Design and implementation of dynamic cipher component involutory MDS matrix
With the continuous expansion of the application fields of cryptography,deepening of application level,and increasing recognition of applications,the demand for ciphers is increasing.It is necessary to effectively segment similar algorithms used in different fields.The fourth-order matrices over GF(2m)are studied in this paper,and the involutory Maximum Distance Separable(MDS)matrices with m=8 are carefully analyzed and designed.Firstly,the form of the involutory matrix G'is proposed with restriction conditions over the finite field GF(28).Secondly,the properties and the range of parameters of fourth-order involutory MDS matrices are given based on the judgment conditions of MDS matrices.Finally,the number of involutory MDS matrices is calculated,which is not less than 258.9.The research results provide a large number of safe and efficient dynamic diffusion components for the design of block ciphers suitable for software implementation,which can ensure that the block ciphers based on SP structure do not increase the computational complexity for the same structure of encryption and decryption.These involutory MDS matrices can be used as parameters to segment the cryptographic algorithm for different fields.
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