Layered cellular automata for pseudorandom number generation

The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set {A ^f| = 1, 2,..., 2ⁿ -1} formed by the transformation matrix A of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L = 1, 2, 3, 4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions f₃₀ and f₄₅ in place of the linear function f₂₀₄ used in the L-LCA. Linear complexity is significantly increased when f₃₀ or f₄₅ is used.