Full Description
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.
Contents
Modifications of the Rao-Nam Cryptosystem.- Efficient Reduction on the Jacobian Variety of Picard Curves.- Continued Fractions in Hyperelliptic Function Fields.- Discrete Logarithms: Recent Progress.- One-weight Z4-linear Codes.- Efficient Algorithms for the Jacobian Variety of Hyperelliptic Curves y2 = xp — x + 1 Over a Finite Field of Odd Characteristic p.- On Weierstrass Semigroups and One-point Algebraic Geometry Codes.- On the Undetected Error Probability of m-out-of-n Codes on the Binary Symmetric Channel.- Skew Pyramids of Function Fields Are Asymptotically Bad.- A Public Key Cryptosystem Based on Sparse Polynomials.- Higher Weights of Grassmann Codes.- Toric Surfaces and Error-correcting Codes.- Decoding Spherical Codes Generated by Binary Partitions of Symmetric Pointsets.- Worst-Case Analysis of an Algorithm for Computing the Greatest Common Divisor of n Inputs.- Zeta Functions of Curves over Finite Fields with Many Rational Points.- Codes on Drinfeld Modular Curves.- Elliptic Curves, Pythagorean Triples and Applications.- Exponential Sums and Stationary Phase (I).- Exponential Sums in Several Variables over Finite Fields.- Decoding Reed-Solomon Codes Beyond Half the Minimum Distance.- Reed-Muller Type Codes on the Veronese Variety over Finite Fields.- Cryptography Primitives Based on a Cellular Automaton.- Factoring the Semigroup Determinant of a Finite Commutative Chain Ring.
