A scalable method for constructing non-linear cellular automata with period 2n − 1

Abstract

Non-linear functions are very essential in different crypto primitives as they increase the security of the cipher designs. On the other hand, maximum length sequences help to prevent repeatability of a pseudorandom generator. Linear functions such as LFSR and linear cellular automata are used to generate maximum length sequences. However linear maximum length sequences are not secure. So there is a necessity of a construction that can provide both non-linearity and maximum length sequence for optimized cipher designs. In this work, we propose an algorithm for synthesizing a maximum length non-linear cellular automata to fulfill the requirement. Extensive experimentation on the proposed scheme shows that the construction achieves high non-linearity. Moreover, we have implemented and tested the design in Xilinx Spartan-3 FPGA platform and the hardware overhead is shown to be nominal.