Cryptographic Transformations Research Articles

Synthesis of sets of non-symmetric two-operand two-bit crypto operations within the permutation accuracy

The object of research is the processes of building operations for cryptographic protection of information, as the requirements for information security are constantly increasing. Increasing the stability of cryptographic transformations directly depends on the complexity and variability of the crypto algorithm. It is possible to increase variability by increasing the range of crypto operations. Significantly increasing the number of crypto operations is possible through the synthesis of asymmetric operations. This paper is devoted to the creation of methodological support for the synthesis and analysis of sets of two-operand two-bit cryptographic operations with precision permutation. The conducted researches are based on the results of a computational experiment, which consists in the synthesis of two-operand two-bit crypto operations based on single-operand, with the subsequent search for pairs of operations of direct and correct inverse crypto transformation on the basis of complete search. In the course of the computational experiment, pairs of two-operand operations were presented, represented by tuples of four single-operand operations. The formalization of the results provided a mathematical representation of operations, suitable for practical implementation. To simplify the complexity of practical implementation, the synthesized operations are divided into 24 sets of 24 operations. Separation of operations occurred due to the use of templates of tables of truth of sets of operations with precision to permutation of operands. It is established that the entire set of operations can be constructed with the precision of permutation based on the use of the template of any operation. In addition, the analysis of the synthesized sets showed that the sets of symmetric and asymmetric operations do not intersect. 20 sets of asymmetric two-operand two-bit operations, as well as 4 sets of symmetric operations are obtained. Further investigation of each synthesized set of asymmetric crypto operations will allow for the relationship between the operands of the operation and between the operations as a whole. The use of synthesized asymmetric operations will improve the reliability of crypto algorithms for streaming encryption of information by significantly increasing the variability of cryptographic transformations. In turn, the use of synthesized sets of operations will simplify practical implementation in computer cryptography

IMPLEMENTATIONOFARBITRARYBITNESSPERMUTATIONS IN ONE OF THE CLASSES OF LINEAR STRUCTURES

Speed of transformation and simplicity of implementation are one of the key contributors in permutation researches. The paper reviews the implementation of arbitrary bitness permutation in the field of computer engineering on one of the classes of combination structures of linear complexity from the number of variables –one-dimensional cascades of structural units.The fact that the reflectionformed by the specified linear structure is completely the same asthe reflectionof the corresponding Mealyfinite state machine as a prototype of the structural module of the cascadeis used.This allowed us to explore the properties of structural units and the cascade as a whole in the context of the concepts of the theory of digital automata.The implementation of arbitrary bitnesspermutationsis based on usage of the connected graphs for state table and on usage of unique combinations without repeats for each row of output table. The purpose of this permutation is to convert large volumes of data in fastand simplewayusing hardware or software with the ability to be used in multiple areas of researches. The study of providing the bijectivity of the reflection and the equivalence analysis of permutations was performed. The algorithm of constructionof finite-statemachines for implementationof direct and invertedpermutationsis shown, as well as examples ofstateand outputtablesconstruction. Examplesofhardware implementationusingfield-programmable gate arraysare given. The sizeof stateand output tables for the software implementation is estimated. The number of unique bijective reflections and amount of key information for the investigated permutation in cryptographic transformations has been estimated. The theoretical speed of transformations of the bijective reflection is estimated for both field-programmable gate arrays and software implementation according to the modern indicators of types of computing devices memory speed. The practicalverification of processingspeed is made with software implementation. Areas of application of the investigatedarbitrary bitnesspermutation are proposed.

Automorphisms of Finite Quasi-Groups without Sub-Quasi-Groups

Finite quasi-groups without sub-quasi-groups are considered. It is shown that polynomially complete quasi-groups with this property are quasi-primal. The case in which the automorphism groups act transitively on these quasi-groups is considered. Quasi-groups of prime-power order defined on an arithmetic vector space over a finite field are also studied. Necessary conditions for a multiplication in this space given in coordinate form to determine a quasi-group are found. The case of a vector space over the two-element field is considered in more detail. A criterion for a multiplication given in coordinate form by Boolean functions to determine a quasi-group is obtained. Under certain assumptions, quasi-groups of order 4 determined by Boolean functions are described up to isotopy. Polynomially complete quasi-groups are important in that the problem of solving polynomial equations is NP-complete in such quasi-groups. This property suggests using them for protecting information, because cryptographic transformations are based on quasi-group operations. In this context, an important role is played by quasi-groups containing no sub-quasi-groups.

