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.
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Flon, S., Oyono, R. (2004). Fast Arithmetic on Jacobians of Picard Curves. In: Bao, F., Deng, R., Zhou, J. (eds) Public Key Cryptography – PKC 2004. PKC 2004. Lecture Notes in Computer Science, vol 2947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24632-9_5
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DOI: https://doi.org/10.1007/978-3-540-24632-9_5
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