Cryptology and Computational Number Theory

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American Mathematical Soc., 1990 - Computers - 171 pages
In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.
 

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Contents

Cryptology and Computational Number TheoryAn Introduction
1
Primality Testing
13
Factoring
27
The Discrete Logarithm Problem
49
The Rise and Fall of Knapsack Cryptosystems
75
The Search for Provably Secure Cryptosystems
89
Pseudorandom Number Generators in Cryptography and Number Theory
115
Odds and Ends from Cryptology and Computational Number Theory
145
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