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The Transformation from the Galois NLFSR to the Fibonacci Configuration

Two configurations of nonlinear feedback shift registers (NLFSRs) are considered. Conventional NLFSRs use the Fibonacci configuration in which the feedback is applied to the last bit only. The Galois configuration, in which the feedback can be applied to every bit, is attractive for stream ciphers to which high throughput is very important. In this paper, we show how to transform a Galois NLFSR into an equivalent NLFSR in the Fibonacci configuration. The mapping between the initial states of the Galois NLFSR and its equivalent Fibonacci configuration is also derived. Moreover, some properties of Galois NLFSRs are found with the transformation.