Rsa and Public-Key Cryptography

by Mollin; Richard A.

• ISBN13: 9781584883388
• ISBN10: 1584883383
• Edition: 1st
• Format: Hardcover
• Copyright: 2002-11-12
• Publisher: Chapman & Hall/

Summary

Although much literature exists on the subject of RSA and public-key cryptography, until now there has been no single source that reveals recent developments in the area at an accessible level. Acclaimed author Richard A. Mollin brings together all of the relevant information available on public-key cryptography (PKC), from RSA to the latest applications of PKC, including electronic cash, secret broadcasting, secret balloting systems, various banking and payment protocols, high security logins, smart cards, and biometrics. Moreover, he covers public-key infrastructure (PKI) and its various security applications.Throughout the book, Mollin gives a human face to cryptography by including nearly 40 biographies of the individuals who helped develop cryptographic concepts. He includes a number of illustrative and motivating examples, as well as optional topics that go beyond the basics, such as Lenstra's elliptic curve method and the number field sieve. From history and basic concepts to future trends and emerging applications, this book provides a rigorous and detailed treatment of public-key cryptography. Accessible to anyone from the senior undergraduate to the research scientist, RSA and Public-Key Cryptography offers challenging and inspirational material for all readers.

Author Biography

Richard A. Mollin is a full professor in the Mathematics Department at the University of Calgary, Alberta, Canada

Table of Contents

History and Basic Cryptographic Concepts	1	(32)
Terminology	1	(12)
Classical Ciphers	13	(12)
Classification of Attacks	25	(8)
Protocols, Discrete Log, and Diffie-Hellman	33	(20)
Cryptographic Protocols	33	(6)
The Discrete Log Problem	39	(8)
Exponentiation Ciphers and Diffie-Hellman	47	(6)
Public-Key Cryptography	53	(26)
One-Way Functions	53	(7)
Public-Key Cryptosystems and RSA	60	(7)
ElGamal Cryptosystems	67	(6)
Symmetric vs. Asymmetric Cryptosystems	73	(4)
Secret History of Public-Key Cryptography	77	(2)
Probabilistic Primality Tests	79	(14)
Introduction	79	(2)
Pseudoprimes and Carmichael Numbers	81	(3)
Solovay-Strassen Test	84	(3)
Miller-Selfridge-Rabin Test	87	(6)
Factoring	93	(18)
Universal Exponent Method	93	(3)
Pollard's p -- 1 Method	96	(3)
Lenstra's Elliptic Curve Method	99	(5)
Multipolynomial Quadratic Sieve	104	(4)
The Number Field Sieve	108	(3)
Security of RSA	111	(16)
Implementation Attacks	111	(4)
Exponent Attacks	115	(5)
Strong Moduli	120	(4)
Generation of Random Primes	124	(3)
Authentication	127	(26)
Identification, Impersonation, and Signatures	127	(8)
Digital Signature Schemes	135	(8)
Digital Cash and Electronic Commerce	143	(10)
Key Management	153	(26)
Secret Sharing	153	(7)
Key Establishment	160	(13)
Public-Key Infrastructure (PKI)	173	(6)
Applications and the Future	179	(24)
Secrecy and Authentication	179	(6)
Other Threats to System Security	185	(5)
Wireless Security	190	(8)
Smart Cards and Biometrics	198	(5)
Appendix A: Letter Frequency Analysis	203	(2)
Appendix B: Elementary Complexity Theory	205	(7)
Appendix C: Fundamental Facts	212	(12)
Solutions to Odd-Numbered Exercises	224	(25)
Bibliography	249	(18)
List of Symbols	267	(1)
Index	268