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.
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Table of Contents
Secure Communications. Cryptographic Applications
2 Classical Cryptosystems.
Shift Ciphers. Affine Ciphers. The Vige&ngrave;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.
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.
Most Helpful Customer Reviews
I highly, highly recommend this book to anyone who either is taking a course in cryptography in school or wants to learn about it. It is a very well written book which clarifies a lot of basic concepts. I bought it as it was recommended by my professor in school and managed to get an A in the course. It is a good book and I think it helped me come back after a lecture and find all the matter that I needed. Good reference material.
Trappe and Washington give us a very up to date education in cryptography, circa 2005. The discourse is for a sophisticated maths student who, however, need never have encountered cryptography before. The level of mathematical treatment is good and rigourous. With theorems stated and proved at a level that should satisfy even a picky mathematician. The recent nature of the book is reflected in several places. Notably where it explains the Advanced Encryption Standard, or Rijndael. This is significant because it is endorsed by the US National Institute of Standards and Technology as the replacement for DES, in such contexts as electronic commerce. (DES is also covered by the book.) Interestingly, the authors offer a short chapter on digital cash. A fascinating look at a possible future direction of a (physically) cashless society. Other texts on cryptography rarely cover the topic, so it's good to see it here. Yes, the first implementations of digital cash largely died in the dot com crash. But the idea lives on, and may yet take fruit. It has solid intellectual foundations, as shown by the book. Then there is an even more speculative chapter on quantum cryptography. Radically different from the symmetric and public key cryptosystems described in the rest of the book. Who knows how quantum cryptography will turn out? Some very hard physical problems need to be solved.