Analytic Methods in the Analysis and Design of Number-Theoretic Algorithms.

Abstract

This book makes a substantial contribution to the understanding of a murky area of number theory that is important to computer science, an area relevant to the design and analysis of number-theoretic algorithms and to the construction of cryptographic protocols.Contents: Introduction; 1: Explicit Bounds for Primality Testing; Ankeny's Theorem and its Algorithmic Consequences; Background from Number Theory; Roots; Asymptotic Theorems; Zeta-function Estimates; Numerical Theorems; Computing Bounds for Specific Moduli; Comparisons with Empirical Results; 2: The Generation of Random Factorizations; Introduction; A Method That Almost Works; Doctoring the Odds; A Factor Generation Procedure; The Complete Algorithm; 2.5 Bounds for the Number of Prime Tests; A Single-precision Time Bound; The Use of Probabilistic Primality Tests.Eric Bach received his doctorate from the University of California at Berkeley. He is currently an Assistant Professor of Computer Science at the University of Wisconsin at Madison. Analytic Methods in the Analysis and Design of Number Theoretic Algorithms is a 1984 ACM Distinguished Dissertation.