Efficient multiplications in F(5)5n and F(7)7n

Date

2011-08-15

Author

Cenk, Murat
Özbudak, Ferruh

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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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Citation Formats

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.