Introduction to Cryptography with Coding Theory

by Trappe, Wade; Washington, Lawrence C.

• ISBN13: 9780131862395
• ISBN10: 0131862391
• Edition: 2nd
• Format: Hardcover
• Copyright: 2005-07-15
• Publisher: Pearson

Summary

With its conversational tone and practical focus, this text mixes applied and theoretical aspects for a solid introduction to cryptography and security, including the latest significant advancements in the field. Assumes a minimal background. The level of math sophistication is equivalent to a course in linear algebra. Presents applications and protocols where cryptographic primitives are used in practice, such as SET and SSL. Provides a detailed explanation of AES, which has replaced Feistel-based ciphers (DES) as the standard block cipher algorithm. Includes expanded discussions of block ciphers, hash functions, and multicollisions, plus additional attacks on RSA to make readers aware of the strengths and shortcomings of this popular scheme. For engineers interested in learning more about cryptography.

Table of Contents

Preface	xi
Overview of Cryptography and Its Applications	1	(11)
Secure Communications	2	(7)
Cryptographic Applications	9	(3)
Classical Cryptosystems	12	(51)
Shift Ciphers	13	(1)
Affine Ciphers	14	(2)
The Vigenere Cipher	16	(8)
Substitution Ciphers	24	(3)
Sherlock Holmes	27	(3)
The Playfair and ADFGX Ciphers	30	(4)
Block Ciphers	34	(4)
Binary Numbers and ASCII	38	(1)
One-Time Pads	39	(2)
Pseudo-random Bit Generation	41	(2)
LFSR Sequences	43	(7)
Enigma	50	(5)
Exercises	55	(4)
Computer Problems	59	(4)
Basic Number Theory	63	(50)
Basic Notions	63	(6)
Solving ax + by = d	69	(1)
Congruences	70	(6)
The Chinese Remainder Theorem	76	(2)
Modular Exponentiation	78	(1)
Fermat and Euler	79	(4)
Primitive Roots	83	(2)
Inverting Matrices Mod n	85	(1)
Square Roots Mod n	86	(2)
Legendre and Jacobi Symbols	88	(5)
Finite Fields	93	(9)
Continued Fractions	102	(2)
Exercises	104	(7)
Computer Problems	111	(2)
The Data Encryption Standard	113	(38)
Introduction	113	(1)
A Simplified DES-Type Algorithm	114	(4)
Differential Cryptanalysis	118	(5)
DES	123	(8)
Modes of Operation	131	(8)
Breaking DES	139	(4)
Meet-in-the-Middle Attacks	143	(1)
Password Security	144	(2)
Exercises	146	(3)
Computer Problems	149	(2)
The Advanced Encryption Standard: Rijndael	151	(13)
The Basic Algorithm	152	(2)
The Layers	154	(4)
Decryption	158	(3)
Design Considerations	161	(1)
Exercises	162	(2)
The RSA Algorithm	164	(37)
The RSA Algorithm	164	(5)
Attacks on RSA	169	(7)
Primality Testing	176	(5)
Factoring	181	(6)
The RSA Challenge	187	(2)
An Application to Treaty Verification	189	(1)
The Public Key Concept	189	(3)
Exercises	192	(5)
Computer Problems	197	(4)
Discrete Logarithms	201	(17)
Discrete Logarithms	201	(1)
Computing Discrete Logs	202	(7)
Bit Commitment	209	(1)
Diffie-Hellman Key Exchange	210	(2)
The ElGamal Public Key Cryptosystem	212	(2)
Exercises	214	(2)
Computer Problems	216	(2)
Hash Functions	218	(26)
Hash Functions	218	(4)
A Simple Hash Example	222	(2)
The Secure Hash Algorithm	224	(5)
Birthday Attacks	229	(3)
Multicollisions	232	(3)
