Ordinary Pairing-Friendly Genus 2 Hyperelliptic Curves with Absolutely Simple Jacobians

More generally, if k is finite, then we can apply the explicit theta function-based algorithms of Lubicz and Robert [10], implemented in the freely- available avIsogenies package

We give a general framework for uniform, constant-time one- and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate

Galbraith, Lin, and Scott [9] and the author [26] have already con- structed families of endomorphisms equipped with a convenient ready-made basis; in this work, we generalize

Our techniques generalize with- out any difficulty to more general curves and Kummer surfaces, and then re- placing the fast Kummer operations described in Appendix A with more

We conclude that φ is a three-dimensional family of (Z/2Z) 6 -isogenies of (generically) absolutely simple Jacobians, thus proving Theorem 1.1 for the third row of the table..

There exists an algorithm for the point counting problem in a family of genus 2 curves with efficiently computable RM of class number 1, whose complexity is in O((log e q) 5

In this work, we focus on p-adic algorithms that compute the explicit form of a rational representation of an isogeny between Jacobians of hyperelliptic curves for fields of

In Section 3, we review families of pairing friendly curves and in particular the Barreto–Naehrig complete family [2], and explain why Estimate 1 is expected to fail when .k;