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

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

2011-02-05

arxiv.org/abs/1102.1053v1

Mathematics

Number Theory

Scientific paper

Given a prime $p$, an elliptic curve $\E/\F_p$ over the finite field $\F_p$ of $p$ elements and a binary \lrs\ $\(u(n)\)_{n =1}^\infty$ of order~$r$, we study the distribution of the sequence of points $$ \sum_{j=0}^{r-1} u(n+j)P_j, \qquad n =1,..., N, $$ on average over all possible choices of $\F_p$-rational points $P_1,..., P_r$ on~$\E$. For a sufficiently large $N$ we improve and generalise a previous result in this direction due to E.~El~Mahassni.

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