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Researchers Discover Mathematical Expression for ‘Blockchain Trilemma’
Blockchain trilemma. Credit: KyotoU/Kazuyuki Shudo
In blockchain development, there is a rule of thumb that only two of the following are valid at the same time: scalability, security, and decentralization. However, the mathematical expression of this rule was still a work in progress.
Now, a team of researchers from Kyoto University has discovered a mathematical expression for the blockchain trilemma. In the formula for Proof of Work blockchains, including Bitcoin, the product of the three terms (scalability, security, and decentralization) is 1.
“By looking at the trilemma formula, we can find ways to improve scalability without sacrificing security or decentralization,” says team leader Kazuyuki Shudo of KyotoU’s Academic Center for Computing and Media Studies.
Two of these methods include:
1) reduce the size of a block or set of transactions
2) send and receive blocks faster
Existing methods can also improve scalability. For example, Bitcoin’s Compact Block Relay reduces the size of transactions in a block.
Furthermore, increasing one of the terms decreases the others, resulting in the blockchain failing to achieve all three requirements at the same time.
The ambiguous statement of the trilemma by Vitalik Buterin, co-founder of the public blockchain platform Ethereum, has generated various interpretations. Many developers have put forward their ideas to solve the trilemma but have yet to prove trial.
“Many have also proposed techniques to improve scalability, but it is still unclear to what extent they have sacrificed security and decentralization,” Shudo notes.
In a previous study on Blockchain safety, the team found another formula that rigorously represents a safety index F, namely the probability of occurrence of the fork. They noticed that not only the safety but also scalability—transactions per second—appear in the formula. The inspiration led the team to produce the trilemma formula by transforming the previous safety formula.
By regulating the time spent on communication on the Internet, P influences the Herfindahl-Hirschman Index, or HHI, of block generation hash rates, which refers to the block building power. The HHI represents the decentralization of the industry market for selected companies.
“The fact that we highlighted Bitcoin’s adoption of Proof of Work does not diminish the growing importance of Ethereum’s recent move to Proof of Stake, which inspired us to find formulas for realizing it,” concludes Taishi Nakai, also of KyotoU’s Graduate School of Informatics.
The paper is published in the newspaper IEEE Access.
More information:
Taishi Nakai et al, A formulation of the trilemma in Proof of Work blockchain, IEEE Access (2024). DOI: 10.1109/ACCESS.2024.3410025
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Kyoto University
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