Coding theory, cryptography, and related areas : proceedings of an International Conference on Coding Theory, Cryptography, and Related Areas, held in Guanajuato, Mexico, in April 1998

This book contains 23 contributions presented at the "International Conference on Coding Theory, Cryptography and Related Areas (ICCC)", held in Guanajuato, Mexico, in April 1998. It comprises a series of research papers on various aspects of coding theory (geometric-algebraic, decoding, exponential sums, etc.) and cryptography (discrete logarithm problem, public key cryptosystems, primitives, etc.), as well as in other research areas, such as codes over finite rings and some aspects of function fields and algebraic geometry over finite fields. The book contains new results on the subject, never published in any other form. It will be useful to students, researchers, professionals, and tutors interested in this area of research. Modifications of the Rao-Nam cryptosystem / Ángela I. Barbero and Øyvind Ytrehus Efficient reduction on the Jacobian variety of Picard curves / Ernesto Reinaldo Barreiro, Jorge Estrada Sarlabous, and Jean-Pierre Cherdieu Continued fractions in hyperelliptic function fields / T.G. Berry Discrete logarithms : recent progress / Johannes Buchmann and Damian Weber One-weight Z4-linear codes / Claude Carlet Efficient algorithms for the Jacobian variety of hyperelliptic curves y2=x[superscript p]-x+1 over a finite field of odd charactieristc p / Iwan Duursma and Kouichi Sakurai On Weierstrass semigroups and one-point algebraic geometry codes / J.I. Farrán On the undetected error probability of m-out-of-n codes on the binary symmetric channel / Fang-Wei Fu, Torleiv Kløve, and Shu-Tao Xia Skew pyramids of function fields are asymptotically bad / Arnaldo Garcia and Henning Stichtenoth A public key cryptosystem based on sparse polynomials / D. Grant ... [et al.] Higher weights of Grassman codes / Sudhir R. Ghorpade and Gilles Lachaud Toric surfaces and error-correcting codes / Johan P. Hansen Decoding spherical codes generated by binary partitions of symmetric pointsets / John K. Karlof and Guodong Liu Worst-case analysis of an algorithm for computing the greatest common divisor of n inputs / Charles Lam, Jeffrey Shallit, and Scott Vanstone Zeta functions of curves over finite fields with many rational points / Kristin Lauter Codes on Drinfeld modular curves / Bartolomé López and Ignacio Luengo Elliptic curves, Pythagorean triples and applications / J. Miret, J. Tena, and M. Valls Exponential sums and stationary phase (I) / Carlos Julio Moreno Exponential sums in several variables over finite fields / Oscar Moreno, Francis N. Castro, and Alberto Cáceres Decoding Reed-Solomon codes beyond half the minimum distance / R. Refslund Nielsen and T. Høholdt Reed-Muller type codes on the Veronese variety over finite fields / C. Rentería and H. Tapia-Recillas Cryptography primitives based on a cellular automaton / Jesús Urías Factoring the semigroup determinant of a finite commutative chain ring / Jay A. Wood. Front Matter....Pages I-VIII Modifications of the Rao-Nam Cryptosystem....Pages 1-12 Efficient Reduction on the Jacobian Variety of Picard Curves....Pages 13-28 Continued Fractions in Hyperelliptic Function Fields....Pages 29-41 Discrete Logarithms: Recent Progress....Pages 42-56 One-weight Z 4 -linear Codes....Pages 57-72 Efficient Algorithms for the Jacobian Variety of Hyperelliptic Curves y 2 =x p -x+1 Over a Finite Field of Odd Characteristic p ....Pages 73-89 On Weierstrass Semigroups and One-point Algebraic Geometry Codes....Pages 90-101 On the Undetected Error Probability of m -out-of- n Codes on the Binary Symmetric Channel....Pages 102-110 Skew Pyramids of Function Fields Are Asymptotically Bad....Pages 111-113 A Public Key Cryptosystem Based on Sparse Polynomials....Pages 114-121 Higher Weights of Grassmann Codes....Pages 122-131 Toric Surfaces and Error-correcting Codes....Pages 132-142 Decoding Spherical Codes Generated by Binary Partitions of Symmetric Pointsets....Pages 143-155 Worst-Case Analysis of an Algorithm for Computing the Greatest Common Divisor of n Inputs....Pages 156-166 Zeta Functions of Curves over Finite Fields with Many Rational Points....Pages 167-174 Codes on Drinfeld Modular Curves....Pages 175-183 Elliptic Curves, Pythagorean Triples and Applications....Pages 184-194 Exponential Sums and Stationary Phase (I)....Pages 195-208 Exponential Sums in Several Variables Over Finite Fields....Pages 209-220 Decoding Reed-Solomon Codes Beyond Half the Minimum Distance....Pages 221-236 Reed-Muller Type Codes on the Veronese Variety over Finite Fields....Pages 237-243 Cryptography Primitives Based on a Cellular Automaton....Pages 244-248 Factoring the Semigroup Determinant of a Finite Commutative Chain Ring....Pages 249-264

A series of research papers on various aspects of coding theory, cryptography, and other areas, including new and unpublished results on the subjects. The book will be useful to students, researchers, professionals, and tutors interested in this area of research.