Method of structuring code constructions based on the Gaussian mixture model and separation of its components - Голубничий, Олексій Георгійович (Ukrainian Information Security Research Journal, 2019)
Methods and approaches of the linear cryptanalysis of cryptographic algorithms are aimed at analyzing and detecting interconnections between plaintext, ciphertext and key elements. In the case of linear cryptanalysis of pseudorandom sequences and signal-code constructions based on them, the interconnections between elements of these sequences and signal-code constructions, as well as between their internal structures and their components in systems of code constructions, etc., are subject to analysis and detection. The effectiveness of linear cryptanalysis at its different stages can be enhanced by structuring (detecting internal structures and interconnections between them) code constructions, in respect of which there is no a priori information about their structure, or code constructions, which a priori can be considered as constructions with a stochastic nature of their formation. The method of structuring code constructions with a priori unknown structures, which based on an analysis of cross-correlations between code constructions that are represented in this method by the Gaussian mixture model with a further separation of its components and clustering code constructions by means of modification (parametric and criteria features) of the EM-algorithm with removing components, is suggested in the article. The method allows selecting groups of code constructions with interconnected structures and then to detect these interconnected structures in an explicit form, which can be the solution of a number of problems of linear cryptanalysis related to the detection of structures and interconnections between them. An example of implementation of the proposed method for the structuring of binary pseudo-random Barker sequences, which are used as signal-code constructions in spread-spectrum telecommunications and were synthesized by the direct search method (as is known according to literary sources), and therefore have a stochastic a priori unstructured character, is shown in the article.