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 { | 1, 2, , 2 1} f n A f = − ... 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

more »

... 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 30 f and 45 f in place of the linear function 204 f used in the L-LCA. Linear complexity is significantly increased when 30 f or 45 f is used. Index Termscellular automata, programmable cellular automata, pseudorandom number generation.