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

2011/02/05 by Simon R. Blackburn⋆, Simon R. Blackburn, Alina Ostafe +4
Computer Science · Mathematics · #Chaos-based Image/Signal Encryption #Coding theory and cryptography #advanced mathematical theories #cs.CR #math.NT #msc:11G05 #msc:11K45 #msc:11T23 #msc:11T71 #msc:65C05 #msc:94A60

paper · pdf · doi:10.48550/arxiv.1102.1053

arxiv created 2011/02/05 · arxiv updated 2011/02/08

Abstract

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}^∞ of order~r, we study the distribution of the sequence of points ∑_j=0^r-1 u(n+j)P_j, n =1,..., N, on average over all possible choices of \F_p-rational points P₁,..., 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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