Discrete logarithm based cryptosystems in quadratic function fields of characteristic 2
type: Item
instance of: scholarly article
title: Discrete logarithm based cryptosystems in quadratic function fields of characteristic 2
zbMATH Open document ID: 0922.94005
DOI: 10.1023/A:1008240113843
author: Volker Müller
author: Scott A. Vanstone
author: Robert J. Zuccherato
published in: Designs, Codes and Cryptography
publication date: 1998-08-12T00:00:00Z
review text: A key exchange scheme in the infrastructure of a quadratic function field of even characteristic is described. It extends earlier work of \textit{R. Scheidler, J. A. Buchmann} and \textit{H. C. Williams} [J. Cryptology 7, 171-199 (1994; Zbl 0816.94018)] in fields of odd characteristic, using the equivalence class in the ideal class group, to function fields of even characteristic. Such key exchanges take place in an algebraic system which is not a group. The infrastructure of quadratic function fields of even characteristic is first examined. Two operations in the infrastructure are defined, the Baby-Step and the Giant-Step. The Baby-Step corresponds to one iteration of the continued fraction algorithm and a Giant-Step corresponds to ideal multiplication and reduction. The concept of distance in the algebraic system is introduced and algorithms are developed for computing ideals `closest to' a given value. These algorithms are used to define the key exchange and digital signature schemes in the structure. Section 3 of the paper gives the algorithms needed to implement the key exchange and digital signature protocols using the quadratic function fields. The following two sections give the protocols and examine their security in a manner similar to the Pohlig-Hellman attack in finite groups. The final section discusses implementations of the protocols.
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 1164303
zbMATH Keywords: digital signatures
zbMATH Keywords: key exchange
zbMATH Keywords: function fields
zbMATH Keywords: discrete logarithm
zbMATH Keywords: characteristic two
zbMATH Keywords: ideal multiplication
reviewed by: Ian Blake
MaRDI profile type: Publication
full work available at URL: a:1008240113843
OpenAlex ID: W1969772521
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description: scientific article; zbMATH DE number 1164303