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Efficient multiplications in F(5)5n and F(7)7n
Date
2011-08-15
Author
Cenk, Murat
Özbudak, Ferruh
Metadata
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Efficient multiplications in finite fields of characteristics 5 and 7 are used for computing the Eta pairing over divisor class groups of the hyperelliptic curves Lee et al. (2008) [1]. In this paper, using the recent methods for multiplication in finite fields, the explicit formulas for multiplication in F(5)5n and F(7)7n are obtained with 10 multiplications in F(5)n for F(5)5n and 15 multiplications in F(7)n for F(7)7n improving the results in Cenk and Ozbudak (2008) [4], Cenk et al. (2009) [5], Lee et al. (2008) [11 and Montgomery (2005) [12]. The timing results of implementations of the Karatsuba type formulas and the proposed formula for multiplication in F(5)5.89 are given.
Subject Keywords
Finite field multiplication
,
Algebraic function fields
,
Pairing based cryptography
URI
https://hdl.handle.net/11511/32584
Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
DOI
https://doi.org/10.1016/j.cam.2011.06.016
Collections
Graduate School of Applied Mathematics, Article
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M. Cenk and F. Özbudak, “Efficient multiplications in F(5)5n and F(7)7n,”
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
, pp. 177–183, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32584.