## Cryptology ePrint Archive: Report 2006/466

Prime Order Primitive Subgroups in Torus-Based Cryptography

Jason E. Gower

Abstract: We use the Bateman-Horn conjecture to study the order of the set of $\mathbb{F}_q$-rational points of primitive subgroups that arise in torus-based cryptography. We provide computational evidence to support the heuristics and make some suggestions regarding parameter selection for torus-based cryptography.

Category / Keywords: finite field, primitive subgroup, torus-based cryptography, Bateman-Horn conjecture