Shared Variable Extraction and Hardware Implementation for Nonlinear Boolean Functions Based on Swarm Intelligence

Abstract

To solve the problem of complex relationships among variables and the difficulty of extracting shared variables from nonlinear Boolean functions (NLBFs), an association logic model of variables is established using the classical Apriori rule mining algorithm and the association analysis launched during shared variable extraction (SVE). This work transforms the SVE problem into a traveling salesman problem (TSP) and proposes an SVE based on particle swarm optimization (SVE-PSO) method that combines the association rule mining method with swarm intelligence to improve the efficiency of SVE. Then, according to the shared variables extracted from various NLBFs, the distribution of the shared variables is created, and two corresponding hardware circuits, Element A and Element B, based on cascade lookup table (LUT) structures are proposed to process the various NLBFs. Experimental results show that the performance of SVE via SVE-PSO method is significantly more efficient than the classical association rule mining algorithms. The ratio of the rules is 80.41%, but the operation time is only 21.47% when compared to the Apriori method, which uses 200 iterations. In addition, the area utilizations of Element A and Element B expended by the NLBFs via different parallelisms are measured and compared with other methods. The results show that the integrative performances of Element A and Element B are significantly better than those of other methods. The proposed SVE-PSO method and two cascade LUT-structure circuits can be widely used in coarse-grained reconfigurable cryptogrammic processors, or in application-specific instruction-set cryptogrammic processors, to advance the performance of NLBF processing and mapping.