Abstract
In this paper, we present an average-case efficient algorithm to resolve the problem of determining whether two Boolean functions in trace representation are identical. Firstly, we introduce a necessary and sufficient condition for null Boolean functions in trace representation, which can be viewed as a generalization of the well-known additive Hilbert-90 theorem. Based on this condition, we propose an algorithmic method with preprocessing to address the original problem. The worst-case complexity of the algorithm is still exponential; its average-case performance, however, can be improved. We prove that the expected complexity of the refined procedure is O(n), if the coefficients of input functions are chosen i.i.d. according to the uniform distribution over F2n; therefore, it performs well in practice.
