Balanced Rotation Symmetric Boolean Functions With Good Autocorrelation Properties

Rotation symmetric Boolean functions (RSBFs) are used widely in symmetric cryptography. In this paper, a systematic construction of balanced odd-variable RSBFs satisfying strict avalanche criterion is proposed. Hence, a class of
$(6k+3)$
-variable resilient RSBFs satisfying strict avalanche criterion is also presented for any
$k\geq 2$
. Some of the obtained RSBFs have many other good cryptographic properties at the same time, that is, optimal algebraic degree, good global avalanche characteristics, high nonlinearity and nonexistence of nonzero linear structures. Moreover, we obtain some count results of RSBFs satisfying strict avalanche criterion. This is the first time that the autocorrelation properties of RSBFs are investigated systemically.