Achieving Better Security Using Nonlinear Cellular Automata as a Cryptographic Primitive

Abstract

Nonlinear functions are essential in different crypto-primitives as they play an important role on the security of a cipher design. Wolfram identified Rule 30 as a powerful nonlinear function for cryptographic applications. However, Meier and Staffelbach mounted an attack (MS attack) against Rule 30 Cellular Automata (CA). MS attack is a real threat on a CA based system. Nonlinear rules as well as maximum period CA increase randomness property. In this work, nonlinear rules of maximum period nonlinear hybrid CA (M-NHCA) are studied and it is shown to be a better crypto-primitive than Rule 30 CA. It has also been analysed that the M-NHCA with single nonlinearity injection proposed in the literature is vulnerable against MS attack, whereas M-NHCA with multiple nonlinearity injections provide better cryptographic primitives and they are also secure against MS attack.