Navrotskyi D. Methods of Constructing Symmetric Cryptographic Ciphers Using Three-Dimensional Controlled Transformations

The dissertation addresses practical problems in modern cryptography by presenting new and more effective methods of constructing symmetric key cryptosystems (i.e. block and stream ciphers) in order to improve information security. Obtained results prove efficiency increase (improved quality of cryptography, increased speed, improved re-source management) of the presented cipher implementation. This work deals with the three-dimensional matrix transformation methods of building dynamically controlled cryptographic primitives. In particular, a generalization of the three-dimensional Gray transformations has been developed, which apart from the classical (left-side) and the so-called right-side and compound code, also includes randomized Gray codes, allowing to solve a number of problems related to constructing dynamically controlled cryptographic primitives. Besides, three-dimensional cryptographic shuffle primitives have been synthe-sized, as well as primitives for non-linear substitutions, matrix transformation, stochastic cyclic shift and «sliding» encoding. Furthermore, methods for a primitive Galois and Fibonacci matrices synthesis are improved, as are their jointed compounds over finite Galois fields of characteristic two, allowing to expand generalized pseudo-random se-quence generators’ set, as well as to propose new approaches to a problem of providing secret encryption keys for communication network participants over open channels. A further development in the methods of symmetric block transformation with dynamically controlled parameters of encryption is provided, in particular, the cryptographic transfor-mations are performed in a three-dimensional space and the parameters of cryptographic primitives during encryption are modified each time a new block of text is being pro-cessed. Moreover, a cryptographic communication protocol is developed to encode telem-etry information of unmanned aerial vehicle. Hardware and software for 3D cipher proto-type are manufactured and successfully tested.