Cryptology ePrint Archive: Report 2003/079

Fast arithmetic on Jacobians of Picard curves

Stéphane Flon and Roger Oyono

Abstract: 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.

Category / Keywords: public-key cryptography / Jacobians, Picard curves, algebraic curves cryptography, discrete logarithm problem

Date: received 25 Apr 2003, last revised 21 Aug 2003

Contact author: flon at math uni-bonn de, oyono@exp-math uni-essen de

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Version: 20030821:103203 (All versions of this report)

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