**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

**Date: **received 5 Jun 2007

**Contact author: **kestutis luksys at ktu lt

**Available format(s): **PDF | BibTeX Citation

**Version: **20070606:082404 (All versions of this report)

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