Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography.

The Handbook of Applied Cryptography provides a treatment that is multifunctional:

Alfred J Menezes, Paul C. van Oorschot, Scott A. Vanstone

Foreword by Ronald L. Rivest
Overview of Cryptography
Introduction
Information security and cryptography
Background on functions
Functions(1-1, one-way, trapdoor one-way)
Permutations
Involutions
Basic terminology and concepts
Symmetric-key encryption
Overview of block ciphers and stream ciphers
Substitution ciphers and transposition ciphers
Composition of ciphers
Stream ciphers
The key space
Digital signatures
Authentication and identification
Identification
Data origin authentication
Public-key cryptography
Public-key encryption
The necessity of authentication in public-key systems
Digital signatures from reversible public-key encryption
Symmetric-key versus public-key cryptography
Hash functions
Protocols and mechanisms
Key establishment, management, and certification
Key management through symmetric-key techniques
Key management through public-key techniques
Trusted third parties and public-key certificates
Pseudorandom numbers and sequences
Classes of attacks and security models
Attacks on encryption schemes
Attacks on protocols
Models for evaluating security
Perspective for computational security
Notes and further references
Mathematical Background
Probability theory
Basic definitions
Conditional probability
Random variables
Binomial distribution
Birthday attacks
Random mappings
Information theory
Entropy
Mutual information
Complexity theory
Basic definitions
Asymptotic notation
Complexity classes
Randomized algorithms
Number theory
The integers
Algorithms in Z
The integers modulo n
Algorithms in Zn
The Legendre and Jacobi symbols
Blum integers
Abstract algebra
Groups
Rings
Fields
Polynomial rings
Vector spaces
Finite fields
Basic properties
The Euclidean algorithm for polynomials
Arithmetic of polynomials
Notes and further references
Number-Theoretic Reference Problems
Introduction and overview
The integer factorization problem
Trial division
Pollard's rho factoring algorithm
Pollard's p - 1 factoring algorithm
Elliptic curve factoring
Random square factoring methods
Quadratic sieve factoring
Number field sieve factoring
The RSA problem
The quadratic residuosity problem
Computing square roots in Zn
Case (i): n prime
Case (ii): n composite
The discrete logarithm problem
Exhaustive search
Baby-step giant-step algorithm
Pollard's rho algorithm for logarithms
Pohlig-Hellman algorithm
Index-calculus algorithm
Discrete logarithm problem in subgroups of Z*p
The Diffie-Hellman problem
Composite moduli
Computing individual bits
The discrete logarithm problem in Z*p - individual bits
The RSA problem - individual bits
The Rabin problem - individual bits
The subset sum problem
The L3-Iattice basis reduction algorithm
Solving subset sum problems of low density
Simultaneous diophantine approximation
Factoring polynomials over finite fields
Square-free factorization
Beriekamp's Q-matrix algorithm
Notes and further references
Public-Key Parameters
Introduction
Generating large prime numbers naively
Distribution of prime numbers
Probabilistic primality tests
Fermat's test
Solovay-Strassen test
Miller-Rabin test
Comparison: Fermat, Solovay-Strassen and Miller-Rabin
(True) Primality tests
Testing Mersenne numbers
Primality testing using the factorization of n - 1
Jacobi sum test
Tests using elliptic curves
Prime number generation
Random search for probable primes
Strong primes
NIST method for generating DSA primes
Constructive techniques for provable primes
Irreducible polynomials over Zp
Irreducible polynomials
Irreducible trinomials
Primitive polynomials
Generators and elements of high order
Selecting a prime p and generator of Z*p
Notes and further references
Pseudorandom Bits and Sequences
Introduction
Classification and framework
Random bit generation
Pseudorandom bit generation
ANSI X9.17
FIPS 186
Statistical tests
The normal and chi-square distributions
Hypothesis testing
Golomb's randomness postulates
Five basic tests
Maurer's universal statistical test
Cryptographically secure pseudorandom bit generation
RSA pseudorandom bit generator
Blum-Blum-Shub pseudorandom bit generator
Notes and further references
Stream Ciphers
Introduction
Classification
Feedback shift registers
Linear feedback shift registers
Linear complexity
Berlekamp-Massey algorithm
Nonlinear feedback shift registers
Stream ciphers based on LFSRs
Nonlinear combination generators
Nonlinear filter generators
Clock-controlled generators
Other stream ciphers
SEAL
Notes and further references
Block Ciphers
Introduction and overview
Background and general concepts
Introduction to block ciphers
Modes of operation
Exhaustive key search and multiple encryption
Classical ciphers and historical development
Transposition ciphers
Substitution ciphers
Polyalphabetic substitutions and Vigenère ciphers
Polyalphabetic cipher machines and rotors (historical)
Cryptanalysis of classical ciphers
DES
Product ciphers and Feistel ciphers
DES algorithm
DES properties and strength
FEAL
IDEA
SAFER, RC5, and other block ciphers
SAFER
RC5
Other block ciphers
Notes and further references
Public-Key Encryption
Introduction
Basic principles
RSA public-key encryption
Description
Security of RSA
RSA encryption in practice
Rabin public-key encryption
ElGamal public-key encryption
Basic ElGamal encryption
Generalized ElGamal encryption
McEliece public-key encryption
Knapsack public-key encryption
Merkle-Hellman knapsack encryption
Chor-Rivest knapsac…