Efficient multiplications in F55n and F77n

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Cenk, Murat²  Ozbudak, Ferruh^1,2 

[1] Middle E Tech Univ, Dept Math, TR-06531 Ankara, Turkey

[2] Middle E Tech Univ, Inst Appl Math, TR-06531 Ankara, Turkey

关键词: Finite field multiplication;    Algebraic function fields;    Pairing based cryptography;   

DOI  :  10.1016/j.cam.2011.06.016

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free