ДОСЛІДЖЕННЯ І СИНТЕЗ ГРУПИ СИМЕТРИЧНИХ МОДИФІКОВАНИХ ОПЕРАЦІЙ ПРАВОСТОРОННЬОГО ДОДАВАННЯ ЗА МОДУЛЕМ ЧОТИРИ

В статті представлено основні результати дослідження і синтезу групи двохоперандних двохрозрядних симетричних операцій правостороннього додавання за модулем чотири шляхом використання групи двохрозрядних однооперандних операцій крипто перетворення. Синтез групи операцій на основі операції правостороннього додавання за модулем чотири, раніше не досліджувався. Встановлено, що побудована група операцій криптографічних перетворень відрізняється від груп криптооперацій побудованих на основі додавання за модулем два та класичним лівостороннім додаванням за модулем чотири. Використання нової синтезованої групи дає змогу підвищити якість потокового шифрування за рахунок збільшення варіативності криптографічних перетворень. Встановлено, що за рахунок симетричних синтезованих операцій в системах потокового шифрування буде використовуватися додатково до двадцяти чотирьох таблиць підстановки

НОВИЙ ПІДХІД ДО ПОБУДОВИ ПОСТ-КВАНТОВОЇ СХЕМИ ЕЛЕКТРОННОГО ЦИФРОВОГО ПІДПИСУ

Cryptographic information security techniques are essential in building a modern cybersecurity infrastructure. Recently, there have been new challenges and threats to cryptographic transformation. In particular, the emergence and rapid development of the latest quantum computing technologies necessitates the urgent need for the development and research of new methods of post-quantum cryptographic transformations, that is, those that will be sustainable even if quantum cryptanalysis is possible. This article is devoted to the analysis of possibilities of implementation of digital signature schemes based on using error-correcting codes. This approach allows cryptographers to build schemes that are resistant to both classic cryptanalysis and cryptanalysis which uses quantum computing. The article describes the principles of the classic digital signature scheme which is named CFS and built using a Niederreiter-like transform, and also we propose a new approach that enables an implementation of signature according to the McEliece transformations. This approach preserves the advantages of its predecessor and provides additional protection against special attacks. Also, a comparative analysis and characterization of the considered schemes according to the criteria of resistance to classic and quantum cryptanalysis, complexity of necessary transformations and length of generated signatures are made. The results show that reliable and secure cryptographic transformations can be built, in particular, electronic digital signature algorithms that are code-based and secure even in the case of quantum cryptanalysis. However, it should be noted that the drawback of code-based signature schemes is the large amount of key data required by the algorithm, as well as the difficulty in creating a signature due to the need for multiple decryption of the syndrome, which remains a topical topic and needs further research

МЕТОД ОЦІНЮВАННЯ ФУНКЦІОНАЛЬНОЇ БЕЗПЕКИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ ДЛЯ СТВОРЕННЯ ГАРАНТОЗДАТНИХ АВТОМАТИЗОВАНИХ СИСТЕМ

The components of ensuring the warranty of automated systems, which are subject to increased requirements in connection with their use in many sensitive areas of public activity, including national security and defense, critical industrial technologies, energy and communications, banking, environmental protection , technologies of legitimate distance learning, etc. Certain components can significantly affect the quality and reliability of information services in regulatory conditions. In particular, the special role of the functional security of the cryptographic subsystem in terms of supporting the performance of the automated system for its tasks and functions in general, as well as in terms of ensuring the confidentiality and integrity of information. The components of the cryptographic subsystem have been identified, the poor or incorrect operation of which negatively affects the security of these subsystems. The types of the most dangerous attacks on these subsystems are analyzed, their classification from the point of view of possibility of realization in modern scientific and technical conditions and depending on capacity of available computing means and technologies on the basis of which the most real and dangerous variant of realization of remote attacks on software implementation of cryptographic subsystem is defined. . Based on the analysis, a method for evaluating the quality of cryptographic transformations based on a modified algorithm for solving the problem of finding solutions of systems of linear equations with distorted right-hand parts using the so-called decoding based on "lists" of first-order "shortened" Reed-Muller codes is proved. the correctness of the proposed algorithm.

