Computational and Algorithmic Problems in Finite Fields
By: by Igor E. Shparlinski
Series: Mathematics and Its Applications (Soviet Series) -- 88; Mathematics and Its Applications (Soviet Series) -- 88
Publisher: Springer Netherlands
Published: 1992
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 240
ISBN-13: 9789401047968; 9789401118064
Subjects: Mathematics; Information theory; Field theory (Physics); Data processing; Algebra
Description: This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
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