Algorithmic Number Theory

Invited Talk 1: Shimura Curve Computations Noam D. Elkies (Harvard University) Invited Talk 2: The Decision Diffie-Hellman Problem Dan Boneh (Stanford University) GCD Algorithms Parallel Implementation of Schonhages Integer GCD Algorithm Giovanni Cesari (Università degli Studi di Trieste) The Complete Analysis of the Binary Euclidean Algorithm Brigitte Vallée (Université de Caen) Primality Cyclotomy Primality Proving -- Recent Developments Preda Mihailescu (FingerPIN AG & ETH, Institut fur wissentschaftliches Rechnen) Primality Proving Using Elliptic Curves: An Update F. Morain (Laboratoire d informatique de l'Ecole Polytechnique) Factoring Bounding Smooth Integers (extended abstract) Daniel J. Bernstein (The University of Illinois at Chicago) Factorization of the Numbers of the Form m 3 + c 2 m 2 + c 1 m+ c 0 Zhang Mingzhi (Sichuan Union University) Modelling the Yield of Number Field Sieve Polynomials Brian Murphy (Australian National University) A Montgomery-Like Square Root for the Number Field Sieve Phong Nguyen (Ecole Normale Supérieure) Sieving Robert Bennions Hopping Sieve William F. Galway (University of Illinois at Urbana-Champaign) Trading Time for Space in Prime Number Sieves Jonathan P. Sorenson (Butler University) Analytic Number Theory Do Sums of 4 Biquadrates Have a Positive Density? Jean-Marc Deshouillers, Francois Hennecart, Bernard Landreau (Université Bordeaux) New Experimental Results Concerning the Goldbach Conjecture J-M. Deshouillers (Université Bordeaux), H.J.J. te Riele (CWI), Y. Saouter (Institut de Recherche en Informatique de Toulouse) Dense Admissible Sets Daniel M. Gordon, Gene Rodemich (Center for Communications Research) An Analytic Approach to Smooth Polynomials over Finite Fields Daniel Panario (University of Toronto), Xavier Gourdon (INRIA), Philippe Flajolet (INRIA) Cryptography Generating a Product of Three Primes with an Unknown Factorization Dan Boneh, Jeremy Horwitz (Stanford University) On the Performance of SignatureSchemes Based on Elliptic Curves Erik De Win (Katholieke Universiteit Leuven), Serge Mister (Queens University) Bart Preneel (Katholieke Universiteit Leuven), Michael Wiener (Entrust Technologies) NTRU: A Ring-Based Public Key Cryptosystem Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman (Brown University) Finding Length-3 Positive Cunningham Chains and their Cryptographic Significance Adam Young (Columbia University), Moti Yung (CertCo) Linear Algebra, Lattices Reducing Ideal Arithmetic to Linear Algebra Problems Stefan Neis (Darmstadt University of Technology) Evaluation of Linear Relations between Vectors of a Lattice in Euclidean Space I. A. Semaev An Efficient Parallel Block-Reduction Algorithm Susanne Wetzel (Universitat des Saarlandes) Series, Sums Fast Multiprecision Evaluation of Series of Rational Numbers Bruno Haible (ILOF), Thomas Papanikolaou (Laboratoire A2X) A Problem Concerning a Character Sum --- Extended Abstract E. Teske (Technische Universitat Darmstadt), H.C. Williams (University of Manitoab) Formal Power Series and Their Continued Fraction Expansion Alf van der Poorten (Centre for Number Theory Research) Algebraic Number Fields Imprimitive Octic Fields with Small Discriminants Henri Cohen, Francisco Diaz y Diaz, Michel Olivier (Université Bordeaux I) A Table of Totally Complex Number Fields of Small Discriminants Henri Cohen, Francisco Diaz y Diaz, Michel Olivier (Université Bordeaux I) Generating Arithmetically Equivalent Number Fields with Elliptic Curves Bart de Smit (Rijksuniversiteit Leiden) Computing the Lead Term of an Abelian L-Function David S. Dummit (University of Vermont), Brett A. Tangedal (College of Charleston Timing Analysis of Targeted Hunter Searches John W. Jones (Arizona State University), David P. Roberts (Rutgers University) On Successive Minima of Rings of Algebraic Integers Jacques Martinet (Université Bordeaux I) Class Groups and Fields Computation of Relative Quadratic Class Groups Henri Cohen, Francisco Diaz y