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Copyright of Informatics & Mathematical Methods in Simulation / Informatika ta Matematičnì Metodi v Modelûvannì is the property of Odessa Polytechnic University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Informatics & Mathematical Methods in Simulation / Informatika ta Matematičnì Metodi v Modelûvannì is the property of Odessa Polytechnic University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article aims to trace the Second South Slavic influence on Russian literature with the help of rather specific material that one can find in Old Russian manuscripts of the 14–15th centuries. The material the author focuses his attention on consists of cryptographic writings and cryptographic insertions in manuscript books, phenomena of book culture that according to the original theory developed in the article, represent one particular section of monuments using alternative writing systems (inopisanie) (the neologism proposed in this paper). Under the monuments using alternative writing systems (inopisanie) the author understands any and all specific text elements of manuscript codices that stand out by some signals against the general background of the text. Signals of this kind were used to inform the recipient that the scribe (or anybody else armed with a pen) was about to change over to a new register of writing. The author insists that the change of register in the books of religious content (other kinds of books did not exist at that time) necessarily had a religious motivation. Moreover, as demonstrated in the article, the border separating the period of the Second South Slavic influence from the previous one is quite tangible in the history of ancient Russian cryptography and alternative writing systems (inopisanie). Phenomena of “inopisanie” started to be by far more widespread, and the assortment of the “inopisanie” was enriched by new encrypting systems and with new ways of highlighting the texts. This tendency reflects a general striving for a noumenal world and a universal thirst for a mystical union with the Divine that are typical for this time. On the other hand, the onset of a new period in the history of culture was marked for Russian literature by the loss of the attributes that had been typical for it in previous years. Among those attributes that were lost one should pay attention to the dichotomous perception of the manuscript page onto which the dualistic picture of the world was projected (the degeneration of the teratological style, the disappearance of naturalistic and even sacrilegious margin notes in the manuscripts). [ABSTRACT FROM AUTHOR]

Copyright of Informatics & Mathematical Methods in Simulation / Informatika ta Matematičnì Metodi v Modelûvannì is the property of Odessa Polytechnic University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Informatics & Mathematical Methods in Simulation / Informatika ta Matematičnì Metodi v Modelûvannì is the property of Odessa Polytechnic University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A database is an organized collection of structured information, typically stored electronically in a computer system and usually controlled by a database management system (DBMS). Confidentiality, integrity and availability are the main requirements for database security. Data within the most common types of modern databases in operation is typically stored in rows and columns in a series of tables, but other configurations are also used. The use of public networks and the development of information technologies (including cloud ones) impose new increased requirements on the formation of databases. The paramount requirement is the security of databases from unauthorized actions of both the users themselves and third-party observers (potential violators). Cryptographic security tools are becoming an important tool to meet this requirement. In this paper, based on new (introduced by the author in a recent publication) concepts of generalized discrete differentiation and integration, a fundamentally new scheme for hidden compact storage of user group data in a common open database is proposed. The components of the table are elements of the ring 𝐾 that encode the data. The paper proposes to use residue rings. The database does not have subsections related to the data of individual users. The corresponding table is a component-by-component sum of individual tables built by a certain algorithm according to the data of each user. Any user can retrieve his data from the database using his own individual key. The construction of the table and the algorithms for extracting individual user data from it are carried out efficiently. A user gets the key at the time of his registration in the system, when his table (obtained on the basis of his data) is created and added to the database. The key has the form of two polynomials with coefficients from 𝐾 with invertible leading coefficients. At the same time, a particular user does not have the opportunity to obtain the data of other users. An outside observer (potential intruder) cannot obtain any data. The scheme allows changing and deleting data without replacing keys. Free access to the database and reuse of keys are the main advantages of the scheme.

There are perfect and ideal threshold secret sharing schemes, for example, Shamir’s secret sharing scheme. For the case of general secret sharing schemes with an arbitrary access structure, it is possible to construct a perfect scheme for any access structure (for example, the Ito – Saito – Nishizeki scheme, the Benaloh – Leichter scheme), but in general, such a scheme will not be an ideal secret sharing scheme. In the paper, for some classes of access structures, the construction of perfect and ideal secret sharing schemes based on linear codes is given. We also give a construction of perfect verifiable secret sharing schemes for any access structure for which there is a line code that implements this structure.

