Cryptography and secure communication / Richard E. Blahut.

Includes bibliographical references (pages 558-575) and index.

Machine generated contents note: 1.Introduction -- 1.1.Classical cryptography -- 1.2.Notions of cryptographic secrecy -- 1.3.Block ciphers -- 1.4.Stream ciphers -- 1.5.Public-key cryptography -- 1.6.Iterated and cascade ciphers -- 1.7.Cryptanalysis -- 1.8.Implementation attacks -- 1.9.Complexity theory -- 1.10.Authentication and identification -- 1.11.Ownership protection -- 1.12.Covert communications -- 1.13.History of information protection -- 2.The integers -- 2.1.Basic number theory -- 2.2.The euclidean algorithm -- 2.3.Prime fields -- 2.4.Quadratic residues -- 2.5.Quadratic reciprocity -- 2.6.The Jacobi symbol -- 2.7.Primality testing -- 2.8.The Fermat algorithm -- 2.9.The Solovay--Strassen algorithm -- 2.10.The Miller--Rabin algorithm -- 2.11.Factoring of integers -- 2.12.The Pollard algorithm for factoring -- 2.13.Square roots in a prime field -- 3.Cryptography based on the integer ring -- 3.1.Biprime cryptography -- 3.2.Implementing biprime cryptography --

Contents note continued: 3.3.Protocol attacks on biprime cryptography -- 3.4.Direct attacks on biprime encryption -- 3.5.Factoring biprimes -- 3.6.The quadratic sieve -- 3.7.The number-field sieve -- 3.8.The Rabin cryptosystem -- 3.9.The rise and fall of knapsack cryptosystems -- 4.Cryptography based on the discrete logarithm -- 4.1.Diffie--Hellman key exchange -- 4.2.Discrete logarithms -- 4.3.The Elgamal cryptosystem -- 4.4.Trapdoor one-way functions -- 4.5.The Massey--Omura cryptosystem -- 4.6.The Pohlig--Hellman algorithm -- 4.7.The Shanks algorithm -- 4.8.The Pollard algorithm for discrete logarithms -- 4.9.The method of index calculus -- 4.10.Complexity of the discrete-log problem -- 5.Information-theoretic methods in cryptography -- 5.1.Probability space -- 5.2.Entropy -- 5.3.Perfect secrecy -- 5.4.The Shannon--McMillan theorem -- 5.5.Unicity distance -- 5.6.Entropy of natural language -- 5.7.Entropy expansion -- 5.8.Data compaction -- 5.9.The wiretap channel --

Contents note continued: 6.Block ciphers -- 6.1.Block substitution -- 6.2.The Feistel network -- 6.3.The Data Encryption Standard -- 6.4.Using the Data Encryption Standard -- 6.5.Double and triple DES encryption -- 6.6.The Advanced Encryption Standard -- 6.7.Differential cryptanalysis -- 6.8.Linear cryptanalysis -- 7.Stream ciphers -- 7.1.State-dependent encryption -- 7.2.Additive stream ciphers -- 7.3.Linear shift-register sequences -- 7.4.The linear-complexity attack -- 7.5.Analysis of linear complexity -- 7.6.Keystreams from nonlinear feedback -- 7.7.Keystreams from nonlinear combining -- 7.8.Keystreams from nonlinear functions -- 7.9.The correlation attack -- 7.10.Pseudorandom sequences -- 7.11.Nonlinear sets of sequences -- 8.Authentication and ownership protection -- 8.1.Authentication -- 8.2.Identification -- 8.3.Authentication signatures -- 8.4.Hash functions -- 8.5.The birthday attack -- 8.6.Iterated hash constructions -- 8.7.Formal hash functions --

