OBSERVATION ON CIRCULANT MDS (MAXIMUM DISTANCE SEPARABLE) MATRICES OVER FINITE RINGS - Salsabila Noor Arifin, Izdihar
An n × n matrix is called MDS (Maximum Distance Separable) if and only if its submatrices are non-singular. MDS matrices are used in cryptography to construct diffusion layer which are part of block ciphers. Diffusion layer is used in encryption process to provide the security of the message. Observation on MDS matrices has been commonly done in finite field F2k := F2[x]/?f(x)?, which f(x) is irreducible polynomial of degree k. In this thesis, we generalize finite fields to finite rings. The finite ring that used in this thesis is obtained by modifying the finite field F2k := F2[x]/?f(x)?, by changing F2 with Z2m or choosing polynomial f(x) which is reducible in the construction of F2[x]/?f(x)?. In particular, this thesis discusses about the existence of circulant MDS matrices which are involutory or orthogonal over those rings.