Polynomial pseudo-random number generator via cyclic phase

Fast and reliable pseudo-random number generator (PRNG) is required for simulation and other applications in scientific computing. In this work, a polynomial PRNG algorithm, based on a linear feedback shift register (LFSR) is presented. LFSR generator of order k   determines a 2k−12k−1 cyclic sequence period when the associated polynomial is primitive. The main drawback of this generator is the cyclicality of the shifted binary sequence. A non-linear transformation is proposed, which eliminates the underlying cyclicality and maintains both the characteristics of the original generator and the feedback function. The modified generator assures a good trade off between fastness and reliability and passes both graphical and statistical tests.