Matrix Power Symmetric Encryption Data Encryption Numerical Algorithms and Problems S-Box
Institute of Information Theories and Applications FOI ITHEA
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.
* Work supported by the Lithuanian State Science and Studies Foundation.