Introduction History of Finite Fields, Roderick Gow Finite fields in the 18th and 19th centuries Introduction to Finite Fields Basic properties of finite fields, Gary L. Mullen and Daniel Panario Tables, David Thomson Theoretical Properties Irreducible Polynomials Counting irreducible polynomials, Joseph L. Yucas Construction of irreducible, Melsik Kyuregyan Conditions for reducible polynomials, Daniel Panario Weights of irreducible polynomials, Omran Ahmadi Prescribed coefficients, Stephen D. Cohen Multivariate polynomials, Xiang-dong Hou Primitive Polynomials Introduction to primitive polynomials, Gary L. Mullen and Daniel Panario Prescribed coefficients, Stephen D. Cohen Weights of primitive polynomials, Stephen D. Cohen Elements of high order, José Felipe Voloch Bases Duality theory of bases, Dieter Jungnickel Normal bases, Shuhong Gao and Qunying Liao Complexity of normal bases, Shuhong Gao and David Thomson Completely normal bases, Dirk Hachenberger Exponential and Character Sums Gauss, Jacobi, and Kloosterman sums, Ronald J. Evans More general exponential and character sums, Antonio Rojas-León Some applications of character sums, Alina Ostafe and Arne Winterhof Sum-product theorems and applications, Moubariz Z.

Garaev Equations over Finite Fields General forms, Daqing Wan Quadratic forms, Robert Fitzgerald Diagonal equations, Francis Castro and Ivelisse Rubio Permutation Polynomials One variable, Gary L. Mullen and Qiang Wang Several variables, Rudolf Lidl and Gary L. Mullen Value sets of polynomials, Gary L. Mullen and Michael E. Zieve Exceptional polynomials, Michael E. Zieve Special Functions over Finite Fields Boolean functions, Claude Carlet PN and APN functions, Pascale Charpin Bent and related functions, Alexander Kholosha and Alexander Pott k -polynomials and related algebraic objects, Robert Coulter Planar functions and commutative semifields, Robert Coulter Dickson polynomials, Qiang Wang and Joseph L. Yucas Schur''s conjecture and exceptional covers, Michael D. Fried Sequences over Finite Fields Finite field transforms, Gary McGuire LFSR sequences and maximal period sequences, Harald Niederreiter Correlation and autocorrelation of sequences, Tor Helleseth Linear complexity of sequences and multisequences, Wilfried Meidl and Arne Winterhof Algebraic dynamical systems over finite fields, Igor Shparlinski Algorithms Computational techniques, Christophe Doche Univariate polynomial counting and algorithms, Daniel Panario Algorithms for irreducibility testing and for constructing irreducible polynomials, Mark Giesbrecht Factorization of univariate polynomials, Joachim von zur Gathen Factorization of multivariate polynomials, Erich Kaltofen and Grégoire Lecerf Discrete logarithms over finite fields, Andrew Odlyzko Standard models for finite fields, Bart de Smit and Hendrik Lenstra Curves over Finite Fields Introduction to function fields and curves, Arnaldo Garcia and Henning Stichtenoth Elliptic curves, Joseph Silverman Addition formulas for elliptic curves, Daniel J.

Bernstein and Tanja Lange Hyperelliptic curves, Michael John Jacobson, Jr. and Renate Scheidler Rational points on curves, Arnaldo Garcia and Henning Stichtenoth Towers, Arnaldo Garcia and Henning Stichtenoth Zeta functions and L-functions, Lei Fu p -adic estimates of zeta functions and L-functions, Régis Blache Computing the number of rational points and zeta functions, Daqing Wan Miscellaneous Theoretical Topics Relations between integers and polynomials over finite fields, Gove Effinger Matrices over finite fields, Dieter Jungnickel Classical groups over finite fields, Zhe-Xian Wan Computational linear algebra over finite fields, Jean-Guillaume Dumas and Clément Pernet Carlitz and Drinfeld modules, David Goss Applications Combinatorial Latin squares, Gary L. Mullen Lacunary polynomials over finite fields, Simeon Ball and Aart Blokhuis Affine and projective planes, Gary Ebert and Leo Storme Projective spaces, James W.P. Hirschfeld and Joseph A. Thas Block designs, Charles J. Colbourn and Jeffrey H. Dinitz Difference sets, Alexander Pott Other combinatorial structures, Jeffrey H.

Dinitz and Charles J. Colbourn ( t, m, s )-nets and ( t, s )-sequences, Harald Niederreiter Applications and weights of multiples of primitive and other polynomials, Brett Stevens Ramanujan and expander graphs, M. Ram Murty and Sebastian M. Cioaba Algebraic Coding Theory Basic coding properties and bounds, Ian Blake and W. Cary Huffman Algebraic-geometry codes, Harald Niederreiter LDPC and Gallager codes over finite fields, Ian Blake and W. Cary Huffman Turbo codes over finite fields, Oscar Takeshita Raptor codes, Ian Blake and W. Cary Huffman Polar codes, Simon Litsyn Cryptography Introduction to cryptography, Alfred Menezes Stream and block ciphers, Guang Gong and Kishan Chand Gupta Multivariate cryptographic systems, Jintai Ding Elliptic curve cryptographic systems, Andreas Enge Hyperelliptic curve cryptographic systems, Nicolas Thériault Cryptosystems arising from Abelian varieties, Kumar Murty Binary extension field arithmetic for hardware implementations, M. Anwarul Hasan and Haining Fan Miscellaneous Applications Finite fields in biology, Franziska Hinkelmann and Reinhard Laubenbacher Finite fields in quantum information theory, Martin Roetteler and Arne Winterhof Finite fields in engineering, Jonathan Jedwab and Kai-Uwe Schmidt Bibliography Index.