Development and investigation of parallel model of bee colony algorithms for cryptanalysis problem solving

Introduction. The research area of “natural calculation” is now widely used for the solution to optimization NP-complete problems including combinatorial tasks of cryptanalysis. A quick overview of the publications devoted to the application of the natural (bioinspired) methods for cryptanalysis is provided. The main work objective is to investigate a possibility of applying bee colony algorithms to the realization of block cipher cryptanalysis. Materials and Methods. The known bee colony techniques belonging to a relatively new class of the bioinspired optimization methods that simulate the processes occurring in wildlife are applied to solve this optimization problem. The description and the block diagram of the bee colony algorithm for the solution to a cryptanalysis task are provided; basic operations performed in parallel at the global level are noted. In the following, a set of independent operators allowing for the concurrent execution is defined. For this purpose, information-logical flowgraphs of the algorithm with the input control and information links are built, as well as matrices of succession, logical incompatibility, and independence are formed. This matrix of independence allows the definition of a set of algorithm operators admitting parallel execution. At that, the dimensionality of the maximal internally stable sets defines the maximum number of the processors used for the algorithm implementation. Research Results. Theoretical estimates of time complexity of the bee colony algorithm are given as the key data. Besides, the problem solution is provided: to find the required smallest number of processors of the homogeneous parallel computing systems with distributed memory, and a uniform plan for the implementation of operators for them, for the cryptanalysis algorithm based on the constructed information-logical graph data-logical graph, and for the preset time. The assessment of the wanted smallest number of processors for the cryptanalysis algorithm implementation, and the evaluation of the total time of the algorithm realization are given. Discussion and Conclusions. The basic research results are: the development of the bee colony algorithm used for the cryptanalysis task solution; the description of its flowchart and the principal par-allel executed stages; the construction of a matrix of independence; the evaluation of the number of processors for the algorithm imple-mentation. It should be noted (and it was observed in the previous works) that the distinctive feature of applying the bioinspired meth-ods of cryptanalysis is the applicability of the encryption-decryption algorithm as a criterion function for the evaluation of the key ac-ceptability defined by the bioinspired method operations. Thus, it can be affirmed that when using the bioinspired methods, the secret key definition process depends not so much on the complexity of the encryption transformations, as on the bioinspired method itself which should provide a sufficient diversity of the key generation