The Random Oracle Model	235	(3)
Using Hash Functions to Encrypt	238	(1)
Exercises	239	(3)
Computer Problems	242	(2)
Digital Signatures	244	(12)
RSA Signatures	245	(1)
The ElGamal Signature Scheme	246	(3)
Hashing and Signing	249	(1)
Birthday Attacks on Signatures	250	(1)
The Digital Signature Algorithm	251	(1)
Exercises	252	(3)
Computer Problems	255	(1)
Security Protocols	256	(31)
Intruders-in-the-Middle and Impostors	257	(2)
Key Distribution	259	(7)
Kerberos	266	(4)
Public Key Infrastructures (PKI)	270	(1)
X.509 Certificates	271	(6)
Pretty Good Privacy	277	(3)
SSL and TLS	280	(3)
Secure Electronic Transaction	283	(2)
Exercises	285	(2)
Digital Cash	287	(9)
Digital Cash	287	(7)
Exercises	294	(2)
Secret Sharing Schemes	296	(11)
Secret Splitting	296	(1)
Threshold Schemes	297	(6)
Exercises	303	(2)
Computer Problems	305	(2)
Games	307	(9)
Flipping Coins over the Telephone	307	(2)
Poker over the Telephone	309	(5)
Exercises	314	(2)
Zero-Knowledge Techniques	316	(9)
The Basic Setup	316	(3)
The Feige-Fiat-Shamir Identification Scheme	319	(2)
Exercises	321	(4)
Information Theory	325	(22)
Probability Review	326	(2)
Entropy	328	(5)
Huffman Codes	333	(2)
Perfect Secrecy	335	(3)
The Entropy of English	338	(5)
Exercises	343	(4)
Elliptic Curves	347	(29)
The Addition Law	347	(5)
Elliptic Curves Mod p	352	(4)
Factoring with Elliptic Curves	356	(4)
Elliptic Curves in Characteristic 2	360	(3)
Elliptic Curve Cryptosystems	363	(3)
Identity-Based Encryption	366	(4)
Exercises	370	(4)
Computer Problems	374	(2)
Lattice Methods	376	(16)
Lattices	376	(1)
Lattice Reduction	377	(5)
An Attack on RSA	382	(3)
NTRU	385	(5)
Exercises	390	(2)
Error Correcting Codes	392	(58)
Introduction	392	(6)
Error Correcting Codes	398	(4)
Bounds on General Codes	402	(6)
Linear Codes	408	(8)
Hamming Codes	416	(1)
Golay Codes	417	(9)
Cyclic Codes	426	(6)
BCH Codes	432	(8)
Reed-Solomon Codes	440	(2)
The McEliece Cryptosystem	442	(2)
Other Topics	444	(1)
Exercises	445	(4)
Computer Problems	449	(1)
Quantum Techniques in Cryptography	450	(17)
A Quantum Experiment	451	(3)
Quantum Key Distribution	454	(2)
Shor's Algorithm	456	(10)
Exercises	466	(1)
A Mathematica® Examples	467	(28)
Getting Started with Mathematica	467	(2)
Some Commands	469	(1)
Examples for Chapter 2	470	(7)
Examples for Chapter 3	477	(3)
Examples for Chapter 6	480	(7)
Examples for Chapter 8	487	(1)
Examples for Chapter 12	487	(1)
Examples for Chapter 13	488	(2)
Examples for Chapter 16	490	(5)
B Maple® Examples	495	(32)
Getting Started with Maple	495	(1)
Some Commands	496	(2)
Examples for Chapter 2	498	(7)
Examples for Chapter 3	505	(4)
Examples for Chapter 6	509	(8)
Examples for Chapter 8	517	(1)
Examples for Chapter 12	518	(1)
Examples for Chapter 13	519	(2)
Examples for Chapter 16	521	(6)
C Matlab® Examples	527	(38)
Getting Started with Matlab	528	(5)
Examples for Chapter 2	533	(11)
Examples for Chapter 3	544	(4)
Examples for Chapter 6	548	(5)
Examples for Chapter 8	553	(1)
Examples for Chapter 12	553	(1)
Examples for Chapter 13	554	(2)
Examples for Chapter 16	556	(8)
D Suggestions for Further Reading	564
Bibliography	565	(6)
Index	571