Pseudorandom Number Generator Using Optimal Normal Basis

This paper proposes a simple pseudorandom number generator [PRNG] by using optimal normal basis. It is well known that the squaring and multiplication in finite field with optimal normal basis is very fast and the basis can be transformed to a canonical form. The suggested PRNG algorithm combines typical multiplications and exclusive-or bit operations, both operations can be easily implemented. It is shown that the algorithm passes all terms of the Diehard and the ENT tests for long sequences. This algorithm can be applied in various applications such as financial cryptography.