Continuing a bestselling tradition, An Introduction to Cryptography, Second Edition provides a solid foundation in cryptographic concepts that features all of the requisite background material on number theory and algorithmic complexity as well as a historical look at the field. With numerous additions and restructured material, this edition presents the ideas behind cryptography and the applications of the subject. The first chapter provides a thorough treatment of the mathematics necessary to understand cryptography, including number theory and complexity, while the second chapter discusses cryptographic fundamentals, such as ciphers, linear feedback shift registers, modes of operation, and attacks. The next several chapters discuss DES, AES, public-key cryptography, primality testing, and various factoring methods, from classical to elliptical curves. The final chapters are comprised of issues pertaining to the Internet, such as pretty good privacy (PGP), protocol layers, firewalls, and cookies, as well as applications, including login and network security, viruses, smart cards, and biometrics. The book concludes with appendices on mathematical data, computer arithmetic, the Rijndael S-Box, knapsack ciphers, the Silver-Pohlig-Hellman algorithm, the SHA-1 algorithm, radix-64 encoding, and quantum cryptography. New to the Second Edition:
An introductory chapter that provides more information on mathematical facts and complexity theory Expanded and updated exercises sets, including some routine exercises More information on primality testing and cryptanalysis Accessible and logically organized, An Introduction to Cryptography, Second Edition is the essential book on the fundamentals of cryptography.
Author(s): Richard A. Mollin
Series: Discrete mathematics and its applications
Edition: 2nd ed
Publisher: Chapman & Hall/CRC
Year: 2007
Language: English
Pages: 394
City: Boca Raton
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1.1 Divisibility......Page 12
1.2 Primes, Primality Testing, and Induction......Page 17
1.3 An Introduction to Congruences......Page 28
1.4 Euler, Fermat, and Wilson......Page 46
1.5 Primitive Roots......Page 55
1.6 The Index Calculus and Power Residues......Page 62
1.7 Legendre, Jacobi, & Quadratic Reciprocity......Page 69
1.8 Complexity......Page 78
Bibliography......Page 0
2.1 Definitions and Illustrations......Page 90
2.2 Classic Ciphers......Page 102
2.3 Stream Ciphers......Page 120
2.4 LFSRs......Page 126
2.5 Modes of Operation......Page 133
2.6 Attacks......Page 138
3.1 S-DES and DES......Page 142
3.2 AES......Page 163
4.1 The Ideas Behind PKC......Page 168
4.2 Digital Envelopes and PKCs......Page 176
(II) RSA Public-Key Cipher......Page 183
(II) ElGamal Public-Key Cipher......Page 192
4.5 DSA — The DSS......Page 198
5.1 True Primality Tests......Page 200
5.2 Probabilistic Primality Tests......Page 209
5.3 Recognizing Primes......Page 215
6.1 Classical Factorization Methods......Page 218
6.2 The Continued Fraction Algorithm......Page 222
6.3 Pollard’s Algorithms......Page 225
6.4 The Quadratic Sieve......Page 228
6.5 The Elliptic Curve Method (ECM)......Page 231
7.1 History of the Internet and the WWW......Page 234
7.2 Pretty Good Privacy (PGP)......Page 238
7.3 Protocol Layers and SSL......Page 252
7.4 Internetworking and Security — Firewalls......Page 261
What Firewalls Cannot Do......Page 262
7.5 Client–Server Model and Cookies......Page 270
8.1 Login and Network Security......Page 274
Attacks on Passwords......Page 275
Ethernet and Promiscuous Mode......Page 277
Packet Sni.er Components......Page 278
Token Applications......Page 279
Basically, How Does SSH work?......Page 280
Key Exchange Protocol......Page 281
Connection......Page 282
Exercises......Page 283
Virus Targets......Page 284
Types of Viruses......Page 286
Examples......Page 287
Virus Detection and Prevention......Page 289
Advanced Protection......Page 290
DIS Closed-Loop Process......Page 291
8.3 Smart Cards......Page 297
8.4 Biometrics......Page 305
Exercises......Page 308
Appendix A: Fundamental Facts......Page 309
Appendix B: Computer Arithmetic......Page 336
Appendix C: The Rijndael S-Box......Page 346
Appendix D: Knapsack Ciphers......Page 348
Appendix E: Silver-Pohlig-Hellman Algorithm......Page 355
Appendix F: SHA-1......Page 357
Appendix G: Radix-64 Encoding......Page 361
Appendix H: Quantum Cryptography......Page 363
Section 1.1......Page 369
Section 1.2......Page 370
Section 1.3......Page 371
Section 1.4......Page 373
Section 1.6......Page 376
Section 1.7......Page 377
Section 2.1......Page 378
Section 2.2......Page 379
Section 2.4......Page 380
Section 4.2......Page 381
Section 4.3......Page 382
Section 5.1......Page 383
Section 5.2......Page 384
Section 6.2......Page 385
Section 8.4......Page 386
Bibliography......Page 387
About the Author......Page 394
