Use of implementations of arbitrary bitness permutations for cryptographic transformations

Background. Cryptographic transformations have always aroused the interest of the educated part of humanity and are an integral part of modern communications. A lot of different cryptographic algorithms exist for different tasks and requirements. Permutation functions are useful for cases where transformation speed is more critical than theoretical secrecy. Hardware implementation of such substitutions is quite simple. 
Objective. Investigate the model and combinational circuits for hardware implementation. Investigate algorithms for permutation functions software implementation. Investigate attack algorithms and cracking of permutation functions for cryptanalysis. 
Methods. The paper reviews algorithms of cryptographic transformations and their cryptanalysis for bijective permutations implemented by means of regular combinational structures of linear complexity. The proposed algorithms provide the rate of processing up to gigabits per second. The paper clarifies the algorithm of formation of elements of regular structures of permutations, specifies volumes of public and private data, reviews data formats, methods of their transfer and hardware implementation of one of the methods. The paper reviews attack types and permutation regular structure schemes cracking algorithms with experimental calculation of necessary operations quantity. The software implementation of the proposed algorithms for results calculation was developed. 
Results. Numerical results of the number of keys, the amount of memory required for hardware implementation and the number of required operations for cryptanalysis were obtained. 
Conclusions. The results show that the proposed algorithms for cryptographic transformations have a sufficient level of protection with a high-speed encryption and decryption.