Key-Exchange in Real Quadratic Congruence Function Fields

Authors:
R. Scheidler;A. Stein;Hugh C. Williams
Affiliations:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716 U.S.A. scheidle@math.udel.edu;FB-9 Mathematik, Universität des Saarlandes, 66041 Saarbrücken, Germany andreas@math.uni-sb.de;Department of Computer Science, University of Manitoba, Winnipeg, MB, Canada R3T 2N2 hugh_williams@csmail.cs.umanitoba.ca
Venue:
Designs, Codes and Cryptography - Special issue dedicated to Gustavus J. Simmons
Year:
1996

Citing 2
Cited 11

An algorithm for determining the regulator and the fundamental unit of hyperelliptic congruence function field

ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
A course in computational algebraic number theory

A course in computational algebraic number theory

SIMATH—a computer algebra system for number theoretic applications

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Discrete Logarithm Based Cryptosystems in Quadratic FunctionFields of Characteristic 2

Designs, Codes and Cryptography
The State of Elliptic Curve Cryptography

Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Cryptography in Quadratic Function Fields

Designs, Codes and Cryptography
The parallelized Pollard kangaroo method in real Quadratic function fields

Mathematics of Computation
Explict bounds and heuristics on class numbers in hyperelliptic function fields

Mathematics of Computation
Computational Aspects of NUCOMP

ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Arithmetic on superelliptic curves

Mathematics of Computation
Abstract Infrastructures of Unit Rank Two (abstract only)

ACM Communications in Computer Algebra
Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation

WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Efficient hyperelliptic arithmetic using balanced representation for divisors

ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show how the theory of real quadratic congruence function fields can be used to produce a secure key distribution protocol. The technique is similar to that advocated by Diffie and Hellman in 1976, but instead of making use of a group for its underlying structure, makes use of a structure which is "almost" a group. The method is an extension of the recent ideas of Scheidler, Buchmann and Williams, but, because it is implemented in these function fields, several of the difficulties with their protocol can be eliminated. A detailed description of the protocol is provided, together with a discussion of the algorithms needed to effect it.