A Parallel Blum-Micali Generator Based on the Gauss Periods

In this paper, the authors propose an algorithm to generate a sequence of bits in parallel to enhance the generating performance of the Blum-Micali method which is for constructing a pseudorandom number generator. More precisely, since the classical definition needs to refer the previous state to generate the next bit, we modify the generation steps in an alternative way by introducing the feature of the Gauss periods. It gives us a unique representation of elements as if a primitive element generates those elements as the powers and this mechanism realizes the parallel algorithm. As a result, the generator achieves to mimic the main concept of the Blum-Micali method in parallel and it is thought to be secure if the discrete logarithm problem is hard to solve.