The linear structures and fast points of rotation symmetric Boolean functions.

The existence of nonzero fast points and linear structures reflects the properties of Boolean function's higher order derivatives, which is closely related to many cryptographic differential attacks. Rotation symmetric Boolean functions (RSBFs) is a super-class of symmetric functions, which are used widely in cryptography. We first obtain some existence results of nonzero linear structures of n-variable RSBFs with degree n - 2 . Moreover, we determine all the possible sets of fast points of n-variable RSBFs with degrees n - 3 and n - 4 based on integer partition. Finally, we investigate the existence of fast points of p-variable and 2p-variable RSBFs when p is an odd prime. [ABSTRACT FROM AUTHOR]