The Blockchain Trilemma. Credit: KyodoU/Kazuko Shuto
In blockchain development, there is a rule of thumb that only two of the following can be effective at the same time: scalability, security, and decentralization. However, the mathematical expression of that rule is still under development.
Now, a research team from Kyoto University has found a mathematical expression of the blockchain trilemma: for proof-of-work-based blockchains, including Bitcoin, the product of the three terms scalability, security, and decentralization is one.
“By observing the trilemma formula, we can see how to improve scalability without sacrificing security or decentralization,” said Kazuyuki Shuto, team leader at Kyoto University’s Academic Computing and Media Center.
There are two such methods:
1) Reduce the size of the block or transaction set.
2) Faster sending and receiving of blocks
Scalability may also be improved by analyzing existing methods, for example Bitcoin’s Compact Block Relay, which reduces the size of transactions in a block.
Additionally, increasing any one condition reduces the others, making it impossible for a blockchain to achieve all three simultaneously.
Vitalik Buterin, co-founder of the public blockchain platform Ethereum, has argued that the trilemma is a nebulous concept that has spawned a variety of interpretations. Many developers have put forward ideas to solve the trilemma, but none have been able to prove it yet.
“Many technologies have been proposed to improve scalability, but it is unclear to what extent security and decentralization are sacrificed,” Shuto points out.
In their previous work on blockchain security, the team found another formula that precisely represents the security metric F, or the probability of a fork occurring. They realized that the formula also reflected scalability (number of transactions per second) as well as security. From this inspiration, the team transformed their previous security formula to derive the trilemma formula:
By adjusting the time it takes to communicate over the internet, P influences the Herfindahl-Hirschman Index (HHI) of the block production hash rate, which represents block building power. The HHI represents the market decentralization of an industry for a given company.
“Emphasis on the proof of work adopted by Bitcoin does not diminish the importance of Ethereum’s recent switch to proof of stake. This switch was the catalyst for us to find the proof of stake formula,” concludes Nakai Hiroshi of Kyoto University’s Graduate School of Informatics.
This paper is published in IEEE Access.
Further information: Taishi Nakai et al., “Formulating the Trilemma in Proof of Work Blockchain,” IEEE Access (2024). DOI: 10.1109/ACCESS.2024.3410025
Provided by Kyoto University
Source: Researchers Discover Mathematical Expression of the “Blockchain Trilemma” (July 22, 2024) Retrieved July 22, 2024 from https://techxplore.com/news/2024-07-mathematical-blockchain-trilemma.html
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