The cardinalities of some certain Hamming constraint sets
Song Bo Ji · 2015
It is difficult to find Boolean functions used in stream ciphers that can meet all the necessary performance criteria. Recently,two classes of Boolean functions with many good cryptographic properties have been proposed by Tu and Deng based on correctness of a combinatorial conjecture about binary strings distribution( we call it Hamming constraint set). Tu-Deng conjecture has attracted much attention from cryptographers. In this paper we give a new method to obtain the explicit formulas for the cardinalities of some certain Hamming constraint sets,which partially proves Tu-Deng conjecture.