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

Simon R.  Blackburn; Alina Ostafe; Igor E.  Shparlinski

Paper 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.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): s blackburn @ rhul ac uk
History: 2011-02-08: received
Short URL: https://ia.cr/2011/067
License: 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},
      url = {https://eprint.iacr.org/2011/067}
}