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Synthesis of Maximum Length Cellular Automata with Nonlinearity Injections
Swapan Maiti and Dipanwita Roy Chowdhury

Nonlinear functions are essential in different crypto primitives as they play an important role in the security of cryptosystems. In literature, elementary nonlinear Cellular Automata (CA) are exploited in designing cryptosystems, but they have some limitations. Nonlinear CA synthesized from linear elementary CA with nonlinearity injections may be explored as better crypto primitives. In this work, we study maximum length nonlinear hybrid CA (M-NHCA) with single nonlinearity injection, and introduce methods for synthesizing M-NHCA with multiple injections, and explore analytical behavior of these synthetic nonlinear CA. It can be shown that the synthetic nonlinear CA with multiple nonlinearity injections are better crypto primitives.

Keywords: Cellular automata, maximum length nonlinear CA, Meier and Staffelbach attack, nonlinear functions

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