Speaker
Description
Since their introduction the Bent functions had an important role in designing S-boxes for block and stream chipers. While the theory behind Bent functions has substantially been developed, their count is still unknown for number of variables $n>8,$ and is probably the most important question left. Recently, some improvements on the upper bound of number of the Bent functions are presented based on the dimensionality of bent rectangles. In this work a novel approach has been established based on the number of minterms of an characteristic function $\chi\colon\mathbb{F}_2^{2^n}\mapsto\mathbb{F}_2$ for the Bent functions. The sets of minterms of the $\chi$ function are carefully built by means of Binary Decision Diagrams and their cardinality is counted from them. A two-dimensional recurrence relation between cardinalities leads to much improved upper bounds on number of Bent functions.
