Abstract
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 5 n and F 7 7 n are obtained with 10 multiplications in F 5 n for F 5 5 n and 15 multiplications in F 7 n for F 7 7 n improving the results in Cenk and Özbudak (2008) [4], Cenk et al. (2009) [5], Lee et al. (2008) [1] 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.
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