News
Kyoto University Reveals Mathematical Formula for Blockchain Trilemma
In blockchain development, there has been a long-standing belief that only two of the following three elements can be achieved simultaneously: scalability, security, and decentralization. This concept, known as the blockchain trilemma, has driven much of the industry’s development. However, until now, there has been no precise mathematical expression to represent this rule.
Researchers at Kyoto University have addressed this gap by discovering a mathematical formula for the blockchain trilemma, specifically for Proof of Work blockchains like Bitcoin. According to their findings, the product of scalability, security, and decentralization in these systems is equal to one.
Implications for Blockchain Development
Team leader Kazuyuki Shudo of Kyoto University’s Academic Center for Computing and Media Studies explained that this formula provides insights into how to improve scalability without compromising security or decentralization. He identified two potential methods: reducing the size of a block or set of transactions, and increasing the speed at which blocks are sent and received.
Shudo’s team analyzed existing methods for improving scalability. One example is Bitcoin’s Compact Block Relay, which reduces the size of transactions within a block. The formula also highlights that increasing one of the three terms inherently decreases the others, thus preventing the simultaneous achievement of scalability, security, and decentralization.
Historical context and further information
The blockchain trilemma was first proposed ambiguously by Vitalik Buterin, co-founder of Ethereum. Since then, this proposal has led to various interpretations and numerous proposed solutions, although none have definitively solved the problem. Shudo noted that while many techniques for improving scalability have been suggested, it is still unclear to what extent these techniques compromise security and decentralization.
In a previous study focused on blockchain security, Shudo’s team identified another formula that represents a security index F, which is related to the probability of a fork occurrence. This formula also included scalability, measured in transactions per second. This previous work inspired the team to develop the trilemma formula by transforming the previous security formula.
Mathematical foundations and future directions
The team found that regulating the time spent on Internet communication, denoted as P, affects the Herfindahl-Hirschman Index (HHI) of block generation hash rates, which in turn affects the decentralization of block building power. The HHI is used to measure market concentration and is applied here to assess decentralization within the blockchain industry.
While the researchers focused on Proof of Work, Taishi Nakai of Kyoto University’s Graduate School of Informatics highlighted the growing importance of Ethereum’s recent transition to Proof of Stake. Nakai said that this transition inspired the team to look for similar formulas that could be applied to Proof of Stake systems.
Conclusion and wider implications
The discovery of a mathematical expression for the blockchain trilemma by researchers at Kyoto University represents a significant milestone in the field of blockchain development. This formula not only validates the concept of the trilemma, but also provides a structured framework for future innovations aimed at balancing scalability, security, and decentralization.
The team’s work opens new avenues to explore how blockchain systems can evolve while maintaining an optimal balance of these three critical elements. As the blockchain industry continues to grow and mature, this fundamental research will be critical to guiding its development and ensuring the robustness and efficiency of future blockchain applications.