Pseudo-random sequence generator based on random selection of an elliptic curve

Pseudo-random numbers generators (PRNG) are one of the main security tools in Radio Frequency IDentification (RFID) technology. Thus, a weak internal embedded generator can directly cause the entire application to be insecure and it makes no sense to employ robust protocols for the security issue. In this paper, we propose a new PRNG constructed by randomly selecting points from two elliptic curves, suitable for ECC based applications. The main contribution of this work is the increasing of the generator internal states by extending the set of its output realizations to two curves randomly selected. The main advantages of this PRNG in comparison to previous works are the large periodicity, a better distribution of the generated sequences and a high security level based on the elliptic curve discrete logarithm problem (ECDLP). Further, the proposed PRNG has passed the different Special Publication 800-22 NIST statistical test suite. Moreover, the proposed PRNG presents a scalable architecture in term of security level and periodicity at the expense of increasing the computation complexity. Thus, it can be adapted for ECC based cryptosystems such as RFID tags and sensors networks and other applications like computer physic simulations, and control coding.