This paper provides implementations of three well-known ciphers – Caesar Cipher, Vigenere Cipher and Hill Cipher in Microsoft Excel. It is shown how the ciphers can be broken by using Brute-force Attack, Frequency Analysis Attack and Known-plaintext Attack. For the purpose of the cryptanalysis the relative occurrence frequencies of the letters and the index of coincidence (κ ) in Bulgarian language are determined. The classical Frequency Analysis Attack is modified using the cross-correlation between frequencies of letters in the natural language and the cipher text. Modular matrix operations in MS Excel are shown. [ABSTRACT FROM AUTHOR]

One of the important problems arising in designing and practical implementation of cryptosystems is provide countermeasures against side-channel attacks. When implemented on a specific physical device, the algorithms, strength of which from the purely mathematical point of view is without great doubt, often employ weaknesses to such attacks.A fault analysis attack is one of the options of the side-channel attack on a cryptosystem. Its essence is that the attacker has an active influence on a physical device that provides computation (for example, a smart card). Faults caused by influence are then analysed in order to restore security information that is stored inside the device. These attacks are often significantly more efficient than passive side-channel attacks.The fault analysis attacks were proposed over 20 years ago. Since then, attacks have been successfully built owing to implementation of a number of symmetric and asymmetric crypto-algorithms. Also, a number of different methods for active influence on computation have been proposed, using specific physical effects and characteristics of the computing environment. Approaches to counteracting such types of attacks are also actively developing. For this, both physical and purely mathematical methods are used. However, it should be noted that cryptographic hash functions, and more complex crypto-schemes containing them as components (for example, some message authentication codes and digital signatures), are slightly presented in these papers.It is important to note that practical implementation of a specific attack requires that a combination of the following factors is available: a possibility of a specific physical impact on computation, an adequate mathematical model of such physical impact and a purely mathematical component of the attack that is a specific algorithms for introducing faults and further analysis of the results. At the same time, the solution of each of these problems separately is of independent theoretical value.The paper results do not involve the physical component of attack, aiming only at mathematics. In other words, a proposal is to present the specific algorithms for introducing faults and further analysis of the results. In this case, a specific fault model is considered known and specified. Several such models have been considered, based on the similar ones previously proposed for other algorithms.As an object of study, two standards to form message authentication codes have been selected: HMAC and NMAC. These standards can be based on any cryptographic hash function that provides the required level of security. The paper examines four examples of widely used hashes: MD5, MD4, SHA-1, SHA-0.The main results of the paper are as follows:- built specific algorithms for introducing faults in computation and their further analysis, allowing to discover secret information (secret keys);- finding and validation of estimates of such attacks (in terms of the number of introduced faults and the work factor of further analysis) for various combinations of parameters (algorithms and fault models); - shown that attacks timing can be reasonable.

The paper presents anew mathematical method for parasitic signal analyzing. NICV (Normalized Inter-Class Variance) method allows reducing considerably of computing and time expenditure in carrying out side channel attacks. To analyze NICV efficiency mathematical statistics methods and theory of probability were used. The paper presents an algorithm implementing NICV within a developed software package. The main shortcomings of the existing solutions have been taking into consideration during development of the new software: architecture of the presented software is easily extensible for adding new tools; unified format is used for all processing data. NICV was tested on the first round of 64-bit Data Encryption Standard algorithm. To assess the effectiveness two attacks based on differential power analysis and correlation power analysis have been simulated. Another advantage of the package is flexibility in adding of new methods for processing, saving, both original information and its new statuses in the database after carrying out signal processing.Side-Channel Attacks (SCA) are considered as a serious threat for data protected by cryptographic devices. Therefore such devices must be tested for resistance to these attacks. It should be taken into account that SCA are very powerful tool but they require significant computation capacity, especially in case of countermeasures. Presented software package program can help to analyze cryptographic devices on resistance to SCA and implemented NICV method allows decreasing of time and computation costs.

