Pseudo-random sequence generation from elliptic curves over a finite field of characteristic 2

In this paper, the randomness of binary sequences generated from elliptic curves over a finite field of characteristic 2 is studied. A scheme of construction based on the Chaos-Driven Elliptic Curve Pseudo-random Number Generator (C-D ECPRNG) is proposed. The generators based of this scheme are verified by using tests from the NIST Statistical Test Suite to analyze their statistical properties. An elliptic curve used in the numerical example is defined over F ₂ 8. The investigations which made for the generated series of two output sequences of the lengths of 2 ¹⁰ and 2 ²⁰ bits shown that 14 generators working according to our general scheme exhibit good randomness properties. Next, the binary sequences generated by these 14 schemes were used for encrypting a 256×256 grayscale Lena image as an application example and the security analysis of the ciphered images was carried out.