Trace Expression of r-th Root over Finite Field
نویسندگان
چکیده
Efficient computation of r-th root in Fq 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 CipollaLehmer type algorithms for general case. More precisely, for given r-th power c ∈ Fq, we show that there exists α ∈ Fqr such that Tr ( α ( ∑r−1 i=0 qi)−r r2 )r = c where Tr(α) = α+α +α 2 + · · ·+αq and α is a root of certain irreducible polynomial of degree r over Fq.
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ورودعنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2013 شماره
صفحات -
تاریخ انتشار 2013