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 $E / F_{p}$ over the finite field $F_{p}$ 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 $\sum_{j = 0}^{r - 1} u (n + j) P_{j}, n = 1, \dots, N,$ on average over all possible choices of -rational points on . For a sufficiently large 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}
}