Matrix Power S-box Analysis

* Work supported by the Lithuanian State Science and Studies Foundation.

Construction of symmetric cipher S-box based on matrix power function and dependant on key is analyzed. The matrix consisting of plain data bit strings is combined with three round key matrices using arithmetical addition and exponent operations. The matrix power means the matrix powered by other matrix. This operation is linked with two sound one-way functions: the discrete logarithm problem and decomposition problem. The latter is used in the infinite non-commutative group based public key cryptosystems. The mathematical description of proposed S-box in its nature possesses a good “confusion and diffusion” properties and contains variables “of a complex type” as was formulated by Shannon. Core properties of matrix power operation are formulated and proven. Some preliminary cryptographic characteristics of constructed S-box are calculated.