Industrial Automatic Control Systems and Controllers Annotation << Back Building Multi-layer and Infinite Gamut for Streaming Encryption S.A. Beletskiy, O.P. Dedov, S.I. Zhuravlev In this paper, we propose an approach to calculating a sequence of pseudo-random numbers, that is, a gamma, which can be used in stream encryption algorithms that are currently widely used. To calculate the gamma, it is proposed to use a matrix approach to construct both the SQ matrix (an analogue of the S(S-box) substitution table) in the RC4 algorithm, and the auxiliary matrix KQ, which is an analogue of the key in the RC4 algorithm, and to obtain pseudo-random numbers as elements of the SQL matrix, which is calculated using matrix transformations over the matrices SQ and KQ. In this method, matrix operations are performed that do not require large computational and, as a result, time costs - matrices are not raised to a power and there is no calculation of inverse matrices (which may not exist), which greatly simplifies the application of this method in real practice. Keywords: gamma, square matrix, row matrix, column matrix, module. DOI: 10.25791/asu.10.2022.1392 Pp. 38-43.