The Mathematics of Ciphers: Number Theory and RSA Cryptography

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9781568810829 | 1568810822
Cover: Hardcover
Copyright: 1/15/1999

Rent

(Recommended)

$150.69

Term

Due

Price

Semester

Dec 12

$158.62

Quarter

Aug 13

$150.69

Short Term

Jul 21

$142.76

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping bag.
Buy New

Usually Ships in 3-5 Business Days

$203.07
eBook

Available Instantly

Online: 180 Days

Downloadable: 180 Days

*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.

$54.78*

The Mathematics of Ciphers is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosystem. It covers many of the familiar topics of elementary number theory, all with an algorithmic twist.

Preface

xiii

Introduction

(1)

Cryptography

(2)

The RSA cryptosystem

(2)

Computer algebra

(2)

The Greeks and the integers

(1)

Fermat, Euler, and Gauss

(3)

The problems of number theory

(1)

Theorems and proofs

(5)

Fundamental algorithms

(16)

Algorithms

(2)

Division algorithm

(2)

Division theorem

(1)

The Euclidean algorithm

(3)

Proof of the Euclidean algorithm

(2)

Extended Euclidean algorithm

(3)

Exercises

(3)

Unique factorization

(16)

Unique factorization theorem

(1)

Existence of the factorization

(2)

Efficiency of the trial division algorithm

(1)

Fermat's factorization algorithm

(1)

Proof of Fermat's algorithm

(2)

A fundamental property of primes

(1)

The Greeks and the irrational

(2)

Uniqueness of factorization

(2)

Exercises

(4)

Prime numbers

(14)

Polynomial formulae

(2)

Exponential formulae: Mersenne numbers

(2)

Exponential formulae: Fermat numbers

(1)

The primorial formula

(1)

Infinity of primes

(2)

The sieve of Erathostenes

(4)

Exercises

(2)

Modular arithmetic

(16)

Equivalence relations

(3)

The congruence relation

(2)

Modular arithmetic

(3)

Divisibility criteria

(1)

Powers

(1)

Diophantine equations

(2)

Division modulo n

(2)

Exercises

(2)

Induction and Fermat

(16)

Hanoi! Hanoi!

(4)

Finite induction

(3)

Fermat's theorem

(2)

Counting roots

(4)

Exercises

(3)

Pseudoprimes

(12)

Pseudoprimes

(2)

Carmichael numbers

(3)

Miller's test

100

(3)

Primality testing and computer algebra

103

(1)

Exercises

104

(3)

Systems of Congruences

107

(14)

Linear equations

107

(1)

An astronomical example

108

(2)

The Chinese remainder algorithm: Co-prime moduli

110

(3)

The Chinese remainder algorithm: General case

113

(1)

Powers, again

114

(2)

On sharing secrets

116

(2)

Exercises

118

(3)

Groups

121

(20)

Definitions and examples

121

(1)

Symmetries

122

(4)

Interlude

126

(3)

Arithmetic groups

129

(3)

Subgroups

132

(1)

Cyclic subgroups

133

(1)

Finding subgroups

134

(2)

Lagrange's theorem

136

(2)

Exercises

138

(3)

Mersenne and Fermat

141

(10)

Mersenne numbers

141

(2)

Fermat numbers

143

(2)

Fermat, again

145

(1)

The Lucas--Lehmer test

146

(3)

Exercises

149

(2)

Primality tests and primitive roots

151

(12)

Lucas's test

151

(3)

Another primality test

154

(1)

Carmichael numbers

155

(1)

Preliminaries

156

(1)

Primitive roots

157

(1)

Computing orders

158

(2)

Exercises

160

(3)

The RSA cryptosystem

163

(12)

On first and last things

163

(1)

Encryption and decryption

164

(2)

Why does it work?

166

(1)

Why is it secure?

167

(1)

Choosing the primes

168

(2)

Signatures

170

(1)

Exercises

171

(4)

Coda

175

(4)

Appendix. Roots and powers

179

(4)

1. Square roots

179

(1)

2. Power algorithm

180

(3)

Bibliography

183

(6)

Index of the main algorithms

189

(2)

Index of the main results

191

(1)

Index

192

Please wait while the item is added to your bag...

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

The Mathematics of Ciphers: Number Theory and RSA Cryptography

Summary

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

The Mathematics of Ciphers: Number Theory and RSA Cryptography

Summary

Table of Contents

Supplemental Materials

Digital License