Computational and algorithmic problems in finite fields

Includes index

Includes bibliography (p. 191-237) and references

Ch. 1. Polynomial Factorization. 1. Univariate factorization. 2. Multivariate factorization. 3. Other polynomial decompositions
Ch. 2. Finding irreducible and primitive polynomials. l. Construction of irreducible polynomials. 2. Construction of primitive polynomials
Ch. 3. The distribution of irreducible and primitive polynomials. 1. Distribution of irreducible and primitive polynomials. 2. Irreducible and primitive polynomials of a given height and weight. 3. Sparse polynomials. 4. Applications to algebraic number fields
Ch. 4. Bases and computation in finite fields. 1. Construction of some special bases for finite fields. 2. Discrete logarithm and Zech's logarithm. 3. Polynomial multiplication and multiplicative complexity in finite fields. 4. Other algorithms in finite fields
Ch. 5. Coding theory and algebraic curves. 1. Codes and points on algebraic curves. 2. Codes and exponential sums. 3. Codes and lattice packings and coverings
Ch. 6. Elliptic curves. 1. Some general properties. 2. Distribution of primitive points on elliptic curves
Ch. 7. Recurrent sequences in finite fields and cyclic linear codes. 1. Distribution of values of recurrent sequences. 2. Applications of recurrent sequences. 3. Cyclic codes and recurrent sequences
Ch. 8. Finite fields and discrete mathematics. 1. Cryptography and permutation polynomials. 2. Graph theory, combinatorics, Boolean functions. 3. Enumeration problems in finite fields
Ch. 9. Congruences. 1. Optimal coefficients and pseudo-random numbers. 2. Residues of exponential functions. 3. Modular arithmetic. 4. Other applications
Ch. 10. Some related problems. 1. Integer factorization, primality testing and the greatest common divisor. 2. Computational algebraic number theory. 3. Algebraic complexity theory. 4. Polynomials with integer coefficients

A treatment of computation and algorithms for finite fields. The book covers such topics as polynomial factorization, distribution of primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and applications of finite fields to areas of mathematics.