Algorithmic Number Theory

Invited Talks.- The Complexity of Some Lattice Problems.- Rational Points Near Curves and Small Nonzero | x 3 ? y 2| via Lattice Reduction.- Coverings of Curves of Genus 2.- Lattice Reduction in Cryptology: An Update.- Contributed Papers.- Construction of Secure C ab Curves Using Modular Curves.- 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 ?-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.- Fast Jacobian Group Arithmetic on C ab Curves.- Lifting Elliptic Curves and Solving the Elliptic Curve Discrete Logarithm Problem.- A One Round Protocol for Tripartite Diffie–Hellman.- On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields.- Component Groups of Quotients of J 0(N).- Fast Computation of Relative Class Numbers of CM-Fields.- On Probable Prime Testing and the Computation of Square Roots mod n.- Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves.- Central Values of Artin L-Functions for Quaternion Fields.- The Pseudoprimes up to 1013.- Computing the Number of Goldbach Partitions up to 5 108.- NumericalVerification of the Brumer-Stark Conjecture.- Explicit Models of Genus 2 Curves with Split CM.- Reduction in Purely Cubic Function Fields of Unit Rank One.- Factorization in the Composition Algebras.- A Fast Algorithm for Approximately Counting Smooth Numbers.- Computing All Integer Solutions of a General Elliptic Equation.- A Note on Shanks’s Chains of Primes.- Asymptotically Fast Discrete Logarithms in Quadratic Number Fields.- Asymptotically Fast GCD Computation in ?[i].

Includes supplementary material: sn.pub/extras