## 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.

**Category / Keywords: **

**Date: **received 7 Feb 2011

**Contact author: **s blackburn at rhul ac uk

**Available format(s): **PDF | BibTeX Citation

**Version: **20110208:132303 (All versions of this report)

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