This article describes a new implementation of MST-based encryption for generalized Suzuki 2-groups. The well-known MST cryptosystem based on Suzuki groups is built on a logarithmic signature at the center of the group, resulting in a large array of logarithmic signatures. An encryption scheme based on multiparameter non-commutative groups is proposed. The multiparameter generalized 2 - Suzuki group was chosen as one of the group constructions. In this case, a logarithmic signature is established for the entire group. The main difference from the known one is the use of homomorphic encryption to construct coverings of logarithmic signatures for all group parameters. This design improves a secrecy of the cryptosystem is ensured at the level of a brute-force attack.

Among the most significant problems that almost any blockchain faces are the problems of increasing its throughput (i.e., the number of transactions per unit of time) and the problem of a long waiting time before block confirmation. Thus, for example, in the most common BTC blockchain, according to various estimates, throughput is from 3 to 7 tps (transactions per second), and the average block confirmation time (block is considered confirmed if it has at least 6 blocks over it) is 1 h. At the same time, it is impossible to solve these problems directly by increasing the block size or increasing block generation intensity because this leads to essentially a decrease in the security of the blockchain in the first turn against double spend and splitting attacks. Such problems lead to the inconvenience of the practical use of cryptocurrencies to pay for goods and services. Proposed a few years ago, the PoP consensus protocol potentially helps to solve the problem of increasing blockchain throughput, although it was originally intended to ensure the stability of “young” blockchains, with “small” PoW, through the use of a secure blockchain, such as BTC. A blockchain that has provable security is called the security-provided blockchain (SPB), and one that uses SPB to achieve its security is called the security-inherited blockchain. In this paper, we give explicit formulas which describe how the number of confirmation blocks in the security-inherited blockchain, which is sufficient to achieve a given security level of this blockchain to a double spend attack, depends on the parameters of both blockchains. It is essential that we use a realistic model to obtain the results, taking into account the synchronization times of both blockchains. Such a model is much closer to the real situation, but at the same time, it leads to significant analytical difficulties in obtaining results. The obtained formulas are convenient for numerical calculations, the numerous examples of which are also given in this work.

We introduce a new method of choosing parameters for margin trading protocols in the Constant Product Model and apply it to our new DeFi Margin Trading protocol Primex, which can work with different DEXs and DeFi platforms. The main advantages of Primex, in comparison with existing DeFi protocols, are the following: (1) the possibility to trade with leverage, using large asset amounts and having only a small part (deposit) in one of the assets; (2) full explanation and justification of the choice of protocol parameters and relations (such as liquidation condition, maximum leverage, different fees, etc.), which allows to estimate different risks (for Lenders and the protocol) and reduce them to the required level; (3) additional decentralization and, at the same time, protection against different faults in protocol functioning, achieved by the usage of the decentralized Keeper; (4) transparent rules and conditions for all participants—Lenders, Traders, and Keepers. We give a detailed explanation for our approach to set protocol parameters and build a corresponding method to obtain their numerical values in the case of the Constant Product Model. The obtained numerical results provide additional indirect confirmation of the consistency of our method. Note that it also may be applied (after the corresponding recalculation of some coefficients) to other models, such as the Order Book Model, Constant Sum Model, or the Mixed Constant Sum/Constant Product Model (as described in the Curve whitepaper), and even other types of DeFi protocols after some modification.

The article proposes a methodology for testing a library of cryptographic transformations with the implementation of an improved encryption scheme on generalized Suzuki 2-groups in the MST3 cryptosystem. The need to improve existing methods of cryptosystem creation is driven by progress in quantum computer development, which possess sufficient computational power to compromise many existing public key cryptosystems. This is especially true for systems based on factorization and discrete logarithm, such as RSA and ECC. Over the last nearly 20 years, there have been proposals for using non-commutative groups to develop quantum-resistant cryptosystems. The unsolved word problem, formulated by Wagner and Magyarik, uses permutation groups and is a promising direction in cryptosystem development. Magliveras proposed logarithmic signatures, a special type of factorization applied to finite groups, and the latest version of this technology is known as MST3, based on the Suzuki group. The first implementation of the cryptosystem on the generalized Suzuki 2-group had limitations in encryption and protection against brute force attacks. Over the past years, many proposals have been made to improve the basic design. The research conducted by the authors expanded the possibilities of using public cryptography by refining parameters based on non-Abelian groups. The article demonstrates the methodology for conducting tests of the practical implementation of the library of cryptographic transformations with the implementation of an improved encryption scheme on Suzuki 2-groups, confirming its functionality.

Hash-based signatures are a wide class of post-quantum cryptographic algorithms, their security is based on the complexity of collision and preimage search problems for cryptographic hash functions. The main advantages of this class are post-quantization, easy modification and a well-researched mathematical base. The disadvantages are large sizes of signatures and limited number of uses of one key pair. The most promising algorithms of this class include algorithms of the SPHINCS type, which have a complex structure, including, among others, a one-time Winternitz signature. The paper analyzes the existing one-time signature algorithms, both well-known Lamport and Winternitz schemes, taking into account modifications of the latter one, and alternative methods. An analysis of the security of modified algorithms has been shown, which showed that their security is based on the same mathematical basis as the security of the original algorithms. The one-time use requirement remains critical to the safety of each of the algorithms studied. The sizes of keys and signatures and computational complexity of various algorithms are compared, in what their basic differences consist. The modified algorithms do not add fundamentally new components in cryptosystems but they make it possible to achieve a certain optimization, shifting the conditions of space-time compromise. The extended Lamport signature is of a particular interest, having the same computational complexity and key sizes as the original algorithm, and at the same time allowing one to halve the signature size. In the context of the SPHINCS cryptosystem, the Winternitz signature remains the best option, since it allows the complete computation of the public key directly from the signature.