Linearization of functions represented as a set of disjoint cubes at the autocorrelation domain

The implementation cost of a multi-output Boolean function, in terms of the number of two-input AND-OR gates, can be reduced by using a linear decomposition. The linearly decomposed Boolean function consists of a linear function followed by the corresponding linearly transformed function. A complexity of the linearized function and therefore, its implementation cost, depends on the linear transform chosen. In this paper we suggest a spectral technique of the linear transformation of functions defined by disjoint cubes. The proposed linearization procedure is defined over the autocorrelation domain where the autocorrelation function is represented as an arithmetic sum of products. The computation complexity of the suggested method is polynomial in both the number of input variables and the number of cubes of the original function. Hence the suggested method is applicable to functions of a large number of input variables. Experimental results over standard benchmarks show reduction in the implementation complexity in comparison with the implementation of the initially given non linearized functions. The efficiency in terms of the computation time is demonstrated on randomly generated functions of large number of inputs.