmic Number Theory $e6th International Symposium, ANTS-VI, Burlington, VT, USA, June 13-18, 2004, Proceedings /$fedited by Duncan Buell 205 $a1st ed. 2004. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2004. 215 $a1 online resource (XII, 456 p.) 225 1 $aLecture Notes in Computer Science,$x0302-9743 ;$v3076 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-22156-5 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aInvited Talks -- Computing Zeta Functions via p-Adic Cohomology -- Using Primitive Subgroups to Do More with Fewer Bits -- Elliptic Curves of Large Rank and Small Conductor -- Contributed Papers -- Binary GCD Like Algorithms for Some Complex Quadratic Rings -- On the Complexity of Computing Units in a Number Field -- Implementing the Arithmetic of C 3,4 Curves -- Pseudocubes and Primality Testing -- Elliptic Curves with a Given Number of Points -- Rational Divisors in Rational Divisor Classes -- Conjectures about Discriminants of Hecke Algebras of Prime Level -- Montgomery Scalar Multiplication for Genus 2 Curves -- Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves -- Elliptic Curves x 3 + y 3 = k of High Rank -- Proving the Primality of Very Large Numbers with fastECPP -- A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii?s Algorithm -- Function Field Sieve in Characteristic Three -- A Comparison of CEILIDH and XTR -- Stable Models of Elliptic Curves, Ring Class Fields, and Complex Multiplication -- An Algorithm for Computing Isomorphisms of Algebraic Function Fields -- A Method to Solve Cyclotomic Norm Equations -- Imaginary Cyclic Quartic Fields with Large Minus Class Numbers -- Nonic 3-adic Fields -- Montgomery Addition for Genus Two Curves -- Numerical Evaluation at Negative Integers of the Dedekind Zeta Functions of Totally Real Cubic Number Fields -- Salem Numbers of Trace -2 and Traces of Totally Positive Algebraic Integers -- Low-Dimensional Lattice Basis Reduction Revisited -- Computing Order Statistics in the Farey Sequence -- The Discrete Logarithm in Logarithmic l-Class Groups and Its Applications in K-theory -- Point Counting on Genus 3 Non Hyperelliptic Curves -- Algorithmic Aspects of Cubic Function Fields -- A Binary Recursive Gcd Algorithm -- Lagrange Resolvents Constructed from Stark Units -- Cryptanalysis of a Divisor Class Group Based Public-Key Cryptosystem. 330 $aThe sixth Algorithmic Number Theory Symposium was held at the University of Vermont, in Burlington, from 13?18 June 2004. The organization was a joint e?ort of number theorists from around the world. There were four invited talks at ANTS VI, by Dan Bernstein of the Univ- sity of Illinois at Chicago, Kiran Kedlaya of MIT, Alice Silverberg of Ohio State University, and Mark Watkins of Pennsylvania State University. Thirty cont- buted talks were presented, and a poster session was held. This volume contains the written versions of the contributed talks and three of the four invited talks. (Not included is the talk by Dan Bernstein.) ANTS in Burlington is the sixth in a series that began with ANTS I in 1994 at Cornell University, Ithaca, New York, USA and continued at Universit´eB- deaux I, Bordeaux, France (1996), Reed College, Portland, Oregon, USA (1998), the University of Leiden, Leiden, The Netherlands (2000), and the University of Sydney, Sydney, Australia (2002). The proceedings have been published as volumes 877, 1122, 1423, 1838, and 2369 of Springer-Verlag?s Lecture Notes in Computer Science series. The organizers of the 2004 ANTS conference express their special gratitude and thanks to John Cannon and Joe Buhler for invaluable behind-the-scenes advice. 410 0$aLecture Notes in Computer Science,$x0302-9743 ;$v3076 606 $aNumber theory 606 $aAlgorithms 606 $aComputer science?Mathematics 606 $aData encryption (Computer science) 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aAlgorithm Analysis and Problem Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/I16021 606 $aDiscrete Mathematics in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17028 606 $aCryptology$3https://scigraph.springernature.com/ontologies/product-market-codes/I28020 606 $aSymbolic and Algebraic Manipulation$3https://scigraph.springernature.com/ontologies/product-market-codes/I17052 606 $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018 615 0$aNumber theory. 615 0$aAlgorithms. 615 0$aComputer science?Mathematics. 615 0$aData encryption (Computer science). 615 14$aNumber Theory. 615 24$aAlgorithm Analysis and Problem Complexity. 615 24$aDiscrete Mathematics in Computer Science. 615 24$aCryptology. 615 24$aSymbolic and Algebraic Manipulation. 615 24$aAlgorithms. 676 $a512.7 702 $aBuell$b Duncan$4edt$4http://id.loc.gov/vocabulary/relators/edt 712 02$aLINK (Online service) 712 12$aAlgorithmic Number Theory Symposium 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144154003321 996 $aAlgorithmic Number Theory$9772632 997 $aUNINA