Exploring Semi-bent Boolean Functions Arising from Cellular Automata

Semi-bent Boolean functions are interesting from a cryptographic standpoint, since they possess several desirable properties such as having low and flat Walsh spectrum, which is useful to resist linear cryptanalysis. In this paper, we consider the search of semi-bent through construction based on cellular automata (CA). particular, defines function by computing XOR all output cells in CA. Since resulting have same algebraic degree CA local rule, devise combinatorial algorithm enumerate quadratic functions. We then apply exhaustively explore space rules up 6 variables, selecting only those for our CA-based always yields 20 variables. Finally, filter obtained with respect their balancedness, remark that generated remaining constant number structures.