Introduction to Cryptography with Coding Theory

by Trappe, Wade; Washington, Lawrence C.

• ISBN13: 9780130618146
• ISBN10: 0130618144
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: Pearson College Div

Summary

For advanced undergraduate courses in cryptography and network security in departments of math and computer science. Assumes a minimal background in programming and a level of math sophistication equivalent to a course in linear algebra.

Table of Contents

Preface	xi
Overview	1	(11)
Secure Communications	2	(7)
Cryptographic Applications	9	(3)
Classical Cryptosystems	12	(47)
Shift Ciphers	13	(1)
Affine Ciphers	14	(2)
The Vigenere Cipher	16	(7)
Substitution Ciphers	23	(3)
Sherlock Holmes	26	(3)
The Playfair and ADFGX Ciphers	29	(4)
Block Ciphers	33	(4)
Binary Numbers and ASCII	37	(1)
One-Time Pads	38	(2)
Pseudo-random Bit Generation	40	(2)
Linear Feedback Shift Register Sequences	42	(7)
Enigma	49	(5)
Exercises	54	(2)
Computer Problems	56	(3)
Basic Number Theory	59	(38)
Basic Notions	59	(6)
Solving ax + by = d	65	(1)
Congruences	66	(6)
The Chinese Remainder Theorem	72	(2)
Modular Exponentiation	74	(1)
Fermat and Euler	75	(4)
Primitive Roots	79	(1)
Inverting Matrices Mod n	80	(1)
Square Roots Mod n	81	(2)
Finite Fields	83	(8)
Exercises	91	(4)
Computer Problems	95	(2)
The Data Encryption Standard	97	(30)
Introduction	97	(1)
A Simplified DES-Type Algorithm	98	(4)
Differential Cryptanalysis	102	(5)
DES	107	(8)
Models of Operation	115	(3)
Breaking DES	118	(5)
Password Security	123	(2)
Exercises	125	(2)
AES: Rijndael	127	(10)
The Basic Algorithm	128	(1)
The Layers	129	(4)
Decryption	133	(3)
Design Considerations	136	(1)
The RSA Algorithm	137	(28)
The RSA Algorithm	137	(5)
Attacks on RSA	142	(3)
Primality Testing	145	(4)
Factoring	149	(5)
The RSA Challenge	154	(2)
An Application to Treaty Verification	156	(1)
The Public Key Concept	156	(3)
Exercises	159	(3)
Computer Problems	162	(3)
Discrete Logarithms	165	(12)
Discrete Logarithms	165	(1)
Computing Discrete Logs	166	(7)
Bit Commitment	173	(1)
The ElGamal Public Key Cryptosystem	173	(2)
Exercises	175	(1)
Computer Problems	176	(1)
Digital Signatures	177	(19)
RSA Signatures	178	(1)
The EIGamal Signature Scheme	179	(3)
Hash Functions	182	(4)
Birthday Attacks	186	(4)
The Digital Signature Algorithm	190	(1)
Exercises	191	(3)
Computer Problems	194	(2)
E-Commerce and Digital Cash	196	(12)
Secure Electronic Transaction	197	(2)
Digital Cash	199	(7)
Exercises	206	(2)
Secret Sharing Schemes	208	(11)
Secret Splitting	208	(1)
Threshold Schemes	209	(6)
Exercises	215	(2)
Computer Problems	217	(2)
Games	219	(9)
Flipping Coins over the Telephone	219	(2)
Poker over the Telephone	221	(5)
Exercises	226	(2)
Zero-Knowledge Techniques	228	(8)
The Basic Setup	228	(3)
Feige-Fiat-Shamir Identification Scheme	231	(2)
Exercises	233	(3)
Key Establishment Protocols	236	(14)
Key Agreement Protocols	237	(2)
Key Pre-distribution	239	(2)
Key Distribution	241	(5)
Public Key Infrastructures (PKI)	246	(2)
Exercises	248	(2)
Information Theory	250	(22)
Probability Review	251	(2)
Entropy	253	(5)
Huffman Codes	258	(2)
Perfect Secrecy	260	(3)
The Entropy of English	263	(5)
Exercises	268	(4)
Elliptic Curves	272	(23)
The Addition Law	272	(4)
Elliptic Curves Mod n	276	(4)
Factoring with Elliptic Curves	280	(4)
Elliptic Curves in Characteristic 2	284	(3)
Elliptic Curve Cryptosystems	287	(3)
Exercises	290	(3)
Computer Problems	293	(2)
Error Correcting Codes	295	(58)
Introduction	295	(6)
Error Correcting Codes	301	(4)
Bounds on General Codes	305	(6)
Linear Codes	311	(8)
Hamming Codes	319	(1)
Golay Codes	320	(9)
Cyclic Codes	329	(6)
BCH Codes	335	(8)
Reed-Solomon Codes	343	(2)
The McEliece Cryptosystem	345	(3)
Other Topices	348	(1)
Exercises	349	(3)
Computer Problems	352	(1)
Quantum Cryptography	353	(19)
A Quantum Experiment	354	(3)
Quantum Key Distribution	357	(2)
Shor's Algorithm	359	(11)
Exercises	370	(2)
A Mathematica	372	(31)
Getting Started with Mathematica	372	(2)
Some Commands	374	(1)
Examples for Chapter 2	375	(7)
Examples for Chapter 3	382	(4)
Examples for Chapter 6	386	(8)
Examples for Chapter 8	394	(1)
Examples for Chapter 10	395	(1)
Examples for Chapter 11	396	(1)
Examples for Chapter 15	397	(6)
B Maple Examples	403	(34)
Getting Started with Maple	403	(1)
Some Commands	404	(2)
Examples for Chapter 2	406	(8)
Examples for Chapter 3	414	(5)
Examples for Chapter 6	419	(9)
Examples for Chapter 8	428	(1)
Examples for Chapter 10	428	(2)
Examples for Chapter 11	430	(2)
Examples for Chapter 15	432	(5)
C MATLAB Examples	437	(41)
Getting Started with MATLAB	438	(6)
Examples for Chapter 2	444	(12)
Examples for Chapter 3	456	(4)
Examples for Chapter 6	460	(6)
Examples for Chapter 8	466	(1)
Examples for Chapter 10	466	(1)
Examples for Chapter 11	467	(3)
Examples for Chapter 15	470	(8)
D Further Reading	478	(1)
Bibliography	479	(6)
Index	485