On the Sum-Product Problem on Elliptic Curves

Omran Ahmadi, Igor Shparlinski

Let $\E$ be an ordinary elliptic curve over a finite field $\F_{q}$ of $q$ elements and $x(Q)$ denote the $x$-coordinate of a point $Q=(x(Q),y(Q))$ on $\E$. Given an $\F_q$-ratio…