Blockchain developers often face the so-called “trillema“: you can simultaneously achieve only two of the three characteristics – scalability, safety, and decentralization. Until recently, the exact mathematical formula for describing the trillema remained unknown.
A team of researchers from Kyoto University has found a mathematical expression for the trillema of the blockchain. According to the formula for blockchains based on Proof of Work (proof of work), including Bitcoin, a work of three parameters – scalability, security, and decentralization – equal to 1.
“Observing the formula of the trilems, you can see ways to improve scalability without prejudice to security or decentralization,” explains the head of the Kadzuyuki team of Caudo from the Academic Center for Computer and Media Research of Kyoto University.
Researchers identified two main methods:
- Reducing the size of the block or set of transactions.
- Acceleration of the process of sending and obtaining blocks.
Analysis of existing methods can also help improve scalability. For example, Compact Block Relay in Bitcoin reduces the size of transactions in the block.
However, an increase in one of the parameters inevitably leads to a decrease in others, which makes it impossible to simultaneously achieve all three characteristics.
The amorphous dilemma proposed by the co -founder of the Ethereum platform Vitalik Buterin caused many interpretations. Many developers have proposed their ideas to solve the problem, but not one of them has yet been proven in practice.
“Many also proposed methods for improving scalability, but the degree in which they sacrificed security and decentralization remained unclear,” said Sudo.
In a previous blockchain security study, the team discovered a formula representing the security index F, that is, the probability of fork (branching). They noticed that in addition to security, scalability (transactions per second) is also taken into account in the formula. This find inspired the command to output the formulas of the Trinity dilemma by transforming the previous security formula.
The setting of the time spent on the transfer of data via the Internet (P) affects the Herfindal-Hirschman (HHI) Herfindal index, which determine the power of the block construction. HHI is a level of market decentralization for selected companies.
“Our attention to Proof of Work, adopted in Bitcoin, does not diminish the