A The article considers the peculiarities of the application of isomorphic matrix representations for modeling the protocol of matching secret keys-permutations of significant dimension. The situation is considered when for cryptographic transformations of blocks with a length of 256 * 256 bytes, presented in the form of a matrix of a black-and-white image, it is necessary to rearrange all bytes in accordance with the matrix keys. To generate a basic matrix key and the appearance of the components KeyA and KeyB in the format of two black and white images, a software module using engineering mathematical software Mathcad is proposed. Simulations are performed, for example, with sets of fixed matrix representations. The essence of the protocol of coordination of the main matrix of permutations by the parties is considered. Also shown are software modules in Mathcad for accelerated methods that display the procedure of iterative permutations in a permutation matrix isomorphic to the elevation of the permutation matrix to the desired degree with a certain side, corresponding to specific bits of bits or other code representations of selected random numbers. It is demonstrated that the parties receive new permutation matrices after the first step of the protocol, those sent to the other party, and the identical new permutation matrices received by the parties after the second step of the protocol, ie the secret permutation matrix. Similar qualitative cryptographic transformations have been confirmed using the proposed representations of the permutation matrix based on the results of modeling matrix affine-permutation ciphers and multi-step matrix affine-permutation ciphers for different cases when the components of affine transformations are first executed in different sequences. , and then permutation using the permutation matrix, or vice versa. The model experiments performed in the study demonstrated the adequacy of the functioning of the models proposed by the protocol and methods of generating a permutation matrix and demonstrated their advantages.
In the paper, we consider the urgent need to create highly efficient hardware accelerators for machine learning algorithms, including convolutional and deep neural networks (CNN and DNNS), for associative memory models, clustering, and pattern recognition. We show a brief overview of our related works the advantages of the equivalent models (EM) for describing and designing bio-inspired systems. The capacity of NN on the basis of EM and of its modifications is in several times quantity of neurons. Such neural paradigms are very perspective for processing, clustering, recognition, storing large size, strongly correlated, highly noised images and creating of uncontrolled learning machine. And since the basic operational functional nodes of EM are such vector-matrix or matrix-tensor procedures with continuous-logical operations as: normalized vector operations “equivalence”, “nonequivalence”, and etc. , we consider in this paper new conceptual approaches to the design of full-scale arrays of such neuron-equivalentors (NEs) with extended functionality, including different activation functions. Our approach is based on the use of analog and mixed (with special coding) methods for implementing the required operations, building NEs (with number of synapsis from 8 up to 128 and more) and their base cells, nodes based on photosensitive elements and CMOS current mirrors. Simulation results show that the efficiency of NEs relative to the energy intensity is estimated at a value of not less than 1012 an. op. / sec on W and can be increased. The results confirm the correctness of the concept and the possibility of creating NE and MIMO structures on their basis.
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