### 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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
s blackburn @ rhul ac uk
History
Short URL
https://ia.cr/2011/067

CC BY

BibTeX

@misc{cryptoeprint:2011/067,
author = {Simon R.  Blackburn and Alina Ostafe and Igor E.  Shparlinski},
title = {On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves},
howpublished = {Cryptology ePrint Archive, Paper 2011/067},
year = {2011},
note = {\url{https://eprint.iacr.org/2011/067}},
url = {https://eprint.iacr.org/2011/067}
}

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