Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6422666 | Journal of Computational and Applied Mathematics | 2014 | 10 Pages |
â¢A new algebraic method to construct cryptographically good 32Ã32 binary matrices.â¢How to construct 32Ã32 involutory binary matrices of branch number 12.â¢To construct non-involutory binary matrices of branch number 11 with a fixed point.
Binary linear transformations (also called binary matrices) have matrix representations over GF(2). Binary matrices are used as diffusion layers in block ciphers such as Camellia and ARIA. Also, the 8Ã8 and 16Ã16 binary matrices used in Camellia and ARIA, respectively, have the maximum branch number and therefore are called Maximum Distance Binary Linear (MDBL) codes. In the present study, a new algebraic method to construct cryptographically good 32Ã32 binary linear transformations, which can be used to transform a 256-bit input block to a 256-bit output block, is proposed. When constructing these binary matrices, the two cryptographic properties; the branch number and the number of fixed points are considered. The method proposed is based on 8Ã8 involutory and non-involutory Finite Field Hadamard (FFHadamard) matrices with the elements of GF(24). How to construct 32Ã32 involutory binary matrices of branch number 12, and non-involutory binary matrices of branch number 11 with one fixed point, are described.