L. V. Kovalchuk

Decentralized governance plays a critical role in blockchain communities, allowing stakeholders to shape the evolution of platforms such as Cardano, Gitcoin, Aragon, and MakerDAO through distributed voting on proposed projects to support the most beneficial ones. In this context, numerous voting protocols for decentralized decision-making have been developed, enabling secure and verifiable voting for individual projects (proposals). However, these protocols are not designed to support more advanced models such as quadratic voting (QV), where the voting power, defined as the square root of a voter's stake, must be distributed among the projects selected by the voter. Simply running multiple instances of a single-choice voting scheme in parallel is insufficient, as it cannot enforce the correct splitting of voting power. To address this, we propose an efficient blockchain-based voting protocol that supports liquid democracy under the QV model, while ensuring voter privacy, fairness, and verifiability of voting results. In our scheme, voters can delegate their votes to trusted representatives (delegates), while having the ability to distribute their voting power across selected projects. We model our protocol in the Universal Composability framework [1] and formally prove its UC-security under the Decisional Diffie-Hellman (DDH) assumption. To evaluate the performance of our protocol, we developed a prototype implementation [2] and conducted performance testing. The results show that the size and processing time of a delegate's ballot scale linearly with the number of projects, while a voter's ballot scales linearly with both the number of projects and the number of available delegation options. In a representative setting with 64 voters, 128 delegates, and 128 projects, the overall traffic is approximately 1.4 MB per voted project, confirming the practicality of our protocol for modern blockchain-based governance systems.

This paper studies the probability of a double-spend attack in an Ouroboros-like Proof-of-Stake (PoS) setting when confirmation decisions must be made for a finite number of blocks. Existing security analyses of Ouroboros-family protocols are mainly asymptotic and therefore do not directly provide the attack probability for a fixed confirmation depth. We consider an analytically tractable model that allows empty slots and multiple slot leaders, and assumes fixed stake distribution within an epoch, one-block growth of the public longest chain in any slot containing at least one honest leader, and next-slot block visibility. These assumptions hold when the time slot length is much greater than the network delay, and are applicable to practical deployment scenarios such as Cardano. Under these assumptions, for the first time, an exact closed-form solution for the success probability of a double-spend attack considering a realistic model with multiple leaders and empty time slots. Numerical examples illustrate how the required confirmation depth depends on the adversarial stake ratio and the active slot coefficient. The results apply to the stated analytical model and do not yet cover delayed fork resolution or the full protocol-level fork-choice and finality mechanisms of Ouroboros Praos.

This paper studies the probability of a double-spend attack in an Ouroboros-like Proof-of-Stake (PoS) setting when confirmation decisions must be made for a finite number of blocks. Existing security analyses of Ouroboros-family protocols are mainly asymptotic and therefore do not directly provide the attack probability for a fixed confirmation depth. We consider an analytically tractable model that allows empty slots and multiple slot leaders, and assumes fixed stake distribution within an epoch, one-block growth of the public longest chain in any slot containing at least one honest leader, and next-slot block visibility. These assumptions hold when the time slot length is much greater than the network delay, and are applicable to practical deployment scenarios such as Cardano. Under these assumptions, for the first time, an exact closed-form solution for the success probability of a double-spend attack considering a realistic model with multiple leaders and empty time slots. Numerical examples illustrate how the required confirmation depth depends on the adversarial stake ratio and the active slot coefficient. The results apply to the stated analytical model and do not yet cover delayed fork resolution or the full protocol-level fork-choice and finality mechanisms of Ouroboros Praos.

The transition from centralized power systems to decentralized infrastructures with a high share of renewable energy sources calls for reliable settlement in P2P electricity trading across “smart” regions. Blockchain platforms can enhance transparency and facilitate automated settlement; however, double-spend attacks still pose a threat to transaction finality and, consequently, undermine trust in the payment layer. This paper quantifies this risk through a probabilistic analysis of classical double-spend scenarios for Proof-of-Work (PoW) and Proof-of-Stake (PoS) blockchains augmented with periodic checkpoints, which render the chain history prior to the latest checkpoint effectively irreversible. We develop attack models for both consensus mechanisms and derive explicit formulas for the attacker’s success probability as a function of the adversarial share, the spacing between checkpoints, and the number of confirmation blocks. On this basis, we compute the minimum confirmation depth needed to satisfy a predefined risk threshold. Numerical evaluation using the derived expressions shows that checkpoints consistently reduce double-spend probability relative to checkpoint-free baselines; in the evaluated settings, the reduction reaches up to 44% and becomes more pronounced as the adversarial share increases. Finally, the analysis yields practical guidance for energy trading applications: accept a payment after the computed number of confirmations when it fits within a single checkpoint interval; otherwise, treat finality as reaching the next checkpoint.

A general approach to determining the parameters of a collateralized protocol is considered, along with the development of an appropriate mathematical framework that accounts for all major risks. The following tasks are addressed: all key factors that traditionally affect an asset’s price and the size of payouts during the position liquidation procedure are identified; risks are incorporated and their potential impact on the price is assessed; the statistical data that must be collected and processed to obtain numerical characteristics of these risks are specified; relevant statistical data are collected across various decentralized platforms and, based on them, a liquidation condition for a collateral position is formulated and justified; the LTV value is determined and substantiated; numerical results for LTV are obtained for different pairs of assets. Keywords: cryptoassets, DeFi-protocols, collateral protocols, loan-to-value (LTV), liquidation condition.

The paper investigates the issues of secure functioning of a two-level blockchain with a complex mixed consensus protocol — Proof-of-Work in the main blockchain (mainchain) and Proof-of-Stake in the secondary (sidechain). The principle of building such a blockchain is based on the Proof-of-Proof protocol, where a stable blockchain (mainchain) is used to ensure the stability of the sidechain, by referring the mainchain blocks to the sidechain blocks using special transactions. Such a structure allows for faster block generation in the sidechain and, accordingly, faster processing of transactions without reducing stability and without increasing the block size. In turn, such a two-level blockchain is of the greatest interest for the creation of a cascade system of state registers, which will be guaranteed to be protected against the substitution and forgery of documents. The main results of the work areexplicit analytical expressions for estimates of the probability of double spend attack on such a two-level blockchain, under the condition of an adversary in the sidechain and in the mainchain. The expressions obtained allow finding the number of confirmation blocks in the sidechain, which guarantees security against the attack with a probability no less than a preset value. Keywords: blockchain, mainchain, sidechain, cryptocurrencies, mining, Proof-of-Proof consensus protocol, double spend attack.