The book introduces new techniques which imply rigorous lower bounds on the complexity of some number theoretic and cryptographic problems. These methods and techniques are based on bounds of character sums and numbers of solutions of some polynomial equations over finite fields…
by Centre International de Rencontres Mathématiques, Kohel, David R., Shparlinski, Igor E., Winter School on Frobenius Distributions on Curves, Marsylia), Workshop on Frobenius Distributions on Curves, Marsylia)
Preface. Acknowledgments. Notation. Introduction. Links flowchart. 1. Polynomial Factorization. 2. Finding Irreducible and Primitive Polynomials. 3. The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices. 4. Bases and Computation in Finite Fields. …
by Hazewinkel, M., Shparlinski, Igor E.
fromMathematics and its applications
This book provides an exhaustive survey of the most recent achievements in the theory and applications of finite fields and in many related areas such as algebraic number theory, theoretical computer science, coding theory and cryptography. Topics treated include polynomial fact…
by Jungnickel, Dieter, Niederreiter, Harald, Shparlinski, Igor E., Kyureghyan, Gohar M., Ostafe, Alina, Gong, Guang, Gyarmati, Katalin, Hernando, Fernando, Huczynska, Sophie, McGuire, Gary, Bundesinstitut für Erwachsenenbildung, Workshop on Finite Fields and Their Applications: Character Sums and Polynomials, Strobl
fromRadon series on computational and applied mathematics
Biographical note: Pascale Charpin, INRIA, Le Chesnay, France;Alexander Pott, Otto-von-Guericke-University Magdeburg, Germany; Arne Winterhof, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria. Main description…
"The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new, sometimes quite unexpected, links between number theory and computer science as well as other areas of mathematics. Possible applications include (but are …