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A new elliptic curve point compression method based on Fp-rationality of some generalized Kummer surfaces
elliptic cryptography point compression Barreto-Naehrig curves
2019/9/19
In the article we propose a new compression method (to 2log2(p)+32log2(p)+3 bits) for the Fp2Fp2-points of an elliptic curve Eb:y2=x3+bEb:y2=x3+b (for b∈F∗p2b∈Fp2∗) of jj-invariant ...
Computing supersingular isogenies on Kummer surfaces
Supersingular isogenies SIDH Kummer surface
2018/11/15
We apply Scholten's construction to give explicit isogenies between the Weil restriction of supersingular Montgomery curves with full rational 2-torsion over GF(p2)GF(p2) and corresponding abelian sur...
Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography
elliptic curve cryptosystem number theory
2017/5/5
We call a simple abelian variety over FpFp super-isolated if its (FpFp-rational) isogeny class contains no other varieties. The motivation for considering these varieties comes from concerns about iso...
Constructing Abelian Surfaces for Cryptography via Rosenhain Invariants
hyperelliptc curves complex multiplication Rosenhain invariants
2016/1/9
This paper presents an algorithm to construct cryptographically strong genus 2 curves and their
Kummer surfaces via Rosenhain invariants and related Kummer parameters. The most common
version of the...
We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatmen...
The arithmetic of characteristic 2 Kummer surfaces
arithmetic characteristic 2 Kummer surfaces
2009/6/3
The purpose of this paper is a description of a model of Kummer
surfaces in characteristic 2, together with the associated formulas
for the pseudo-group law. Since the classical model has bad reduct...