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A Course in Number Theory and Cryptography : Graduate Texts In Mathematics - Neal Koblitz

A Course in Number Theory and Cryptography

Graduate Texts In Mathematics

Hardcover Published: 2nd September 1994
ISBN: 9780387942933
Number Of Pages: 235

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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.

Preface to the Second Edition
Some Topics in Elementary Number Theoryp. 1
Time estimates for doing arithmeticp. 1
Divisibility and the Euclidean algorithmp. 12
Congruencesp. 19
Some applications to factoringp. 27
Finite Fields and Quadratic Residuesp. 31
Finite fieldsp. 33
Quadratic residues and reciprocityp. 42
Cryptographyp. 54
Some simple cryptosystemsp. 54
Enciphering matricesp. 65
Public Keyp. 83
The idea of public key cryptographyp. 83
RSAp. 92
Discrete logp. 97
Knapsackp. 111
Zero-knowledge protocols and oblivious transferp. 117
Primality and Factoringp. 125
Pseudoprimesp. 126
The rho methodp. 138
Fermat factorization and factor basesp. 143
The continued fraction methodp. 154
The quadratic sieve methodp. 160
Elliptic Curvesp. 167
Basic factsp. 167
Elliptic curve cryptosystemsp. 177
Elliptic curve primality testp. 187
Elliptic curve factorizationp. 191
Answers to Exercisesp. 200
Indexp. 231
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387942933
ISBN-10: 0387942939
Series: Graduate Texts In Mathematics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 235
Published: 2nd September 1994
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.13 x 15.88  x 1.91
Weight (kg): 0.48
Edition Number: 2
Edition Type: Revised

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