New Construction Of Q-Variable Rotation Symmetric Resilient Functions Based On Latin Square Over GF(p)

Boolean functions are an important part of stream passwords and packet passwords.The quality of Boolean function directly affects the security of cryptographic system.As a subclass of Boolean function,rotational symmetric Boolean function can have several good cryptographic properties at the same time.Once proposed,the rotational symmetric Boolean function has been widely concerned by cryptography because of its special properties.Rotating symmetric Boolean functions are applied in some cryptographic algorithms,such as MD4 and MD5,which can be implemented quickly by these algorithms.At the same time,the number of rotational symmetric Boolean functions is many and the properties are different.Therefore,in order to obtain more such functions with good properties,it is necessary to construct Boolean functions with some cryptographic properties.This can provide a variety of options for the design of cryptographic algorithms.In this paper,a novel method to construct rotation symmetric resilient functions with q variables is proposed over GF(p) by using a latin square with maximum cycle structure.This method is based on the equivalence between resilient functions and large sets of orthogonal arrays.Additionally,an example is given to demonstrate that some rotation symmetric resilient functions with q variables can be constructed by the method presented in this paper,while these functions cannot be determined according to the earlier constructions over the finite fields GF(p).