Welcome to the resource topic for 2011/067
Title:
On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves
Authors: Simon R. Blackburn, Alina Ostafe, 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.
ePrint: https://eprint.iacr.org/2011/067
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