Introduction: Development of post-quantum digital signature standards represents a current challenge in the area of cryptography. Recently, the signature schemes based on the hidden discrete logarithm problem had been proposed. Further development of this approach represents significant practical interest, since it provides possibility of designing practical signature schemes possessing small size of public key and signature. Purpose: Development of the method for designing post-quantum signature schemes and new forms of the hidden discrete logarithm problem, corresponding to the method. Results: A method for designing post-quantum signature schemes is proposed. The method consists in setting the dependence of the publickey elements on masking multipliers that eliminates the periodicity connected with the value of discrete logarithm of periodic functions constructed on the base of the public parameters of the cryptoscheme. Two novel forms for defining the hidden discrete logarithm problem in finite associative algebras are proposed. The first (second) form has allowed to use the finite commutative (non-commutative) algebra as algebraic support of the developed signature schemes. Practical relevance: Due to significantly smaller size of public key and signature and approximately equal performance in comparison with the known analogues, the developed signature algorithms represent interest as candidates for practical post-quantum cryptoschemes.
Introduction: Effective and prompt formulation of diagnostic conclusions about the presence of anxiety-phobic disorders requires the improvement of existing and the development of new methods for diagnosing and treating patients, including the use of virtual reality technology. Purpose: To analyze a reaction of an individual to a stimulus that triggers a fear response to virtual reality scenes (height exposure). To identify electroencephalographic (EEG) signal markers related to the level of anxiety and virtual reality environment susceptibility of an individual. Methods: A group of nine conditionally healthy males aged 23 to 26 years old who reported neither history of somatic symptoms nor organic brain disorders was formed to conduct the research. The immersion into virtual reality was accompanied by the registration of EEG signals and subsequent completion of a self-assessment questionnaire by the subjects. Results: The state of rest (a reference value) and the state of high emotional stress experience (at the height of a skyscraper) in the virtual reality environment were compared. The results obtained allow to make a conclusion that the simulated situation of being at a height causes a decrease in the indices of alpha, theta, beta rhythms, and an increase in the delta rhythm index of the EEG signal relative to the state of rest in various subjects, regardless of the intensity of fear manifestation. Practical relevance: The conducted research is among the pioneering studies in assessing the effect of virtual reality technologies on human phobic anxiety state. Some objective electrophysiological markers related to the level of anxiety were determined to confirm the presence of patterns in the functional state of the cerebral cortex with a sense of anxiety in individuals immersed in a virtual reality environment.
Introduction: Achievement of specified qualitative indicators in machine learning solutions depends not only on the efficiency of algorithms, but also on data properties. One of the lines for the development of classification and regression models is the specification of local properties of data. Purpose: To improve the qualitative predictors when solving classification and regression problems based on the adaptive selection of various machine learning models on separate local segments of data sample. Results: We propose a method that uses a combination of different models and machine learning algorithms on subsamples in regression and classification problems. The method is based on the calculation of qualitative predictors and the selection of the best models on the local segments of data sample. The finding of transformations of data and time series allows to create sample sets, with the data having different properties (for example, variance, sampling fraction, data range, etc.). We consider the data segmentation based on the change point detection algorithm in time series trends and on analytical information. On the example of the real dataset, we show the experimental values of the loss function for the proposed method with different classifiers on separate segments and on the whole sample. Practical relevance: The results can be used in classification and regression problems for the development of machine learning models and methods. The proposed method allows to improve classification and regression qualitative predictors by assigning models that have the best performance on separate segments.
Introduction: Orthogonal Hadamard matrices consisting of elements 1 and –1 (real number) exist for orders that are multiples of 4. The study considers the product of an orthogonal Hadamard matrix and its core, which is called the Scarpis product, and is similar in meaning to the Kronecker product. Purpose: To show by revealing the symmetries of the block Hadamard matrices that their observance contributes to a product that generalizes the Scarpis method to the nonexistence of a finite field. Results: The study demonstrates that orthogonality is an invariant of the product under discussion, subject to the two conditions: one of the multipliers is inserted into the other one, the sign of the elements of the second multiplier taken into account (the Kronecker product), but with a selective action of the sign on the elements and, most importantly, with the cyclic permutation of the core which depends on the insertion location. The paper shows that such shifts can be completely avoided by using symmetries that are characteristic of the universal forms of Hadamard matrices. In addition, this technique is common for many varieties of adjustable Kronecker products. Practical relevance: Orthogonal sequences and effective methods for their finding by the theory of finite fields and groups are of direct practical importance for the problems of noiseless coding, video compression and visual masking.
Introduction: It is conjectured that the symmetric Hadamard matrices of order 4v exist for all odd integers v>0. In recent years, their existence has been proven for many new orders by using a special method known as the propus construction. This construction uses difference families Xk (k=1, 2, 3, 4) over the cyclic group Zv (integers mod v) with parameters (v; k1, k2, k3, k4; λ) where X1 is symmetric, X2=X3, and k1+2k2+k4=v+λ. It is also conjectured that such difference families (known as propus families) exist for all parameter sets mentioned above excluding the case when all the ki are equal. This new conjecture has been verified for all odd v≤53. Purpose: To construct many new symmetric Hadamard matrices by using the propus construction and to provide further support for the above-mentioned conjecture. Results: The first examples of symmetric Hadamard matrices of orders 4v are presented for v=127 and v=191. The systematic computer search for symmetric Hadamard matrices based on the propus construction has been extended to cover the cases v=55, 57, 59, 61, 63. Practical relevance: Hadamard matrices are used extensively in the problems of error-free coding, and compression and masking of video information.
