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.

非零快点和线性结构的存在反映了布尔函数高阶导数的性质，这与许多密码差分攻击密切相关。旋转对称布尔函数 (RSBF) 是对称函数的超类，广泛用于密码学。我们首先获得度为\(n-2\)的n变量 RSBF的非零线性结构的一些存在性结果。此外，我们基于整数划分确定了度数为\(n-3\)和\(n-4\)的n变量RSBF的所有可能快速点集。最后，我们研究了p变量和 2 p的快点的存在-当p是奇素数时的变量 RSBF 。