Introduction to cryptography with coding theory / by Wade Trappe and Lawrence C. Washington

Index included

1: Overview of Cryptography and Its Applications. Secure Communications ; Cryptographic Applications -- 2: Classical Cryptosystems. Shift Ciphers ; Affine Ciphers ; The Vigenere 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. A Simplified DES-Type Algorithm ; Differential Cryptanalysis ; DES ; Modes of Operation ; Breaking DES ; Meet-in-the-Middle Attacks ; Password Security ; Exercises ; Computer Problems -- 5: The Advanced Encryption Standard : Rijndael. The Basic Algorithm ; The Layers ; Decryption ; Design Considerations ; Exercises -- 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 ; The ElGamal Public Key Cryptosystem ; 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 ; Exercises ; Computer Problems -- 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 p ; 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 ; Exercises -- A Mathematica Examples -- B Maple Examples -- C Matlab Examples.

This text is for a course in cryptography for advanced undergraduate and graduate students. Material is accessible to mathematically mature students having little background in number theory and computer programming. Core material is treated in the first eight chapters on areas such as classical cryptosystems, basic number theory, the RSA algorithm, and digital signatures. The remaining nine chapters cover optional Read more...