Appendix A

This appendix contains a complete implementation in MAGMA of the algorithms described in the paper Fast Jacobian group operations for C3,4 curves over a large finite field.

The list of files is as follows.

  • The file curve.magma contains the code for our algorithms, as well as a sample set of values over the finite field K whose cardinality |K| is the first prime above 108. Larger values of |K| pose no problem, but then elements of K will appear less legible in a printout. The sample set of values includes two data structures FG and FG2 representing the divisors D and D' of our algorithms.
  • The file sample_run_output.txt contains a sample run of our addition and doubling algorithms on the divisors D and D' defined in curve.magma. We verify that the results are correct using the built-in operations in MAGMA for ideals in polynomial algebras.
  • The file sample_run_input.magma is the input that was used to produce the output above.