Elliptic Curves over a Finite Ring.

Let F_q be a finite field, where q is a power of a prime p such that p ≥ 5. Let α be a root of a monic polynomial of a minimal degree over F_q. In this paper, we will study elliptic curves over (F_q[α];+; *), where + is the usual addition and * represent a non-standard product law over F_q[α]. Using elliptic curves over this ring can result in a cryptographic method that is fast, simple and secure. [ABSTRACT FROM AUTHOR]