Items for "Elliptic and hyperelliptic curves"

Rethinking low genus hyperelliptic Jacobian arithmetic over binary fields: interplay of field arithmetic and explicit formulæ

In this paper, we present several improvements on the best known explicit formulæ for hyperelliptic curves of genus three and four in characteristic two, including the issue of reducing memory requirements.

To show the effectiveness of these improvements and to allow a fair comparison of the curves of different genera, we implement all formulæ using a highly optimized software library for arithmetic in binary fields...

Keywords: Elliptic and hyperelliptic curves, cryptography, efficient implementation, explicit formul