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Algorithmic Number Theory : First International Symposium, Ants-I, Ithaca, Ny, Usa, May 6 - 9, 1994. Proceedings - Leonard M. Adleman

Algorithmic Number Theory

First International Symposium, Ants-I, Ithaca, Ny, Usa, May 6 - 9, 1994. Proceedings

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

Paperback Published: 15th November 1994
ISBN: 9783540586913
Number Of Pages: 320

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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.

On the difficulty of finding reliable witnessesp. 1
Density computations for real quadratic 2-class groupsp. 17
Lattice sieving and trial divisionp. 18
A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fieldsp. 28
Computing rates of growth of division fields on CM abelian varietiesp. 41
Algorithms for CM-fieldsp. 42
Schoof's algorithm and isogeny cyclesp. 43
Integer points on rational elliptic curvesp. 59
Counting the number of points on elliptic curves over finite fields of characteristic greater than threep. 60
Straight-line complexity and integer factorizationp. 71
Decomposition of algebraic functionsp. 80
A new modular interpolation algorithm for factoring multivariate polynomialsp. 93
The function field sievep. 108
Heegner point computationsp. 122
Computing the degree of a modular parametrizationp. 134
Galois representations from the cohomology of SL(3, Z)p. 143
An analysis of the Gaussian algorithm for lattice reductionp. 144
A fast variant of the Gaussian reduction algorithmp. 159
Reducing lattice bases by means of approximationsp. 160
Analysis of a left-shift binary GCD algorithmp. 169
The complexity of greatest common divisor computationsp. 184
Explicit formulas for units in certain quadratic number fieldsp. 194
Factorization of polynomials over finite fields in subexponential time under GRHp. 209
On orders of optimal normal basis generatorsp. 220
Computing in the jacobian of a plane algebraic curvep. 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 fieldsp. 248
Efficient checking of computations in number theoryp. 249
Constructing elliptic curves with given group order over large finite fieldsp. 250
Computing [pi](x), M(x) and [Psi](x)p. 264
On some applications of finitely generated semi-groupsp. 265
Improved incremental prime number sievesp. 280
Polynomial time algorithms for discrete logarithms and factoring on a quantum computerp. 289
On dispersion and Markov constantsp. 290
Open problems in number theoretic complexity, IIp. 291
Author Indexp. 323
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540586913
ISBN-10: 3540586911
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 320
Published: 15th November 1994
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.83
Weight (kg): 0.48