Research On Differential Properties Of Three Kinds Of Permutation Functions

Symmetric ciphers are divided into stream ciphers and block ciphers according to different encryption modes,which are widely used in the core of various encryption protocols.As a key stream generator in stream ciphers and an iterative round function in block ciphers,cryptography function is usually the only nonlinear component in the symmetric cipher.Cryptanalysts often attack the whole system based on the cryptographic functions in the systems.In order to improve the security of the cryptographic system,the cryptographic functions should have good cryptographic properties to avoid specific cryptographic attacks.Differential attack is one of the most classical attack modes in the block cipher algorithm,and because of its effectiveness,many variants of differential attack including multiplicative differential attack have been proposed successively.Generally,the lower the(c-)differential uniformity of a cryptographic function is,the better its ability to resist differential attacks(multiplicative differential attacks)is.Based on this,this paper focuses on differential properties and c-differential properties of cryptographic functions,and the specific content is as follows:In this paper,three kinds of permutation functions are designed based on the trace function and "piecewise" construction method.Through the techniques of solving equations in finite field and the subtle analysis of the number of solutions,it is proved that the differential uniformities of these three kinds of permutation functions are 6,8,and 10 respectively,and the c-differential uniformities are 6,7,and 10 respectively.It is worth noting that although the first class of permutation functions in this paper is Carlet-Charpin-Zinoviev(CCZ for short)equivalent to a class of known functions,the class of permutation functions in this paper generalize the known functions formally,and its c-differential uniformity is studied in this paper.In addition,the data indicate that the second and the third kinds of permutation functions are not CCZ equivalent to the all known functions with the same differential uniformity,so two new kinds of permutation functions with lower differential uniformity are obtained in this paper.