Comments on "Constructions of Cryptographically Significant Boolean Functions Using Primitive Polynomials

We show that the first of the two constructions by Q. Wang, J. Peng, H. Kan, and X. Xue, IEEE Transactions on Information Theory, vol. 56, no. 6, pp. 3048-3053, 2010, of Boolean functions satisfying the main criteria for filter functions in stream ciphers, is the same as the construction studied by K. Feng and the author at Asiacrypt 2008, LNCS 5350, pp. 425-440. We observe that the bounds shown on the nonlinearities of the functions in this IEEE paper are similar to those shown in the Asiacrypt paper. We point out that these kinds of functions can be implemented in a more efficient way than usually believed.