Different variants of combined side channel attacks (SCA) on authentication protocol COMP128 are analyzed in the article, paper. Main attack presented in the paper is partitioning attack. In the result, combined SCA increasing breaking of cipher are shown in the research.

Subject of Research. The paper presents an algorithm for pseudorandom number generationbased on properties of cellular automata. Cellular automata have high potential, high speed of calculations, especially at realization in parallel architecture. Method. In the presented algorithm pseudorandom numbers are generated by means of rules of transitions in cells of the cellular automaton depending on templates of the neighborhood and the output data of cells of "neighbors". Through several transitions at the choice of a generation technique the sequence of pseudorandom numbers turns out from zeroes and units. Main Results. The developed algorithm is tested on NIST-tests. The results of testing have shown that the algorithm makes the sequence with uniform distribution with probability of 99-100%. Comparison of the proposed algorithm with linearly congruent method, the main up-to-date method of generation of pseudorandom numbers, is carried out on NIST-tests. According to all tests the developed generator of pseudorandom numbers has shown the best results. The algorithm has the high speed, easy realization and also scaling possibility. Practical Relevance. The generator can be used in various applications, such as the theory of coding or lightweight cryptography. The cryptographic firmness is reached at tests by standard quality estimation techniques for the generator of pseudorandom numbers

Introduction . One of the tasks arising in cryptography is to ensure the safe and honest conduct of e-voting. This procedure provides that voters submit their votes electronically - for example, through electronic terminals. A new algorithm for the distribution of threshold sensitive data for electronic voting is proposed. Materials and Methods . The results are obtained on the basis of the following methodology: finite field theory, theory of algorithms, projective geometry, and linear algebra. The developed cryptosystem is based on the application of geometric objects from projective geometry which makes it possible to use the apparatus of linear algebra to make effective decisions on cryptographic problems. To estimate the complexity of the described algorithms, classical results from the theory of algorithms are applied. Research Results . This paper describes the cryptographic algorithms of secret sharing and its subsequent restoration based on special structural properties of projective spaces over finite fields, and their link with Galois fields of the appropriate order. The component parts of these algorithms, specifically, the construction of injective mapping from a residue ring prime modulo into the projective space over finite field of specific dimension; the generation of secret shares and secret; the procedure of secret sharing and its restoration, are described in great detail. The algorithmic time complexity calculations of the formal algorithms are given. Discussion and Conclusions . The described scheme is useful for electronic voting and in other spheres where methods of threshold cryptography are applied.

This article is sequel to a series of articles concerning with the study of generalized cellular automata and their cryptographic properties. It, mainly, focuses on using the generalized cellular automata, as the basic cryptographic primitives, according to requirements for algorithms of the so-called lightweight cryptography. One of the main requirements is to minimize the hardware resources used. According to this requirement, in case of using a FPGA algorithm for hardware implementation, the paper offers to consider only generalized cellular automata based on the regular graphs of degree k = 4 and k = 6 because their efficient hardware implementations widely practise the FPGA with 4- and 6-input look-up. To construct the generalized cellular automata were used graphs with diameter D = 3 and D = 4 because the generalized cellular automata based on the regular graphs of small diameter have good characteristics of the avalanche effect and the Moore boundary places restrictions on the maximum order of graph for a specified degree value of the graph and diameter.The findings of the research results for the cellular automata based on the maximum order of graphs with diameter D = 3 and D = 4 and the degree of the vertex k = 4 are broadly consistent with previous results for generalized automata in vicinity of 4. They are characterized by quite a large, regarding a diameter of the graph, value of the number of cycles from the start of operating automata till its reaching the maximum value of the integral avalanche effect characteristics.According to the research results, the selected cellular automata-based graphs with diameter D = 3 and D = 4 and the vertex degree k = 6 have shown good values of the avalanche effect characteristics and possess good scattering properties.Thus, all the abovementioned generalized cellular automata have good characteristics of the avalanche effect, and can be used as the basic cryptographic primitives. A promising research area is to create the non-uniform cellular automata, which have different local communication functions for all the cells.