THE INVERSION METHOD OF FOUR-BIT BOOLEAN SAC CRYPTOTRANSFORMS

Context. Nonlinear systems of Boolean functions play a prominent role in the protection of cryptosystems. The creation and use of new four-bit cryptographic transformations with nonlinear Boolean functions that have the property of strict avalanche criterion is an actual task for increasing the reliability of information protection systems. Objective. The goal of the work is creating a method for obtaining inverse four-bit cryptographic transformations with the strict avalanche criterion property, which contain balanced Boolean functions only with the operations of inversion and addition modulo two. Method. A method is proposed for obtaining inverse four-bit cryptographic transformations with the strict avalanche criterion property, each of which contains balanced Boolean functions only with the operations of inversion and addition modulo two. The method simplifies the process of finding inverse cryptographic transformations by creating a class of thirty balanced basic Boolean functions with the required predefined limitations and properties and for finding, within this class, the basic Boolean functions that make up the inverse cryptographic transformation. Results. The effectiveness of the method is shown for obtaining two inverse four-bit cryptographic transformations with the property of a strict avalanche criterion from two direct four-bit cryptographic transformations with the property of a strict avalanche criterion. Conclusions. For the first time, there was proposed a method for obtaining inverse four-bit cryptographic transformations with the strict avalanche criterion property for balanced Boolean functions containing two logical operations (inversion and addition modulo two) to ensure reliable information protection. This method is a method of selecting the already existing basic Boolean functions from a predetermined set of balanced basic Boolean functions for direct and inverse cryptographic transformations, whereas the existing methods of searching for inverse cryptographic transformation are methods for calculating each element of the Boolean functions for the inverse cryptographic transformation. The method can be extended to a larger even number of arguments of the balanced Boolean functions of cryptographic transformations to increase the cryptographic resilience.

ТЕХНОЛОГІЯ ОПИСУ ЛІНІЙНИХ І НЕЛІНІЙНИХ КРИПТОГРАФІЧНИХ ПЕРЕТВОРЕНЬ

The paper deals with the study of the dependence of the calculation of the number of operations, based on recurrent combination of capacities of sets of operations of lower bit rate and elementary functions to describe the process of construction of sets of new operations. The possibility of developing a single technology for the synthesis and investigation of both linear and nonlinear operations of cryptographic transformation of information is studied. An attempt has been made to obtain three-bit operations based on two-bit operations of cryptographic information conversion. For this purpose, logical functions are presented in the form of logical operations of two variables corresponding to them in analytical representation. Two-bit elementary functions in the operation of cryptographic information transformation are combined. The study calculates the number of two-bit, three-bit and four-bit elementary functions, two-bit, three-bit and four-bit operations. According to the results of the study, it is found that our proposed dependence of the calculation of the number of operations of cryptographic transformation, based on recurrent combination of capacities of sets of operations of lower bit rate and elementary functions, is correct and mathematically describes the process of constructing the sets of new operations. Based on the results of this study, it can be considered that the development of a single technology for the synthesis and investigation of both linear and nonlinear operations of cryptographic transformation of information is possible. This approach allows not only to calculate the number of operations of cryptographic information conversion, but also to construct the operations themselves by combining known cryptographic transformation operations and elementary higher bit functions. The proposed approach creates the preconditions for the development of a single technology for the description and synthesis of both linear and nonlinear cryptotransformation operations.

Моделі безпеки постквантових криптографічних примітивів

In this paper, the essence is considered and security models of asymmetric post-quantum cryptographic primitives of different types are investigated. The basis taken security models that are recommended by NIST USA in the requirements of the PQC competition for candidates for post-quantum cryptographic primitives. Such algorithms include asymmetric cryptographic transformations such as asymmetric encryption, digital signature, and key encapsulation mechanism. The following security models are recommended, which are related to: the asymmetric encryption — IND-CCA2 (IND-CPA, IND-CCA); the digital signature — EUF-CMA (and its variations); the key encapsulation mechanisms — СK-model. In this paper, the basic essence of such security models is considered. The use of security models in research of cryptographic primitives is relatively new. A generalization of each of these models and a definition of the necessity and conditions, and the consequences of their application are required. Such models take into account the application environment in which an unauthenticated-links adversarial model and authenticated-links adversarial model can operate. The paper considers the concept of indistinguishability and security model of post-quantum asymmetric ciphers on its basis. The property of indistinguishability under chosen plaintext attack is determined. The concept of semantic security is considered. The types of most common attacks based on indistinguishability are given. Existing versions of the EUF-CMA security model — SUF-CMA, etc. are considered. Definitions of «forward security, forward secrecy» and «perfect forward secrecy (PFS)» are given. In addition, the paper considers the peculiarities of the application regarding to perspective asymmetric transformations of the «game theory». The definition of concept «game theory» is given

