Author(s): Margaret Cozzens, Steven J. Miller
Series: MATHEMATICAL WORLD, VOLUME 29
Publisher: American Mathematical Society
Year: 2013
Language: English
Pages: 355
Contents
Preface
Acknowledgments
Chapter 1. Historical Introduction
1.1. Ancient Times
1.2. Cryptography During the Two World Wars
1.3. Postwar Cryptography, Computers, and Security
1.4. Summary
1.5. Problems
Chapter 2. Classical Cryptology: Methods
2.1. Ancient Cryptography
2.2. Substitution Alphabet Ciphers
2.3. The Caesar Cipher
2.4. Modular Arithmetic
2.5. Number Theory Notation
2.6. The Affine Cipher
2.7. The Vigen`ere Cipher
2.8. The Permutation Cipher
2.9. The Hill Cipher
2.10. Summary
2.11. Problems
Chapter 3. Enigma and Ultra
3.1. Setting the Stage
3.2. Some Counting
3.3. Enigma’s Security
3.4. Cracking the Enigma
3.5. Codes in World War II
3.6. Summary
3.7. Appendix: Proofs by Induction
3.8. Problems
Chapter 4. Classical Cryptography: Attacks I
4.1. Breaking the Caesar Cipher
4.2. Function Preliminaries
4.3. Modular Arithmetic and the Affine Cipher
4.4. Breaking the Affine Cipher
4.5. The Substitution Alphabet Cipher
4.6. Frequency Analysis and the Vigen`ere Cipher
4.7. The Kasiski Test
4.8. Summary
4.9. Problems
Chapter 5. Classical Cryptography: Attacks II
5.1. Breaking the Permutation Cipher
5.2. Breaking the Hill Cipher
5.3. Running Key Ciphers
5.4. One-Time Pads
5.5. Summary
5.6. Problems
Chapter 6. Modern Symmetric Encryption
6.1. Binary Numbers and Message Streams
6.2. Linear Feedback Shift Registers
6.3. Known-Plaintext Attack on LFSR Stream Ciphers
6.4. LFSRsum
6.5. BabyCSS
6.6. Breaking BabyCSS
6.7. BabyBlock
6.8. Security of BabyBlock
6.9. Meet-in-the-Middle Attacks
6.10. Summary
6.11. Problems
Chapter 7. Introduction to Public-Channel Cryptography
7.1. The Perfect Code Cryptography System
7.2. KidRSA
7.3. The Euclidean Algorithm
7.4. Binary Expansion and Fast Modular Exponentiation
7.5. Prime Numbers
7.6. Fermat’s little Theorem
7.7. Summary
7.8. Problems
Chapter 8. Public-Channel Cryptography
8.1. RSA
8.2. RSA and Symmetric Encryption
8.3. Digital Signatures
8.4. Hash Functions
8.5. Diffie–Hellman Key Exchange
8.6. Why RSA Works
8.7. Summary
8.8. Problems
Chapter 9. Error Detecting and Correcting Codes
9.1. Introduction
9.2. Error Detection and Correction Riddles
9.3. Definitions and Setup
9.4. Examples of Error Detecting Codes
9.5. Error Correcting Codes
9.6. More on the Hamming
9.7. From Parity to UPC Symbols
9.8. Summary and Further Topics
9.9. Problems
Chapter 10. Modern Cryptography
10.1. Steganography—Messages You Don’t Know Exist
10.2. Steganography in the Computer Age
10.3. Quantum Cryptography
10.4. Cryptography and Terrorists at Home and Abroad
10.5. Summary
10.6. Problems
Chapter 11. Primality Testing and Factorization
11.1. Introduction
11.2. Brute Force Factoring
11.3. Fermat’s Factoring Method
11.4. Monte Carlo Algorithms and F
T Primality Test
11.5. Miller–Rabin Test
11.6. Agrawal–Kayal–Saxena Primality Test
11.7. Problems
Chapter 12. Solutions to Selected Problems
12.1. Chapter 1: Historical Introduction
12.2. Chapter 2: Classical Cryptography: Methods
12.3. Chapter 3: Enigma and Ultra
12.4. Chapter 4: Classical Cryptography: Attacks I
12.5. Chapter 5: Classical Cryptography: Attacks II
12.6. Chapter 6: Modern Symmetric Encryption
12.7. Chapter 7: Introduction to Public-Channel Cryptography
12.8. Chapter 8: Public-Channel Cryptography
12.9. Chapter 9: Error Detecting and Correcting Codes
12.10. Chapter 10: Modern Cryptography
12.11. Chapter 11: Primality Testing and Factorization
Bibliography
Index
