Introduction to Cryptography with Coding Theory, 2nd edition

Published by Pearson (July 15, 2005) © 2006

  • Wade Trappe
  • Lawrence C. Washington
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  • 1 Overview
    Secure Communications. Cryptographic Applications
  • 2 Classical Cryptosystems.
    Shift Ciphers. Affine Ciphers. The Vigen`ere Cipher. Substitution Ciphers. Sherlock Holmes. The Playfair and ADFGX Ciphers. Block Ciphers. Binary Numbers and ASCII. One-Time Pads. Pseudo-random Bit Generation. LFSR Sequences. Enigma. Exercises. Computer Problems.
  • 3 Basic Number Theory.
    Basic Notions. Solving ax + by = d. Congruences. The Chinese Remainder Theorem. Modular Exponentiation. Fermat and Euler. Primitive Roots. Inverting Matrices Mod n. Square Roots Mod n. Legendre and Jacobi Symbols. Finite Fields. Continued Fractions. Exercises. Computer Problems.
  • 4 The Data Encryption Standard
    Introduction. A Simplified DES-Type Algorithm. Differential Cryptanalysis. DES. Modes of Operation. Breaking DES. Meet-in-the-Middle Attacks. Password Security. Exercises.
  • 5 AES: Rijndael
    The Basic Algorithm. The Layers. Decryption. Design Considerations.
  • 6 The RSA Algorithm
    The RSA Algorithm. Attacks on RSA. Primality Testing. Factoring. The RSA Challenge. An Application to Treaty Verification. The Public Key Concept. Exercises. Computer Problems
  • 7 Discrete Logarithms
    Discrete Logarithms. Computing Discrete Logs. Bit Commitment Diffie-Hellman Key Exchange. ElGamal Public Key Cryptosystems. Exercises. Computer Problems.
  • 8 Hash Functions
    Hash Functions. A Simple Hash Example. The Secure Hash Algorithm. Birthday Attacks. Multicollisions. The Random Oracle Model. Using Hash Functions to Encrypt.
  • 9 Digital Signatures
    RSA Signatures. The ElGamal Signature Scheme. Hashing and Signing. Birthday Attacks on Signatures. The Digital Signature Algorithm. Exercises. Computer Problems.
  • 10 Security Protocols
    Intruders-in-the-Middle and Impostors. Key Distribution. Kerberos Public Key Infrastructures (PKI). X.509 Certificates. Pretty Good Privacy. SSL and TLS. Secure Electronic Transaction. Exercises.
  • 11 Digital Cash
    Digital Cash. Exercises.
  • 12 Secret Sharing Schemes
    Secret Splitting. Threshold Schemes. Exercises. Computer Problems.
  • 13 Games
    Flipping Coins over the Telephone. Poker over the Telephone. Exercises.
  • 14 Zero-Knowledge Techniques
    The Basic Setup. The Feige-Fiat-Shamir Identification Scheme. Exercises.
  • 15 Information Theory
    Probability Review. Entropy. Huffman Codes. Perfect Secrecy. The Entropy of English. Exercises.
  • 16 Elliptic Curves
    The Addition Law. Elliptic Curves Mod n. Factoring with Elliptic Curves. Elliptic Curves in Characteristic 2. Elliptic Curve Cryptosystems. Identity-Based Encryption. Exercises. Computer Problems.
  • 17 Lattice Methods
    Lattices. Lattice Reduction. An Attack on RSA. NTRU. Exercises
  • 18 Error Correcting Codes
    Introduction. Error Correcting Codes. Bounds on General Codes. Linear Codes. Hamming Codes. Golay Codes. Cyclic Codes. BCH Codes. Reed-Solomon Codes. The McEliece Cryptosystem. Other Topics. Exercises. Computer Problems.
  • 19 Quantum Techniques in Cryptography
    A Quantum Experiment. Quantum Key Distribution. Shor’s Algorithm. 4 Exercises.
  • Mathematica Examples
  • Maple Examples
  • MATLAB Examples
  • Further Reading
  • Bibliography
  • Index

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