Аналіз властивостей електронних підписів на базі MQ-перетворень

Recently, the most critical studies in the field of cryptographic information security are studies that relate to the possibility of using existing algorithms in the post quantum period, as well as studies that seek to find promising algorithms that will be resistant to quantum attacks, and therefore meet all requirements of the post. quantum world. The paper is devoted to the analysis of MQ-based electronic signature algorithms (Multivariate Quadratic Transformations) of transformations relative to the unconditional and conditional criteria that were proposed as candidates for the post-quantum standard of the NIST PQC competition. The paper presented the general scheme of creating an electronic signature using multivariate transformations. The analysis of candidates and their peculiarities was also conducted. The results of the evaluation of the electronic signature mechanisms in relation to generally accepted unconditional criteria, as well as regarding the conditional criteria based on the techno-economic and technical-operational requirements for nominated candidates for the post-quantum standard are presented. The main conditional criteria were the lengths of key data and the result of the cryptographic transformation, that is, the electronic signature, as well as the computational efficiency of signature creation and verification. The comparison was made on the electronic signatures of LUOV, Gui, Rainbow, MQDSS, TPSig, DualModeMS, HiMQ-3, DME and GeMSS. During the analysis, the technique of comparing cryptographic mechanisms on the basis of expert evaluations using a combination of conditional and unconditional criteria by weighting coefficients method was used. On the basis of the conducted researches, the most perspective candidates for the post quantum standard of electronic signature were selected, as well as recommendations for their application were proposed

STUDIES ON STATISTICAL ANALYSIS AND PERFORMANCE EVALUATION FOR SOME STREAM CIPHERS

This paper presents the results of the comparative analysis of safety statistics and performance of encryption, the Strumok stream symmetric cipher (proposed for the national encryption standard of Ukraine) with other known cryptographic transformation algorithms, such as SALSA20, SNOW2.0, HC, AES with usages in stream mode, etc. They are accepted as national, international standards or are presented by the New European Schemes for Signatures, Integrity, and Encryptions (NESSI), Cryptography Research and Evaluation Committees (CRYPTREC) and others. The result of safety statistics is an analysis of the cryptographic properties of the output sequences using statistical test sets developed by the National Institute of Standards and Technology (NIST STS) and the DIEHARD tests. The result of the study of performance is the evaluation of the use of central processing unit (CPU) time to convert one octet of data to 64-bit computing platforms, following the test profile used in the eSTREAM contest.

Development of Niederreiter hybrid crypto-code structure on flawed codes

The use of the Niederreiter modified crypto-code structure (MCCS) with additional initialization vectors (with many invalid positional vectors of the error vector and multiple positions of shortening the error vector) requires an increase in the speed of cryptographic transformation of the system as a whole. For this purpose, it is proposed to use flawed codes. Flawed codes allow you to increase the speed of code transformations by reducing the power of the field while damaging the plaintext and reducing the amount of data transferred by damaging the ciphertext. This approach allows the construction of hybrid crypto-code structures based on the synthesis of Niederreiter modified crypto-code structures on modified (shortened or extended) codes on elliptic curves with damaging procedures. A significant difference from classical hybrid (complex) cryptosystems is the use of asymmetric cryptosystems to ensure data security with fast crypto-transformation procedures (generation and decoding of a codogram). The paper discusses methods for constructing flawed codes and approaches for using the Niederreiter hybrid crypto-code structure on modified elliptic codes. Practical algorithms are proposed for using the MV2 damage mechanism in the Niederreiter crypto-code structure on modified elliptic codes, which makes it possible to implement a hybrid crypto-code structure. The results of a comparative assessment of energy consumption for the formation of an information package with various methods of damage, which determined the choice of damage method in practical algorithms. The conducted studies confirm the competitive efficiency of the proposed cryptosystem in Internet technologies and mobile networks, ensuring practical implementation on modern platforms and the necessary cryptographic strength under post-quantum cryptography

CALCULATION OF GENERAL PARAMETERS FOR NTRU PRIME UKRAINE OF 6-7 LEVELS OF STABILITY

The research was carried out and the development of an effective practical algorithm for the construction of system-wide parameters and keys for cryptographic transformations such as asymmetric ciphers and the key encapsulation protocol was performed. The experimental confirmation of the built-in system-wide parameters and keys of cryptographic transformations such as asymmetric cipher and the key encapsulation protocol of 6 – 7 stability levels based on transformations in the ring of polynomials over the finite fields is presented. The types of attacks that are possible with respect to the specified cryptographic transformations are also presented in this work.

