From the reviews:
"The book contains 39 articles about computational algebraic number theory, arithmetic geometry and cryptography. … The articles in this book reflect the broad interest of the organizing committee and the participants. The emphasis lies on the mathematical theory as well as on computational results. We recommend the book to students and researchers who want to read about current research in number theory and arithmetic geometry and its applications." (R. Carls, Nieuw Archief voor Wiskunde, Vol. 6 (3), 2005)
Author(s): Manjul Bhargava (auth.), Claus Fieker, David R. Kohel (eds.)
Series: Lecture Notes in Computer Science 2369
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2002
Language: English
Pages: 522
Tags: Algorithm Analysis and Problem Complexity; Discrete Mathematics in Computer Science; Numeric Computing; Data Encryption; Algorithms; Field Theory and Polynomials
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
