Algorithmic Number Theory

First International Symposium, ANTS-I, Ithaca, NY, USA, May 6 - 9, 1994. Proceedings

By: Leonard M. Adleman (Editor), Ming-Deh Huang (Editor)

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Paperback | 15 November 1994

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This volume presents the refereed proceedings of the First Algorithmic Number Theory Symposium, ANTS-I, held at Cornell University, Ithaca, NY in May 1994.
The 35 papers accepted for inclusion in this book address many current issues of algorithmic, computational and complexity-theoretic aspects of number theory and thus report the state-of-the-art in this exciting area of research; the book also contributes essentially to foundational research in cryptology and coding.
Of particular value is a collection entitled "Open Problems in Number Theoretic Complexity, II" contributed by Len Adleman and Kevin McCurley. This survey presents on 32 pages 36 central open problems and relates them to the literature by means of some 160 references.

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On the difficulty of finding reliable witnesses	p. 1
Density computations for real quadratic 2-class groups	p. 17
Lattice sieving and trial division	p. 18
A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields	p. 28
Computing rates of growth of division fields on CM abelian varieties	p. 41
Algorithms for CM-fields	p. 42
Schoof's algorithm and isogeny cycles	p. 43
Integer points on rational elliptic curves	p. 59
Counting the number of points on elliptic curves over finite fields of characteristic greater than three	p. 60
Straight-line complexity and integer factorization	p. 71
Decomposition of algebraic functions	p. 80
A new modular interpolation algorithm for factoring multivariate polynomials	p. 93
The function field sieve	p. 108
Heegner point computations	p. 122
Computing the degree of a modular parametrization	p. 134
Galois representations from the cohomology of SL(3, Z)	p. 143
An analysis of the Gaussian algorithm for lattice reduction	p. 144
A fast variant of the Gaussian reduction algorithm	p. 159
Reducing lattice bases by means of approximations	p. 160
Analysis of a left-shift binary GCD algorithm	p. 169
The complexity of greatest common divisor computations	p. 184
Explicit formulas for units in certain quadratic number fields	p. 194
Factorization of polynomials over finite fields in subexponential time under GRH	p. 209
On orders of optimal normal basis generators	p. 220
Computing in the jacobian of a plane algebraic curve	p. 221
Under the assumption of the generalized Riemann Hypothesis verifying the class number belongs to [actual symbol not reproducible]	p. 234
Calculating the class number of certain Hilbert class fields	p. 248
Efficient checking of computations in number theory	p. 249
Constructing elliptic curves with given group order over large finite fields	p. 250
Computing [pi](x), M(x) and [Psi](x)	p. 264
On some applications of finitely generated semi-groups	p. 265
Improved incremental prime number sieves	p. 280
Polynomial time algorithms for discrete logarithms and factoring on a quantum computer	p. 289
On dispersion and Markov constants	p. 290
Open problems in number theoretic complexity, II	p. 291
Author Index	p. 323
Table of Contents provided by Blackwell. All Rights Reserved.

Algorithmic Number Theory

First International Symposium, ANTS-I, Ithaca, NY, USA, May 6 - 9, 1994. Proceedings

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