Inferring sequences produced by a linear congruential generator on elliptic curves using coppersmith’s methods

Abstract

We analyze the security of the Elliptic Curve Linear Congruential Generator (EC-LCG). We show that this generator is insecure if sufficiently many bits are output at each iteration. In 2007, Gutierrez and Ibeas showed that this generator is insecure given a certain amount of most significant bits of some consecutive values of the sequence. Using the Coppersmith’s methods, we are able to improve their security bounds.