Algorithmic Number Theory: 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000 Proceedings (Lecture Notes in Computer Science, 1838)

This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums. Front Matter....Pages - The Complexity of Some Lattice Problems....Pages 1-32 Rational Points Near Curves and Small Nonzero | x 3 − y 2 | via Lattice Reduction....Pages 33-63 Coverings of Curves of Genus 2....Pages 65-84 Lattice Reduction in Cryptology: An Update....Pages 85-112 Construction of Secure C ab Curves Using Modular Curves....Pages 113-126 Curves over Finite Fields with Many Rational Points Obtained by Ray Class Field Extensions....Pages 127-134 New Results on Lattice Basis Reduction in Practice....Pages 135-152 Baby-Step Giant-Step Algorithms for Non-uniform Distributions....Pages 153-168 On Powers as Sums of Two Cubes....Pages 169-184 Factoring Polynomials over ρ -Adic Fields....Pages 185-208 Strategies in Filtering in the Number Field Sieve....Pages 209-231 Factoring Polynomials over Finite Fields and Stable Colorings of Tournaments....Pages 233-245 Computing Special Values of Partial Zeta Functions....Pages 247-256 Construction of Tables of Quartic Number Fields....Pages 257-268 Counting Discriminants of Number Fields of Degree up to Four....Pages 269-283 On Reconstruction of Algebraic Numbers....Pages 285-296 Dissecting a Sieve to Cut Its Need for Space....Pages 297-312 Counting Points on Hyperelliptic Curves over Finite Fields....Pages 313-332 Modular Forms for GL(3) and Galois Representations....Pages 333-346 Modular Symbols and Hecke Operators....Pages 347-357 Fast Jacobian Group Arithmetic on C ab Curves....Pages 359-376 Lifting Elliptic Curves and Solving the Elliptic Curve Discrete Logarithm Problem....Pages 377-384 A One Round Protocol for Tripartite Diffie–Hellman....Pages 385-393 On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields....Pages 395-404 Component Groups of Quotients of J 0 ( N )....Pages 405-412 Fast Computation of Relative Class Numbers of CM-Fields....Pages 413-422 On Probable Prime Testing and the Computation of Square Roots mod n ....Pages 423-437 Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves....Pages 439-447 Central Values of Artin L -Functions for Quaternion Fields....Pages 449-458 The Pseudoprimes up to 10 13 ....Pages 459-473 Computing the Number of Goldbach Partitions up to 5 10 8 ....Pages 475-490 Numerical Verification of the Brumer-Stark Conjecture....Pages 491-503 Explicit Models of Genus 2 Curves with Split CM....Pages 505-513 Reduction in Purely Cubic Function Fields of Unit Rank One....Pages 515-532 Factorization in the Composition Algebras....Pages 533-537 A Fast Algorithm for Approximately Counting Smooth Numbers....Pages 539-549 Computing All Integer Solutions of a General Elliptic Equation....Pages 551-561 A Note on Shanks’s Chains of Primes....Pages 563-580 Asymptotically Fast Discrete Logarithms in Quadratic Number Fields....Pages 581-594 Asymptotically Fast GCD Computation in Z[ i ]....Pages 595-613 Back Matter....Pages - Algorithmic Number Theory: 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000. Proceedings Author: Wieb Bosma Published by Springer Berlin Heidelberg ISBN: 978-3-540-67695-9 DOI: 10.1007/10722028 Table of Contents: The Complexity of Some Lattice Problems Rational Points Near Curves and Small Nonzero | x Coverings of Curves of Genus 2 Lattice Reduction in Cryptology: An Update Construction of Secure C Curves over Finite Fields with Many Rational Points Obtained by Ray Class Field Extensions New Results on Lattice Basis Reduction in Practice Baby-Step Giant-Step Algorithms for Non-uniform Distributions On Powers as Sums of Two Cubes Factoring Polynomials over ρ-Adic Fields Strategies in Filtering in the Number Field Sieve Factoring Polynomials over Finite Fields and Stable Colorings of Tournaments Computing Special Values of Partial Zeta Functions Construction of Tables of Quartic Number Fields Counting Discriminants of Number Fields of Degree up to Four On Reconstruction of Algebraic Numbers Dissecting a Sieve to Cut Its Need for Space Counting Points on Hyperelliptic Curves over Finite Fields Modular Forms for GL(3) and Galois Representations Modular Symbols and Hecke Operators

This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000.
The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.

Among the topics addressed are in these conference papers are: gcd algorithms; primality; factoring; sieve methods; cryptography; linear algebra; lattices; algebraic number fields; class groups and fields; elliptic curves; polynomials; function fields; and power sums. For many years now both in my talks and my writings I have been suggesting that real progress in software technology requires a scientific base and framework such as those that support other engineering technologies.