## Cryptology ePrint Archive: Report 2011/067

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

Simon R. Blackburn, Alina Ostafe and Igor E. Shparlinski

Abstract: Given a prime $p$, an elliptic curve $\mathcal{E}/\mathbb{F}_p$ over the finite field $\mathbb{F}_p$ of $p$ elements and a binary linear recurrence sequence $$u(n)$_{n =1}^\infty$ of order~$r$, we study the distribution of the sequence of points $$\sum_{j=0}^{r-1} u(n+j)P_j, \qquad n =1,\ldots, N,$$ on average over all possible choices of $\mathbb{F}_p$-rational points $P_1,\ldots, P_r$ on $\mathcal{E}$. For a sufficiently large $N$ we improve and generalise a previous result in this direction due to E.~El~Mahassni.

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