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Group arithmetic in C_{3,5} curves

Roger Oyono and Nicolas Thériault

Abstract: In this paper we present a fast addition algorithm in the Jacobian of a C_{3,5} curve over a finite field F _q. We give formulae for D_1⊕ D_2=-(D_1+D_2) which require 2I+264M+10S when D_1 ≠ D_2 and 2I+297M+13S when D_1 = D_2; and for the computation of -D which require 2I+41M+3S. The ⊕ operation is sufficient to compute scalar multiplications after performing a single (initial) -D. Computing the scalar multiplication [k]D, based on the previous fact combined with our algorithm for computing D_1⊕ D_2, is to date the fastest one performing this operation for C_{3,5} curves. These formulae can be easily combined to compute the full group addition and doubling in 3I+308M+13S and 3I+341M+16S respectively, which compares favourably with previously presented formulae.


The following files contain the implementation (in MAGMA) of the arithmetic on the Jacobian of C_{3,5} curves via explicit formulae.

All the programs and documentation are in the following zip archive, C_35.zip (???k).
e-mail : Roger Oyono

Last update November 17, 2011