Description 
1 online resource (ix, 322 pages) : illustrations 
Series 
Lecture notes in computer science ; 877 

Lecture notes in computer science ; 877.

Contents 
On the difficulty of finding reliable witnesses  Density computations for real quadratic 2class groups  Lattice sieving and trial division  A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields  Computing rates of growth of division fields on CM Abelian varieties  Algorithms for CMFields  Schoof's algorithm and isogeny cycles  Integer points on rational elliptic curves  Counting the number of points on elliptic curves over finite fields of characteristic greater than three  Straightline complexity and integer factorization  Decomposition of algebraic functions  A new modular interpolation algorithm for factoring multivariate polynomials  The function field sieve  Heegner point computations  Computing the degree of a modular parametrization  Galois representations from the cohomology of SL(3,?)  An analysis of the Gaussian algorithm for lattice reduction  A fast variant of the Gaussian reduction algorithm  Reducing lattice bases by means of approximations  Analysis of a leftshift binary GCD algorithm  The complexity of greatest common divisor computations  Explicit formulas for units in certain quadratic number fields  Factorization of polynomials over finite fields in subexponential time under GRH  On orders of optimal normal basis generators  Computing in the jacobian of a plane algebraic curve  Under the assumption of the Generalized Riemann Hypothesis verifying the class number belongs to NP? coNP  Calculating the class number of certain Hilbert class fields  Efficient checking of computations in number theory  Constructing elliptic curves with given group order over large finite fields  Computing?(x), M(x) and?(x)  On some applications of finitely generated semigroups  Improved incremental prime number sieves  Polynomial time algorithms for discrete logarithms and factoring on a quantum computer  On dispersion and Markov constants  Open problems in number theoretic complexity, II 
Summary 
This volume presents the refereed proceedings of the First Algorithmic Number Theory Symposium, ANTSI, 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 complexitytheoretic aspects of number theory and thus report the stateoftheart 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 
Notes 
Proceedings of the first Algorithmic Number Theory Symposium 
Bibliography 
Includes bibliographical references and index 
Subject 
Number theory  Data processing  Congresses


Number theory  Data processing

Genre/Form 
Conference papers and proceedings

Form 
Electronic book

Author 
Adleman, Leonard M.


Huang, MingDeh A.


ANTS (Symposium : Algorithmic number theory) (1st : 1994 : Ithaca, N.Y.)

LC no. 
94238714 
ISBN 
9783540490449 

3540490442 

3540586911 

9783540586913 

0387586911 

9780387586915 
