| The cryptanalysis and design of block ciphers are one of the hotspots in modern cryptography. In this paper, we discuss the method of error-correcting codes on the design of block ciphers. A summary of the codes and block ciphers will be given first, then we focus on the codes used in the design of S box and P permutation. We have got some interesting results.The S box is one of the most important parts of block ciphers. The method to design it is always the important problem in cryptography. In this paper, we study the relationships between the cyclic codes and APN functions, AB functions. Then we discuss the cryptographic property of affine inverse function on the finite field, which is used in many famous block ciphers. It show that there is a linear equivalence between the coordinate functions in the affine inverse functions, and further more, we give the equivalent expression of the coordinate functions in the S box of Camellia which is one of the candidates in NESSIE.As another important part, P permutation is also the hotspot in the design of block ciphers. In this paper, we also discuss the relationships between the MDS codes and the best P permutations in block ciphers. With the good property of the self-dual codes, we construct many good MDS transforms. At last of the paper, a new method to construct the MDS matrix is given, and this method is based on the generalized Reed-Solomon codes. |
