SYNTHESIS OF MODEL OF REVERSE NONLINEAR OPERATION OF EXTENDED MATRIX CRYPTOGRAPHIC TRANSFORMATION

The operations used for cryptographic transformations should be strong to linear cryptanalysis, so they must have the property of non-linearity.

To synthesize the operations of extended matrix cryptographic transformation the authors used a particular set of three-digit logical functions obtained on the basis of simulation experiment using special software. A classification of these functions following the arguments that produce the first term was carried out and three basic groups were respectively received.

The main advantage of the extended matrix cryptographic transformation operations is one of their main properties - non-linearity, which causes the difficulty of identifying of reverse transformation operations.

The analysis of generalized matrix model of expanded matrix cryptographic transformation operations formed by the replacement of one line of basic elementary function of extended matrix representation showed that the matrix describing the operation of the extended matrix transformation can be represented as the modulo 2 sum of linear matrix transformation and the nonlinear matrix extensions. The experiment proved that the sequence of extension indices forms the increasing sequence. The authors laid down the main rule of extension synthesis and obtained the basic stages of the process of synthesis of the model of reverse nonlinear operation of cryptographic transformation.

The article presents the model of synthesis of nonlinear operation of extended matrix cryptographic transformation on the base of one substitution, and formulates and proved a theorem on the construction of reverse operation of extended matrix cryptographic transformation using one substitution.

The applying of proposed nonlinear operations of extended matrix cryptographic transformation allows to extend a number of operations for construction of cryptographic information protection systems and to improve their cryptographic strength by additional use of these operations.