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Fast addition on non-hyperelliptic genus 3 curves
Abstract: We present a fast addition algorithm in the Jacobian of a genus 3 non-hyperelliptic 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 non-hyperelliptic curve of genus 3 can not be an arc.
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The following files contain the implementation (in MAGMA) of the arithmetic on the Jacobian of non-hyperelliptic 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.
Enjoy! If you have any suggestion, the authors invite you to write them to:
e-mail : Roger Oyono
Last update November 17, 2011