Кодування і класифікація перестановок за спеціальним перетворенням з оцінками потужностей класів

Scientific articles investigating properties and estimates of the number of so-called complete permutations are surveyed and analyzed. The paper introduces a special S-transform on the set of permutations and determines the permutation properties according to this transform. Classification and coding of permutations by equivalence classes according to their properties with respect to S-transformation is proposed. This classification and permutation properties, in particular, generalize known results for complete permutations regarding determining certain cryptographic properties of substitutions that affect the cryptographic transformations security. The exact values of the number of permutations in equivalence classes for certain permutation sizes are calculated and the estimates of the cardinality of classes with various properties are constructed by statistical modeling. The complete list of permutation classes with the exact values of their sizes for permutations of order n = 11 is presented. The interval estimates for the size of classes with various characteristics for permutations of order n = 11, 26, 30, 31, 32, 33, 45, 55 are obtained. Monte Carlo estimates and bounds of confidence intervals used the approximation of the binomial distribution by the normal and Poisson distributions, as well as the Python programming language package Scipy. Statistical tables have been calculated that can be used for further conclusions and estimates. The classification of permutations by their properties with respect to the introduced transform can be used in constructing high-quality cryptographic transformations and transformations with special features. The classes of complete permutations with their properties are selected as the best for rotary cryptosystems applications. The obtained results can be used, in particular, to search for permutations with certain characteristics and properties, to find the probability that the characteristic of the generated permutation belongs to a collection of given characteristics, to estimate the complexity of finding permutations with certain properties. A statistical criterion of consent, which uses the characteristics of permutations by S-transformation to test the generators of random permutations and substitutions is proposed.

C# parser for extracting cryptographic protocols structure from source code

Cryptographic protocols are the core of any secure system. With the help of them, data is transmitted securely and protected from third parties' negative impact. As a rule, a cryptographic protocol is developed, analyzed using the means of formal verification and, if it is safe, gets its implementation in the programming language on which the system is developed. However, in the practical implementation of a cryptographic protocol, errors may occur due to the human factor, the assumptions that are necessary for the possibility of implementing the protocol, which entail undermining its security. Thus, it turns out that the protocol itself was initially considered to be safe, but its implementation is in fact not safe. In addition, formal verification uses rather abstract concepts and does not allow to fully analyze the protocol. This paper presents an algorithm for analyzing the source code of the C# programming language to extract the structure of cryptographic protocols. The features of the implementation of protocols in practice are described. The algorithm is based on the searching of important code sections that contain cryptographic protocol-specific constructions and finding of a variable chain transformations from the state of sending or receiving messages to their initial initialization, taking into account possible cryptographic transformations, to compose a tree, from which a simplified structure of a cryptographic protocol will be extracted. The algorithm is implemented in the C# programming language using the Roslyn parser. As an example, a cryptographic protocol is presented that contains the basic operations and functions, namely, asymmetric and symmetric encryption, hashing, signature, random number generation, data concatenation. The analyzer work is shown using this protocol as an example. The future work is described.

METHODS OF BUILDING GENERAL PARAMETERS AND KEYS FOR NTRU PRIME UKRAINE OF 5TH – 7TH LEVELS OF STABILITY. PRODUCT FORM

The research was carried out and the development of an effective practical algorithm for the construction of system-wide parameters and keys of cryptographic transformations such as asymmetric ciphers for a special form of setting the Product Form polynomial was performed. The experimental confirmation of the built-in system-wide parameters for 5–7 stability levels NTRU PRIME UKRAINE, taking into account a combined attack is given.

Practical Implementation Effectiveness of the Speed Increasing Method of Group Matrix Cryptographic Transformation

Practical Implementation Effectiveness of the Speed Increasing Method of Group Matrix Cryptographic Transformation

Calculation of general parameters for NTRU PRIME UKRAINE of 6-7 levels of stability

The research was carried out and the development of an effective practical algorithm for the construction of system-wide parameters and keys for cryptographic transformations such as asymmetric ciphers and the key encapsulation protocol was performed. The experimental confirmation of the built-in system-wide parameters and keys of cryptographic transformations such as asymmetric cipher and the key encapsulation protocol of 6 – 7 stability levels based on transformations in the ring of polynomials over the finite fields is presented. The types of attacks that are possible with respect to the specified cryptographic transformations are also presented in this work.

Methods for constructing system-wide parameters and keys for NTRU PRIME UKRAINE 5 – 7 stabvility levels. Product form

The research was carried out and the development of an effective practical algorithm for the construction of system-wide parameters and keys of cryptographic transformations such as asymmetric ciphers for a special form of setting the Product Form polynomial was performed. The experimental confirmation of the built-in system-wide parameters for 5 – 7 stability levels NTRU PRIME UKRAINE, taking into account a combined attack. is given.

Essence and features of Grover’s method implementation on a classical computer for symmetric cryptanalysis

This paper is devoted to detailing, mastering for use, checking cryptanalytic properties and demonstrating the use of Grover’s method for cryptanalysis of symmetric cryptographic transformations. The essence of the method and its refinement are presented in order to implement Grover’s quantum algorithm on a classical computer.