Contents note continued: 8.8.Practical hash functions -- 9.Groups, rings, and fields -- 9.1.Groups -- 9.2.Rings -- 9.3.Fields -- 9.4.Prime fields -- 9.5.Binary fields and ternary fields -- 9.6.Univariate polynomials -- 9.7.Extension fields -- 9.8.The multiplication cycle in a finite field -- 9.9.Cyclotomic polynomials -- 9.10.Vector spaces -- 9.11.Linear algebra -- 9.12.The Fourier transform -- 9.13.Existence of finite fields -- 9.14.Bivariate polynomials -- 9.15.Modular reduction and quotient groups -- 9.16.Factoring of univariate polynomials -- 10.Cryptography based on elliptic curves -- 10.1.Elliptic curves -- 10.2.Elliptic curves over finite fields -- 10.3.The operation of point addition -- 10.4.The order of an elliptic curve -- 10.5.The group of an elliptic curve -- 10.6.Supersingular elliptic curves -- 10.7.Elliptic curves over binary fields -- 10.8.Computation of point multiples -- 10.9.Elliptic curve cryptography -- 10.10.The projective plane --

Contents note continued: 10.11.Point counting in an extension field -- 10.12.Morphisms of elliptic curves over the rationals -- 10.13.Morphisms of elliptic curves over finite fields -- 10.14.Point counting in a ground field -- 10.15.The method of xedni calculus -- 10.16.Elliptic curves and the complex field -- 10.17.Curves constructed using complex multiplication -- 11.Cryptography based on hyperelliptic curves -- 11.1.Hyperelliptic curves -- 11.2.Coordinate rings and function fields -- 11.3.Poles and zeros -- 11.4.Divisors -- 11.5.Principal divisors -- 11.6.Principal divisors on elliptic curves -- 11.7.Jacobians as quotient groups -- 11.8.The group of a hyperelliptic curve -- 11.9.Semireduced divisors and jacobians -- 11.10.The Mumford transform -- 11.11.The Cantor reduction algorithm -- 11.12.Reduced divisors and jacobians -- 11.13.The Cantor--Koblitz algorithm -- 11.14.Hyperelliptic-curve cryptography -- 11.15.Order of the hyperelliptic jacobians --

Contents note continued: 11.16.Some examples of the jacobian group -- 12.Cryptography based on bilinear pairings -- 12.1.Bilinear pairings -- 12.2.Pairing-based cryptography -- 12.3.Pairing-based key exchange -- 12.4.Identity-based encryption -- 12.5.Pairing-based signatures -- 12.6.Attacks on the bilinear Diffie--Hellman protocol -- 12.7.Torsion points and embedding degree -- 12.8.The torsion structure theorem -- 12.9.The structure of a pairing -- 12.10.Attacks using bilinear pairings -- 12.11.The Tate pairing -- 12.12.The Miller algorithm -- 12.13.The Weil pairing -- 12.14.Pairing-friendly curves -- 12.15.Barreto--Naehrig elliptic curves -- 12.16.More pairing-friendly curves -- 13.Implementation -- 13.1.Pairing enhancements -- 13.2.Accelerated pairings -- 13.3.Doubling and tripling -- 13.4.Point representations -- 13.5.Algorithms for elliptic-curve arithmetic -- 13.6.Modular addition in an integer ring -- 13.7.Modular multiplication in an integer ring --

Contents note continued: 13.8.Representations of binary fields -- 13.9.Multiplication and squaring in a binary field -- 13.10.Complementary bases -- 13.11.Division in a finite field -- 14.Cryptographic protocols for security and identification -- 14.1.Protocols for cryptographic security -- 14.2.Identification protocols -- 14.3.Zero-knowledge protocols -- 14.4.Methods of secure identification -- 14.5.Signature protocols -- 14.6.Protocols for secret sharing -- 15.More public-key cryptography -- 15.1.Introduction to lattices -- 15.2.Elementary problems in lattice theory -- 15.3.Reduction of a lattice basis -- 15.4.Lattice-based cryptography -- 15.5.Attacks on lattice cryptosystems -- 15.6.Introduction to codes -- 15.7.Subspace projection -- 15.8.Code-based cryptography.