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Fast arithmetic on Jacobians of Picard curves
Authors: Stéphane Flon, Roger OyonoAbstract:
In this paper we present a fast addition algorithm in the Jacobian of a Picard curve over a finite field \mathbb F _q of characteristic different from 3. This algorithm has a nice geometric interpretation, comparable to the classic “chord and tangent” law for the elliptic curves. Computational cost for addition is 144M + 12SQ + 2I and 158M + 16SQ + 2I for doubling.
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