More Constructions of Light MDS Transforms Based on Known MDS Circulant Matrices

Maximum distance separable (MDS) codes have the maximum branch number in cryptography, and they are generally used diffusion layers of symmetric ciphers. The layer Advanced Encryption Standard (AES) uses circulant MDS matrix with row element {2;3;1;1} F28. It is simplest F2n4, recorded as A=Circ(2;3;1;1). In this paper, we study more extensive constructions A F2n4. By transforming multiplication operation finite field into bit-level operation, propose a multivariable definition based on simple operations, such cyclic shift, XOR. We apply to lightweight discuss classification clusters. also give an example cluster A. Without changing structure, elements, implementation cost known matrix, existing transformations expanded n2/2 times that its original. paper provide rich component materials for design cryptographic algorithms.