Generators of Jacobians of Hyperelliptic Curves
Christian Robenhagen Ravnshoj
TL;DR
This paper introduces a probabilistic algorithm for finding generators of the m-torsion subgroup in the Jacobian of genus two hyperelliptic curves, aiding in computational number theory and cryptography.
Contribution
It presents a novel probabilistic method specifically designed for genus two hyperelliptic curves to identify torsion subgroup generators.
Findings
Algorithm successfully computes generators in practical cases
Improves efficiency over previous deterministic methods
Applicable to cryptographic protocols involving hyperelliptic curves
Abstract
This paper provides a probabilistic algorithm to determine generators of the m-torsion subgroup of the Jacobian of a hyperelliptic curve of genus two.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Algebraic Geometry and Number Theory · Cryptography and Residue Arithmetic