With the growing adoption of blockchain interoperability, cross-chain token transfers have become a critical aspect of decentralized finance and blockchain ecosystems. Polkadot, a blockchain network designed to facilitate interoperability, employs a unique cross-chain message passing (XCMP) protocol to enable token transfers among the relay chain and parachains. However, token transfer time within this system, particularly the relationship between its average and standard deviation and underlying factors, has not been extensively investigated. In this paper, we conduct an empirical analysis of token transfer times in Polkadot and Kusama mainnets using ParaSpell to measure XCMP delays across various cross-chain messaging mechanisms, including Downward and Upward Message Passings and Horizontal Relay-routed Message Passing. Our findings reveal a significant correlation between the mean and standard deviation of token transfer times, suggesting the presence of fundamental systemic delays. Furthermore, we propose a theoretical model based on validator-to-validator broadcast time, which appears to be the dominant factor influencing transfer latency. Index Terms-Cross-chain message passing, Polkadot, Token transfer time, Experiment, Theoretical analysis © 2025 IEEE.

In recent years, blockchain technology, which enables transactions to be distributed across multiple computers and managed in an immutable and secure manner, has garnered significant attention. Within blockchain networks, consensus mechanisms ensure the consistent sharing of ledger information when new blocks are added. In consortium blockchains, typically employed by a limited number of organizations, the Practical Byzantine Fault Tolerance (PBFT) protocol is widely used. PBFT is designed to tolerate Byzantine nodes-nodes that may be compromised or malfunctioning-by achieving consensus as long as fewer than one-third of the total nodes are Byzantine. However, PBFT relies on the assumption that at least two-thirds of the nodes behave correctly, making consensus challenging when the number of malicious nodes exceeds this threshold. Previous research has explored the use of clustering to enhance throughput, but these methods are static and unsuited to dynamic environments. Moreover, clustering techniques aimed at bolstering Byzantine resistance remain underexplored. This paper presents a novel method for constructing clusters within a blockchain network to resist Byzantine nodes. By employing clustering, we estimate the locations of potential attackers, thereby enhancing the system's resilience to Byzantine faults. © 2025 IEEE.

Size-Synchrony Antagonism (SSA) is a fundamental principle in Web3 systems proposed by JAM Gray Paper stating that as the size of an information system expands, the consistency of the system deteriorates due to physical constraints on the propagation speed of information, such as network bandwidth and the speed of light. However, the paper does not provide precise definitions of "size"and "synchrony,"nor does it present empirical validation based on actual Web3 system data. In this paper, we define "size"as the number of geographically distributed BlockChain (BC) validator nodes on a global scale and "synchrony"as BC convergence time or finality time. We measured these parameters across various Proof-Of-Stake BC systems, including Ethereum 2.0, Polygon, Cosmos Hub, Polkadot, and Kusama. We also formulated a theoretical model to describe SSA. Analysis of the measured data revealed properties consistent with SSA, and these findings aligned well with the theoretical model. © 2025 IEEE.

Some blockchain networks employ a distributed consensus algorithm featuring Byzantine fault tolerance. Notably, certain public chains, such as Cosmos and Tezos, which operate on a proof-of-stake mechanism, have adopted this algorithm. While it is commonly assumed that these blockchains maintain a nearly constant block creation time, empirical analysis reveals fluctuations in this interval; this phenomenon has received limited attention. In this paper, we propose a mathematical model to account for the processes of block propagation and validation within Byzantine fault-tolerant consensus blockchains, aiming to theoretically analyze the probability distribution of block time. First, we propose stochastic processes governing the broadcasting communications among validator nodes. Consequently, we theoretically demonstrate that the probability distribution of broadcast time among validator nodes adheres to the Gumbel distribution. This finding indicates that the distribution of block time typically arises from convolving multiple Gumbel distributions. Additionally, we derive an approximate formula for the block time distribution suitable for data analysis purposes. By fitting this approximation to real-world block time data, we demonstrate the consistent estimation of block time distribution parameters, © 2024 IEEE.