On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves

Given a prime $p$, an elliptic curve $\E/\Fp$ over the finite field $\Fp$ of $p$ elements and a binary \lrs\ $(u(n)){n =1}^\infty$ of order~$r$, we study the distribution of the sequence of points $$ \sum{j=0}^{r-1} u(n+j)Pj, \qquad n =1,..., N, $$ on average over all possible choices of $\Fp$-rational points $P1,..., Pr$ on~$\E$. For a sufficiently large $N$ we improve and generalise a previous result in this direction due to E.~El~Mahassni.