Hierarchical Dawson's Summation Generator

In 1986, Rueppel has pioneered the notion of summation generator and shown that the proposed summation generator obtained maximum correlation immunity as well as nonlinearity by adding 1 bit of memory to the memoryless nonlinear combiner. Since then, various ideas on improving the correlation properties of the summation generator had emerged. One prominent improved version of Rueppel's summation generator is Dawson's summation generator, which exhibits superior cryptographic properties. In this paper, we propose a hierarchical framework of pseudorandom generator based on the combination modules of Dawson's summation generator. To ensure the practicality and security of such a hierarchical model, we analyze the cryptographic properties in terms of period, linear complexity and randomness.