Mathematics behind the Ethereum consensus mechanism: Developing the secret of 6 confirmations
Ethereum, one of the greatest and successful decentralized applications (DAPPS) in blockchain, has been operating since 2015. Ethereum is an algorithm of evidence (Jed), which protects transactions in its network, requiring that it requires, a mining one to solve complex mathematical problems. But what makes this special number of confirmations – six – so safe? In this article, we delve into the mathematical foundations of the Ethereum consensus mechanism and examine the reasons for this seemingly arbitrary choice.
Mathematical framework: shortcut functions
To understand why 6 is considered the right number of confirmations, it is necessary to understand the basic mathematics behind the consensus of Ethereum. This process involves creating a digital fingerprint, known as a “abbreviation” for each transaction. This shortcut serves as a unique identifier of this particular transaction.
The key insight is how to generate and verify shortcuts. In Ethereum, each block contains a list of unconfirmed transactions, which are then combined into a single shortcut using a combination of cryptographic techniques. This process is repeated many times in each block, until the total length of the block of block exceeds the specific threshold (known as the “target abbreviation”).
The difficulty of achieving this target shortcut is to solve a complex mathematical problem: finding a set of numbers called “nonce”, so that they meet the following equation:
H (n) = h (n + 1) ^ r + s
where H (n) is the value of the current block of the block, H (n+1) `is the target shortcut value,ri sare parameters set by miners (more on this subject below) and N This is the number of unconfirmed transactions in the block.
Relationship between the number of confirmations and difficulties
Now, when we understood the mathematical framework behind the consensus of the Ethereum, let’s check how the number of confirmations refers to the level of difficulty. Simply put, a larger number of confirmations requires more computing power than miners to solve complex mathematical problems.
With the increase in the total number of transactions (i.e. apric blocks are extracted), as well as the likelihood that at least one miner will find a solution to the above equation in a reasonable time. This is known as a “target abbreviation” or “difficulty level”. Basically, increasing the number of confirmations means increasing the level of difficulty.
Why 6? The answer lies in a historical context
Although mathematical explanations are necessary, they do not always take into account the historical context and practical considerations. It is possible that choosing six as a threshold is simply a matter of the decision of the convention or design by the Ethereum programmers team.
One theory suggests that the number seven was chosen due to its relationship with perfection (e.g. in mathematics). Another idea suggests that it can be associated with seven fatal sins, a concept used by some ancient philosophers. However, these theories are unfounded and there is a lack of specific evidence.
Conclusion: 6 confirmations, but why?
To sum up, while mathematical explanations can provide insight into the Ethereum consensus mechanism, they do not fully explain why six are considered the optimal number of confirmations. The answer lies in combination of historical context, practical considerations and design decisions made by a team of programmers.
In the event of the future and scalability, it is necessary to balance the computing force with the level of difficulty. While higher numbers can ensure greater security, too high a level of difficulty can make Ethereum less suitable for some cases of use.
