The hidden weighted bit function (HWBF) is a well-known benchmark function in the branching program literature. In Wang et al. (2014),authors investigated the cryptographic properties of the HWBF and found that it seems to be a very good candidate for being used in real ciphers. In this paper, we make the following contributions:#R##N##R##N#(1) We study the behavior of the HWBF against the quadratic approximation attack and give an upper bound on its second-order nonlinearity, which is much lower than the maximum possible second-order nonlinearity of Boolean functions. Therefore, the HWBF may be weak for being used in real ciphers to resist quadratic approximation attacks. But, how to launch the quadratic approximation attack effectively is still in the research stage.#R##N##R##N#(2) Two bounds on the higher-order nonlinearities were given by C. Carlet in Carlet (2008). In general, one bound is better than the other one. But it was unknown whether it is always better. We give an example to show that it is not always better.
['Qichun Wang', 'Chik How Tan']
On the second-order nonlinearity of the hidden weighted bit function