Public Key Cryptography Applications and Attacks 1st Edition by Lynn Margaret Batten 9781118482254

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ISBN 13: 9781118482254 

Author: Lynn Margaret Batten

Complete coverage of the current major public key cryptosystems their underlying mathematics and the most common techniques used in attacking them Public Key Cryptography: Applications and Attacks introduces and explains the fundamentals of public key cryptography and explores its application in all major public key cryptosystems in current use, including ElGamal, RSA, Elliptic Curve, and digital signature schemes. It provides the underlying mathematics needed to build and study these schemes as needed, and examines attacks on said schemes via the mathematical problems on which they are based – such as the discrete logarithm problem and the difficulty of factoring integers.

The book contains approximately ten examples with detailed solutions, while each chapter includes forty to fifty problems with full solutions for odd-numbered problems provided in the Appendix.

Public Key Cryptography Applications and Attacks 1st Table of contents:

0 Introduction

0.1 The Meaning of the Word Cryptography

0.2 Symmetric Key Cryptography

0.3 Public Key (Asymmetric) Cryptography

0.4 Key Establishment

0.5 Cryptography — More Than Just Hiding Secrets

0.6 Standards

0.7 Attacks

1 Congruence Equations

1.1 Congruence Arithmetic

1.1.1 Computer Examples

1.1.2 Problems

1.2 The Euclidean Algorithm — Finding Inverses

1.2.1 Computer Examples

1.2.2 Problems

1.3 Discrete Logarithms and Diffie-Hellman Key Exchange

1.3.1 Computer Examples

1.3.2 Problems

1.4 Attacking the Discrete Logarithm

1.4.1 Computer Examples

1.4.2 Problems

2 The ElGamal Scheme

2.1 Primitive Roots

2.1.1 Computer Examples

2.1.2 Problems

2.2 The ElGamal Scheme

2.2.1 Computer Examples

2.2.2 Problems

2.3 Security of the ElGamal Scheme

2.3.1 Computer Examples

2.3.2 Problems

3 The RSA Scheme

3.1 Euler’s Theorem

3.1.1 Computer Examples

3.1.2 Problems

3.2 The RSA Algorithm

3.2.1 Computer Examples

3.2.2 Problems

3.3 RSA Security

3.3.1 Computer Examples

3.3.2 Problems

3.4 Implementing RSA

3.4.1 Computer Examples

3.4.2 Problems

4 Elliptic Curve Cryptography

4.1 Elliptic Curves and Elliptic Curve Groups

4.1.1 Computer Examples

4.1.2 Problems

4.2 Elliptic Curve Cryptography

4.2.1 Computer Examples

4.2.2 Problems

4.3 The Elliptic Curve Factoring Scheme

4.3.1 Computer Examples

4.3.2 Problems

5 Digital Signatures

5.1 Hash Functions

5.1.1 Computer Examples

5.1.2 Problems

5.2 Digital Signature Schemes

5.2.1 Computer Examples

5.2.2 Problems

5.3 Attacks on Digital Signatures

5.3.1 Computer Examples

5.3.2 Problems

6 Primality Testing

6.1 Fermat’s Approach and Wilson’s Theorem

6.1.1 Computer Examples

6.1.2 Problems

6.2 The Miller-Selfridge-Rabin Primality Test

6.2.1 Computer Examples

6.2.2 Problems

6.3 True Primality Tests

6.3.1 Computer Examples

6.4 Mersenne Primes and the Lucas-Lehmer Test

6.4.1 Computer Examples

6.4.2 Problems

6.5 Primes is in P

6.5.1 Computer Examples

6.5.2 Problems

7 Factoring Methods

7.1 Fermat Again

7.1.1 Computer Examples

7.1.2 Problems

7.2 The Quadratic Sieve

7.2.1 Computer Examples

7.2.2 Problems

7.3 Pollard’s p – 1 and rho Methods

7.3.1 Computer Examples

7.3.2 Problems

7.4 Continued Fractions and Factoring

7.4.1 Computer Examples

7.4.2 Problems

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