Abstract
Recently, efficient deterministic and invertible encodings on some hyperelliptic curves in genus 1 and 2 using the technique in Elligator 2 (ACM CCS 2013) have been proposed. We have successfully generalized their encodings for hyperelliptic curves of genus 3, 4 and 5. We have found unified formulas (using Mersenne numbers) for the encodings into the hyperelliptic curves of genus \(g\le 5\): \( \mathbb {H}_g : y^2=f_{g}(x)=x^{(2g+1)}+a_{(2g-1)}x^{(2g-1)} + a_{(2g-3)}x^{(2g-3)}+\ldots +a_1x+a_0\). We have conjectured that our method works on arbitrary genus.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.