Hyperelliptic Isogeny Based Cryptography

Isogeny based cryptography is a cryptosystem that uses isogenies between Abelian varieties.  While the cryptosystems that use isogenies among elliptic curves have become part of the folklore, we focus on isogenies of genus two curves and hyperelliptic genus 3 curves.

Since most of our activities are related to grants and involvement in industry, we publish relatively little on the topic and only with permission from our partners.  If you are a mathematician or computer scientist interested in getting involved, please fill the following form 

Activities

• Isogeny based post-quantum cryptography, NATO-Science for Peace and Security, Advanced Research Workshops, Hebrew University of Jerusalem, July 29-31, 2024

Timeline on (n,n)-split Jacobians

Legendre, Jacobi, Hermite, Goursat, Burkhardt, Brioschi, Bolza, Kani, Kuhn, Frey, Shaska, Kumar

Literature and some preprints

• Curves, Jacobians, and cryptography, G. Frey, T. Shaska, Contemp. Math, vol. 724,   AMS,  (2019), pg. 279--344

• Machine learning for moduli space of genus two curves and an application to post-quantum cryptograph, (submitted)

• Isogenies of genus 2 Jacobians and cryptography, NATO D-series, (to appear)