Welcome to the resource topic for 2013/041
Title:
Trace Expression of r-th Root over Finite Field
Authors: Gook Hwa Cho, Namhun Koo, Eunhye Ha, Soonhak Kwon
Abstract:Efficient computation of r-th root in \mathbb F_q has many applications in computational number theory and many other related areas. We present a new r-th root formula which generalizes Müller’s result on square root, and which provides a possible improvement of the Cipolla-Lehmer algorithm for general case. More precisely, for given r-th power c\in \mathbb F_q, we show that there exists \alpha \in \mathbb F_{q^r} such that Tr\left(\alpha^\frac{(\sum_{i=0}^{r-1}q^i)-r}{r^2}\right)^r=c where Tr(\alpha)=\alpha+\alpha^q+\alpha^{q^2}+\cdots +\alpha^{q^{r-1}} and \alpha is a root of certain irreducible polynomial of degree r over \mathbb F_q.
ePrint: https://eprint.iacr.org/2013/041
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