| Handbook of Applied Cryptography (1997) |
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| From the Publisher A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper. Table of Contents 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 Book Description 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: |
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| Notes |
| Includes bibliographical references (p. 703-754) and index. |