theta-pairings-dim2

link to the Github repo

This is a repository that implements the computation of the Tate pairing and Weil pairing on abelian varieties of dimension 2 (Jacobians of genus-2 hyperelliptic curves and products of elliptic curves) using the theory of algebraic theta functions and the theory of biextensions of elliptic curves.

It is based on:

• two-isogenies that implements 2-dimensional abelian varieties in the theta model;
• kummer-line that implements biextension-based pairing algorithms in dimension 1.

It was written as a proof-of-concept implementation linked to Chapter 4 of my Master’s thesis. The repo is still in an early stage (no randomized testing, no optimizations) but I hope to clean it up and integrate it in SageMath (after two-isogenies is integrated too) in the future. Contributions or suggestions are welcome!