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

Given a prime p, an elliptic curve E/Fp over the finite field Fp of p elements and a binary linear recurrence sequence (u(n))∞n=1 of order r, we study the distribution of the sequence of points r−1 ∑ j=0 u(n+ j)Pj , n = 1, . . . , N, on average over all possible choices of Fp-rational points P1, . . . , Pr on E . For a sufficiently large N we improve and generalise a previous result in this direction due to E. El Mahassni.