The invention relates to the field of computer engineering and cryptography and, in particular, to methods for implementing linear transformations that operate with a specified speed and require minimum amount of memory, for further usage in devices for cryptographic protection of data. The technical result enables the selection of interrelated parameters (performance and required amount of memory) for a particular computing system when implementing a high-dimensional linear transformation. The use of the present method allows for a reduction of the amount of consumed memory at a given word size of processors employed. To this end, based on a specified linear transformation, a modified linear shift register of Galois-type or Fibonacci-type is generated according to the rules provided in the disclosed method, and the usage thereof enables to obtain the indicated technical result.