Author:
Harrison K.,Page D.,Smart N. P.
Abstract
AbstractIn 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.
Subject
Computational Theory and Mathematics,General Mathematics
Reference13 articles.
1. Reducing elliptic curve logarithms to logarithms in a finite field
2. The art of computer programming;Knuth;2 - Semi-numerical algorithms,1981
3. ‘Efficient elliptic curve exponentiation using mixed coordinates’;Cohen;Advances in Cryptology
4. ‘Short signatures from the Weil pairing’;Boneh;Advances in Cryptology
5. Elliptic Curves in Cryptography
Cited by
29 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Systolic Design Space Exploration of Polynomial Division over $$GF(3^m)$$;Proceedings of the Future Technologies Conference (FTC) 2018;2018-10-20
2. A class of Gaussian normal bases and their dual bases;Journal of Discrete Mathematical Sciences and Cryptography;2017-11-17
3. On the arithmetic operations over finite fields of characteristic three with low complexity;Journal of Computational and Applied Mathematics;2014-03
4. Key Length Estimation of Pairing-Based Cryptosystems Using ηT Pairing over GF(3n);IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences;2014
5. Use of SIMD Features to Speed up Eta Pairing;E-Business and Telecommunications;2014