Book Description
This unique book explains the basic issues of classical and modern cryptography, and provides a self contained essential mathematical background in number theory, abstract algebra, and probability—with surveys of relevant parts of complexity theory and other things. A user-friendly, down-to-earth tone presents concretely motivated introductions to these topics. More detailed chapter topics include simple ciphers; applying ideas from probability; substitutions, transpositions, permutations; modern symmetric ciphers; the integers; prime numbers; powers and roots modulo primes; powers and roots for composite moduli; weakly multiplicative functions; quadratic symbols, quadratic reciprocity; pseudoprimes; groups; sketches of protocols; rings, fields, polynomials; cyclotomic polynomials, primitive roots; pseudo-random number generators; proofs concerning pseudoprimality; factorization attacks finite fields; and elliptic curves. For personnel in computer security, system administration, and information systems.

	Preface
	Introduction
1	Simple Ciphers	1
2	Probability	18
3	Permutations	39
4	A Serious Cipher	58
5	More Probability	88
6	Modern Symmetric Ciphers	96
7	The Integers	108
8	The Hill Cipher	139
9	Complexity	147
10	Public-Key Ciphers	159
11	Prime Numbers	190
12	Roots mod p	199
13	Roots Mod Composites	213
14	Weak Multiplicativity	234
15	Quadratic Reciprocity	242
16	Pseudoprimes	255
17	Groups	265
18	Sketches of Protocols	279
19	Rings, Fields, Polynomials	292
20	Cyclotomic Polynomials	312
21	Random Number Generators	330
22	More on Groups	355
23	Pseudoprimality Proofs	371
24	Factorization Attacks	388
25	Modern Factorization Attacks	411
26	Finite Fields	423
27	Discrete Logs	431
28	Elliptic Curves	444
29	More on Finite Fields	457
	Appendices	484
	Tables	505
	Bibliography	512
	Answers to Selected Exercises	516
	Index	519