Investigation of the best structure for the nonlinear combining function
Sattar B. Sadkhan, Dhilal M. Reda · 2017
In the stream cipher, the Keystream generator can be built depending on the linear feedback shift register (LFSR) or nonlinear feedback shift register (NLFSR). In the case of NLFSR, three general methodologies can be used, two of them (nonlinear combination generator and nonlinear filter generator) depending heavily on the usage of the combining function. In this paper, we proposed a new method to investigate the best structure for the nonlinear combining function. To build a nonlinear combination function, the designer needs to build it in the program and change the part of the chosen nonlinear combination function every time and see the result. In our proposed system, we deal with the inputs (entrances) to the nonlinear combination function as the outputs of several LFSRs or the contents of a single LFSR. The nonlinear combination function can be considered as a constructor consists of n levels. All the possible forms for an arithmetic formula will be generated. So the reduction of this operation for the designer to write only the seed(s) and the level. A proposed method will generate all the possible forms for the structure of the nonlinear combination function, and then analyzes the output sequence resulted from each structure using five known statistical tests to determine the best structure. The contents (entrances, Boolean functions) at each level will be dealt as formula that is similar to an arithmetic formula.