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Software Implementation of Finite Fields of Characteristic Three, for Use in Pairing-based Cryptosystems

Published online by Cambridge University Press:  01 February 2010

K. Harrison ,
D. Page  and
N. P. Smart
K. Harrison
Affiliation:
Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol, BS34 8QZ, keith_harrison@hp.com
D. Page
Affiliation:
Dept. Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, page@cs.bris.ac.uk
N. P. Smart
Affiliation:
Dept. Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, nigel@cs.bris.ac.uk

Abstract

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In this paper, the authors examine a number of ways of implementing characteristic three arithmetic for use in cryptosystems based on the Tate pairing. Three alternative representations of the field elements are examined, and the resulting algorithms for the field addition, multiplication and cubing are compared. Issues related to the arithmetic of supersingular elliptic curves over fields of characteristic three are also examined. Details of how to compute the Tate pairing itself are not covered, since these are well documented elsewhere.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 5 , 2002 , pp. 181 - 193
Copyright
Copyright © London Mathematical Society 2002

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