There’s a long-held belief in blockchain development that only two of the three elements — scalability, security, and decentralization — can be achieved simultaneously. This concept, known as the blockchain trilemma, has guided much of the industry’s development. However, until now, there has been no precise mathematical expression for this rule.
Researchers from Kyoto University have addressed this gap by discovering a mathematical formula for the blockchain trilemma that is specific to proof-of-work-based blockchains like Bitcoin. Their findings show that the product of scalability, security, and decentralization in these systems is one.
Impact on blockchain development
Kazuyuki Shuto, team leader at Kyoto University’s Academic Center for Computing and Media Studies, explained that the formula offers insight into how to improve scalability without compromising security or decentralization. He cited two ways to do this: reducing the size of blocks or transaction sets, and increasing the speed at which blocks are sent and received.
Shudow’s team analyzed existing methods to increase scalability, such as Bitcoin’s Compact Block Relay, which reduces the size of transactions in a block, and found that increasing one of the three terms in the formula necessarily reduces the others, making it impossible to simultaneously achieve scalability, security, and decentralization.
Historical Background and Further Insights
The blockchain trilemma was first vaguely proposed by Ethereum co-founder Vitalik Buterin. The proposition has since led to various interpretations and numerous proposed solutions, none of which have definitively resolved the issue. Shudow noted that while many methods have been proposed to improve scalability, it is unclear to what extent these methods compromise security and decentralization.
In previous work focused on blockchain security, Shudow’s team identified another formula for the security metric F, which is related to the probability of a fork occurring. This formula also includes scalability, measured in transactions per second. Inspired by this previous work, the team transformed their previous security formula to develop the trilemma formula:
Foundations of mathematics and future directions
The research team found that adjusting for the time it takes to communicate over the internet (denoted as P) affects the Herfindahl-Hirschman Index (HHI) of block-producing hash rate, which in turn impacts 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, Hiroshi Nakai of Kyoto University’s Graduate School of Informatics highlighted the growing importance of Ethereum’s recent transition to proof of stake, which he said prompted him to explore a similar formula that could be applied to proof of stake systems.
Conclusions and wider implications
The discovery of a mathematical expression of the blockchain trilemma by Kyoto University researchers marks a significant milestone in the field of blockchain development. The 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 up new avenues for exploring how blockchain systems can evolve while maintaining an optimal balance between these three key elements. As the blockchain industry continues to grow and mature, fundamental research like this will be critical in guiding its development and ensuring the robustness and efficiency of future blockchain applications.
