## Cryptology ePrint Archive: Report 2007/214

Matrix Power S-Box Construction

Eligijus Sakalauskas and Kestutis Luksys

Abstract: 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.

Category / Keywords: secret-key cryptography / symmetric cipher, S-box, matrix power, one-way functions