Andrey Seoev

Yash Madhwal, Andrey Seoev, Raffaele Della Pietra et al.

ECDSA signatures form the bedrock of blockchain transaction authentication, yet their security critically depends on proper nonce generation. We uncover a critical vulnerability in the Polygon MEV ecosystem: systematic nonce reuse that enables complete private key recovery. Analyzing on-chain data reveals that searchers, driven by the need for sub-second response times in sealed-bid auctions, employ predictable nonce patterns. These patterns create linear relationships between signatures, allowing passive attackers to recover private keys using elementary algebra. We provide a compact linear-system formulation for such attacks, including the dangerous case of cross-wallet nonce collisions, and present concrete evidence of exploitable patterns on Polygon. Our findings demonstrate how protocol-induced latency pressures can lead to catastrophic cryptographic failures in production blockchain systems, where a single implementation error compromises multiple accounts simultaneously.

Andrey Voronin, Roman Vlasov, Vladimir Gorgadze et al.

Constant Product Market Makers use fees that are typically fixed proportions of trade size. When these fees are automatically reinvested into the pool, as in Uniswap~V2 and some designs of Uniswap V4, the final state after a trade can depend on how the trade is split into smaller transactions. This path dependence complicates the risk assessment for liquidity providers and affects composability guarantees. We characterize the functional class of fee structures that ensure path independence: the combined fee factor must depend only on the current pool invariant k=xy. For this class, we derive a system of ordinary differential equations governing pool dynamics and obtain a closed-form integral exchange formula. Within this class, we construct a parametric family of fee functions that achieve zero Impermanent Loss for a given initial pool state, and prove that no universal fee function can eliminate Impermanent Loss for all initial states simultaneously. We analyze implications for arbitrage windows and slippage, and validate our theory through controlled simulations. Our framework provides protocol designers with a principled approach to fee optimization that aligns liquidity provider and trader incentives while preserving composability.

Ignat Melnikov, Roman Vlasov, Vladimir Gorgadze et al.

Decentralized Finance (DeFi) is a rapidly evolving segment of blockchain technology that enables a transformative approach to financial services through Web3 applications. By leveraging smart contracts, DeFi allows developers to build flexible and innovative financial instruments. Among the most prominent DeFi primitives by liquidity are decentralized exchange~(DEX) swap protocols~(such as Uniswap, Curve, and Balancer) that facilitate fast token-to-token exchanges. However, new exchange mechanisms also introduce new market inefficiencies that can be systematically exploited by arbitrageurs. This paper focuses on swap protocols based on the Automated Market Maker~(AMM), where the product of reserves is preserved as an invariant. We analyze the interaction between arbitrageurs and AMM liquidity pools and develop a mathematical model grounded in empirical pool configurations. Using this model, we derive bounds on the joint revenue of liquidity providers~(LPs) and arbitrageurs, propose a method to estimate the expected number of blocks until the occurrence of Impermanent Loss~(IL), and obtain a lower bound on the pool fee required to achieve a fixed target probability of staying in the Impermanent Gain (IG) zone within a block. The proposed framework extends existing LP risk-assessment methodologies by quantifying symbiotic profitability zones, providing a principled basis for fee selection that aligns LP-arbitrageur incentives and enhances market stability.