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 $$ \sum_{j=0}^{r1} u(n+j)P_j, \qquad n =1,\ldots, N, $$ 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)
 Publication info
 Published elsewhere. Unknown where it was published
 Contact author(s)
 s blackburn @ rhul ac uk
 History
 20110208: 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}, note = {\url{https://eprint.iacr.org/2011/067}}, url = {https://eprint.iacr.org/2011/067} }