Algorithmic Number Theory: 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000. Proceedings

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 -