A work-in-progress Julia package to implement the degree 3-to-2 and degree 4-to-3 procedures from this paper by Kleinjung and Wesolowski.
In addition, in the vein of Hecke.jl, this aims to implement general as well as finite field elliptic curve projective and affine point arithmetic, as well as structs for divisors on elliptic curves up to linear equivalence (e.g. principal divisors of rational functions on the curve et al.), as well as for models of elliptic curves with a specific divisor and points on them of a fixed degree.
Also incorporates standard cryptographic fare like point counting and elliptic curve generation procedures.
A future goal is to broaden the scope of the library to be a comprehensive
collection of efficient algorithms for group law computations of points
for elliptic curves (genus g = 1) as well as hyperelliptic curves (genus g = 2)
and for their Jacobians.
| [KW2019] | Thorsten Kleinjung and Benjamin Wesolowski. Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic. In arXiv preprint, 2019. |