Ardabek Khompysh

This paper proposes an approach based on a secret sharing scheme with the mandatory participation of predefined subgroups. The proposed scheme allows secret reconstruction only when representatives from each designated group of participants (e.g., cloud providers, legally independent parties, etc.) are present. This mechanism enhances resistance to internal collusion, strengthens access control, and enables distributed management. The structure and mathematical foundations of the proposed scheme are presented, along with an analysis of its properties. A cryptanalysis is conducted, evaluating the scheme’s resilience to various types of attacks, and the results are discussed. The computational complexity of the algorithm is also analyzed, and its resource efficiency is confirmed.

This paper introduces a new block encryption algorithm designed for the cryptographic protection of data. The paper introduces and explains a newly devised exponentiation modulo (EM) transform method, utilized to obtain the S-block, an essential element within the presented algorithm. A method of optimizing the choice of keys and increasing the efficiency of calculation was also used. It is proposed that incorporating characteristics of cryptographic primitives functioning within the Galois field into the algorithm can lead to favorable outcomes. To increase the encryption algorithm's speed, non-positional polynomial notation systems and a working base index table are used. The paper discusses the implementation of an encryption algorithm in C++ and examines the statistical characteristics of the resulting ciphertexts. For experimental testing of statistical safety, a set of statistical tests by National Institute of Standards and Technology (NIST) and D. Knuth was used. Furthermore, the resulting S-box was examined using linear, differential, and algebraic cryptanalysis techniques. In the future, this proposed S-box will be implemented in the encryption algorithm being developed for the preliminary encryption of confidential data.

One of the most important issues in the design of cryptographic algorithms is studying their cryptographic strength. Among the factors determining the reliability of cryptographic algorithms, a good pseudorandom sequence generator, which is used for key generation, holds particular significance. The main goal of this work is to verify the normal distribution of pseudorandom sequences obtained using the generation algorithm and demonstrate that there is no mutual statistical correlation between the values of the resulting sequence. If these requirements are met, we will consider such a generator reliable. This article describes the pseudorandom sequence generation algorithm and outlines the steps for each operation involved in this algorithm. To verify the properties of the pseudorandom sequence generated by the proposed algorithm, it was programmatically implemented in the Microsoft Visual C++ integrated development environment. To assess the statistical security of the pseudorandom sequence generation algorithm, 1000 files with a block length of 10000 bits and an initial data length of 256 bits were selected. Statistical analysis was conducted using tests by D. Knuth and NIST. As shown in the works of researchers, the pseudorandom sequence generation algorithm, verified by these tests, can be considered among the reliable algorithms. The results of each graphical test by D. Knuth are presented separately. The graphical tests were evaluated using values obtained from each test, while the chi-squared criterion with degrees of freedom was used to analyze the evaluation tests. The success or failure of the test was determined using a program developed by the Information Security Laboratory. Analysis of the data from the D. Knuth tests showed good results. In the NIST tests, the P-value for the selected sequence was calculated, and corresponding evaluations were made. The output data obtained from the NIST tests also showed very good results. The proposed pseudorandom sequence generation algorithm allows generating and selecting a high-quality pseudorandom sequence of a specified length for use in the field of information security.

The distinguishing feature of hash-based algorithms is their high confidence in security. When designing electronic signature schemes, proofs of security reduction to certain properties of cryptographic hash functions are used. This means that if the scheme is compromised, then one of these properties will be violated. It is important to note that the properties of cryptographic hash functions have been studied for many years, but if a specific hash function used in a protocol turns out to be insecure, it can simply be replaced with another one while keeping the overall construction unchanged. This article describes a new post-quantum signature algorithm, Syrga-1, based on a hash function. This algorithm is designed to sign r messages with a single secret key. One of the key primitives of the signature algorithm is a cryptographic hash function. The proposed algorithm uses the HAS01 hashing algorithm developed by researchers from the Information Security Laboratory of the Institute of Information and Computational Technologies. The security and efficiency of the specified hash algorithm have been demonstrated in other articles by its authors. Hash-based signature schemes are attractive as post-quantum signature schemes because their security can be quantified, and their security has been proven.

This article presents one of the main transformations of symmetric block ciphers used to protect confidential information, a new method for obtaining a non-linear S block, and an analysis of the results obtained. The S-box obtained by this method can be used as a non-linear transformation in block cipher algorithms to protect confidential data transmitted over an open channel. In most well-known works in the field of analysis and synthesis of modern block symmetric ciphers, S-box is used as a mathematical apparatus for cryptographic Boolean functions. In this case, each S-box is represented by a set of composite Boolean functions whose properties characterize the efficiency of the nonlinear substitution node. Substitution nodes for modern symmetric primitives, including key unfolding functions, are usually implemented as replacement tables. Considering that in most modern block symmetric ciphers for introducing round keys, the encryption algorithm uses a linear operation (bitwise addition modulo 2), S-blocks are the only elements responsible for the cryptographic stability of block encryption algorithms. The required number of rounds of block symmetric ciphers is selected taking into account the results of the cryptographic analysis performed, provided that the properties of S-boxes are specified. As the main criteria and performance indicators, the balance and nonlinearity of composite Boolean functions are used; strict avalanche criterion (SAC), propagation criterion; algebraic degree; the value of the autocorrelation function. In this article, a study was made of the nonlinearity and strict avalanche criterion (SAC) of the S-box used in the block symmetric encryption algorithm. The results of the study were compared with the S-boxes of modern cryptographic algorithms and showed good results.

This paper proposes the new hash algorithm HBC-256 (Hash based on Block Cipher) based on the symmetric block cipher of the CF (Compression Function). The algorithm is based on the wipe-pipe construct, a modified version of the Merkle-Damgard construct. To transform the block cipher CF into a one-way compression function, the Davis-Meyer scheme is used, which, according to the results of research, is recognized as a strong and secure scheme for constructing hash functions based on block ciphers. The symmetric CF block cipher algorithm used consists of three transformations (Stage-1, Stage-2, and Stage-3), which include modulo two addition, circular shift, and substitution box (four-bit S-boxes). The four substitution boxes are selected from the “golden” set of S-boxes, which have ideal cryptographic properties. The HBC-256 scheme is designed to strike an effective balance between computational speed and protection against a preimage attack. The CF algorithm uses an AES-like primitive as an internal transformation. The hash image was tested for randomness using the NIST (National Institute of Standards and Technology) statistical test suite, the results were examined for the presence of an avalanche effect in the CF encryption algorithm and the HBC-256 hash algorithm itself. The resistance of HBC-256 to near collisions has been practically tested. Since the classical block cipher key expansion algorithms slow down the hash function, the proposed algorithm is adapted for hardware and software implementation by applying parallel computing. A hashing algorithm was developed that has a sufficiently large freedom to select the sizes of the input blocks and the output hash digest. This will make it possible to create an almost universal hashing algorithm and use it in any cryptographic protocols and electronic digital signature algorithms

This paper proposes a new block encryption algorithm for cryptographic information protection. It describes a new transformation method EM (Exponentiation Module), which is part of the algorithm, and a method of S-box obtaining. The paper also considers an optimization technique to advance the efficiency of key selection and calculation. We discuss the possibility to obtain good results by applying the peculiar properties of cryptographic primitives in the Galois field. To increase the strength and speed of the encryption algorithm, we used a nonpositional polynomial notation and an indexed view for the Galois field. The paper provides for statistical properties of the ciphertext obtained with the developed algorithm. We also present the results of differential and linear cryptanalysis of the S-box used.