Finite Field Multiplication in Lagrange Representation Using Fast Fourrier Transform
نویسنده
چکیده
The multiplication in Fpn can be performed using a polynomial version of Montgomery multiplication (Montgomery, 1985). In (Bajard et al., 2003) Bajard et al. improved this method by using a Lagrange representation: the elements of Fpn are represented by their values at a fixed set of points. The costly operations in this new algorithm are the two changes of Lagrange representation which require 2r operations in Fp with n ≤ r ≤ 22. In this paper we present a new method to perform the change of Lagrange representation. This method uses Fast Fourier Transform and has a cost equal to 3rlog2(r) operations in Fp with r = 22.
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