Matrix Power S-Box Construction ∗

The new symmetric cipher S-box construction based on matrix power function is presented. 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. The left and right side matrix powers are introduced. 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. It is shown that generic S-box equations are not transferable to the multivariate polynomial equations in respect of input and key variables and hence the algebraic attack to determine the key variables cannot be applied in this case. 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. Some comparative simulation results are presented. Keywords: symmetric cipher, S-box, matrix power, one-way function (OWF), resistance to algebraic attack