Algorithmic Number Theory: 5th International Symposium, ANTS-V Sydney, Australia, July 7–12, 2002 Proceedings

Gauss Composition and Generalizations....Pages 1-8
Elliptic Curves — The Crossroads of Theory and Computation....Pages 9-19
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems....Pages 20-32
Using Elliptic Curves of Rank One towards the Undecidability of Hilbert’s Tenth Problem over Rings of Algebraic Integers....Pages 33-42
On p -adic Point Counting Algorithms for Elliptic Curves over Finite Fields....Pages 43-66
On Arithmetically Equivalent Number Fields of Small Degree....Pages 67-79
A Survey of Discriminant Counting....Pages 80-94
A Higher-Rank Mersenne Problem....Pages 95-107
An Application of Siegel Modular Functions to Kronecker’s Limit Formula....Pages 108-119
Computational Aspects of NUCOMP....Pages 120-133
Efficient Computation of Class Numbers of Real Abelian Number Fields....Pages 134-147
An Accelerated Buchmann Algorithm for Regulator Computation in Real Quadratic Fields....Pages 148-162
Some Genus 3 Curves with Many Points....Pages 163-171
Trinomials ax 7 + bx + c and ax 8 + bx + c with Galois Groups of Order 168 and 8 · 168....Pages 172-188
Computations on Modular Jacobian Surfaces....Pages 189-197
Integral Points on Punctured Abelian Surfaces....Pages 198-204
Genus 2 Curves with (3, 3)-Split Jacobian and Large Automorphism Group....Pages 205-218
Transportable Modular Symbols and the Intersection Pairing....Pages 219-233
Action of Modular Correspondences around CM Points....Pages 234-243
Curves Dy 2 = x 3 — x of Odd Analytic Rank....Pages 244-251
Comparing Invariants for Class Fields of Imaginary Quadratic Fields....Pages 252-266
A Database of Elliptic Curves — First Report....Pages 267-275
Isogeny Volcanoes and the SEA Algorithm....Pages 276-291
Fast Elliptic Curve Point Counting Using Gaussian Normal Basis....Pages 292-307
An Extension of Kedlaya’s Algorithm to Artin-Schreier Curves in Characteristic 2....Pages 308-323
Implementing the Tate Pairing....Pages 324-337
Smooth Orders and Cryptographic Applications....Pages 338-348
Chinese Remaindering for Algebraic Numbers in a Hidden Field....Pages 349-356
An Algorithm for Computing Weierstrass Points....Pages 357-371
New Optimal Tame Towers of Function Fields over Small Finite Fields....Pages 372-389
Periodic Continued Fractions in Elliptic Function Fields....Pages 390-404
Fixed Points and Two-Cycles of the Discrete Logarithm....Pages 405-415
Random Cayley Digraphs and the Discrete Logarithm....Pages 416-430
The Function Field Sieve Is Quite Special....Pages 431-445
MPQS with Three Large Primes....Pages 446-460
An Improved Baby Step Giant Step Algorithm for Point Counting of Hyperelliptic Curves over Finite Fields....Pages 461-474
Factoring N = pq 2 with the Elliptic Curve Method....Pages 475-490
A New Scheme for Computing with Algebraically Closed Fields....Pages 491-505
....Pages 506-515