Course in Number Theory and Cryptography

ISBN-10: 0387942939
ISBN-13: 9780387942933
Edition: 2nd 1994 (Revised)
Authors: Neal Koblitz
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Description: The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. No background in algebra or number theory is  More...

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Book details

List price: $64.95
Edition: 2nd
Copyright year: 1994
Publisher: Springer
Publication date: 9/2/1994
Binding: Hardcover
Pages: 235
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 1.100
Language: English

The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. No background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasizing estimates of the efficiency of the techniques that arise from the theory. A special feature is the inclusion of recent application of the theory of elliptic curves. Extensive exercises and careful answers have been included in all of the chapters. Because number theory and cryptography are fast-moving fields, this new edition contains substantial revisions and updated references.

Foreword
Preface to the Second Edition
Some Topics in Elementary Number Theory
Time estimates for doing arithmetic
Divisibility and the Euclidean algorithm
Congruences
Some applications to factoring
Finite Fields and Quadratic Residues
Finite fields
Quadratic residues and reciprocity
Cryptography
Some simple cryptosystems
Enciphering matrices
Public Key
The idea of public key cryptography
RSA
Discrete log
Knapsack
Zero-knowledge protocols and oblivious transfer
Primality and Factoring
Pseudoprimes
The rho method
Fermat factorization and factor bases
The continued fraction method
The quadratic sieve method
Elliptic Curves
Basic facts
Elliptic curve cryptosystems
Elliptic curve primality test
Elliptic curve factorization
Answers to Exercises
Index

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