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Fast addition on nonhyperelliptic genus 3 curves
Abstract: We present a fast addition algorithm in the Jacobian of a genus 3 nonhyperelliptic curve over a field of any characteristic. When the curve has a rational flex and char(k) > 5, the computational cost for addition is 148M + 15SQ + 2I and 165M + 20SQ + 2I for doubling. An appendix focuses on the computation of flexes in all characteristics. For large odd q, we also show that the set of rational points of a nonhyperelliptic curve of genus 3 can not be an arc. This paper apears in : GENERAL INFORMATION The following files contain the implementation (in MAGMA) of the arithmetic on the Jacobian of nonhyperelliptic curves of genus 3 via explicit formulae. For the moment we only implemented it when the characteristic of base field is at least 7. All the programs and documentation are in the following zip archive, quartic.zip (???k). We have separated it into four files:
Now we get to the VFAQ (Virtually Frequently Asked Questions): HOW TO RUN THE PROGRAMM To run the programm: Run magma in the directory where the files are, and then type: load "input"; To change the input (that is the base field and the curve), edit the file "input" and enter almost what you like. SUGGESTIONS Enjoy! If you have any suggestion, the authors invite you to write them to: Stéphane Flon Roger Oyono Christophe Ritzenthaler email : Roger Oyono
Last update November 17, 2011 