The mathematics behind the consensus mechanism of Ethereum: Dissolve the secret of 6 confirmations
Ethereum, one of the largest and most successful decentralized applications (DAPPS) in the blockchain, has been in operation since 2015. In essence, Ethereum is a consensus algorithm (proof-of work) miners to solve complex mathematical problems. But what makes this specific number of confirmations – six – so safe? In this article, we will deal with the mathematical foundations of the consensus mechanism of Ethereum and examine the reasons for this apparently arbitrary choice.
The mathematical framework: hash functions
In order to understand why 6 is viewed an appropriate number of confirmations, it is important to capture the basic mathematics behind Ethereum’s Pow consensus. The process includes the creation of a digital fingerprint, which is referred to as “hash” for each transaction. This hash serves as a clear identifier for this specific transaction.
The main inspection lies in the way this hashes is generated and verified. In Ethereum, each block contains a list of unconfirmed transactions, which is then combined using a combination of cryptographic techniques to a single hash value. This process is repeated several times in each block until the total hash length of the block exceeds a certain threshold (referred to as the “goal -Hash”).
The difficulty of achieving this goal is to solve a complex mathematical problem: to find a number of numbers that are referred to as “nonce” so that they meet the following equation:
H (n) = h (n + 1) ^ r + s
H (n) The hash value of the current block is, H (n+1) The target hash value, r ands are parameters that are defined by the miners (more on this below ) and `n ‘is the number of unconfirmed transactions in the block.
The relationship between the number of confirmations and difficulties
After understood the mathematical framework behind the Ethereum Pow consensus, let us examine how the number of confirmations relates to the level of difficulty. A higher number of confirmations are easier to solve more computing power from mining workers in order to solve the complex mathematical problems.
If the total number of transactions increases (i.e. further blocks are broken down), the probability that at least one miner will find a solution for the above equation within a reasonable time frame. This is known as a “goal -Hash” or “difficulty level”. If you increase the number of confirmations, this essentially means driving the level of difficulty higher.
Why 6? The answer is in the historical context
Mathematical explanations are essential, although it does not always explain for historical context and practical considerations. It is possible that the selection of six as a threshold is simply a question of the convention or the design decision by the Ethereum development team.
A theory suggests that number seven was selected due to its association with perfection (e.g. in mathematics). Another idea suggests that it is the seven fatal sins, a concept used by some old philosophers. However, these theories are unfounded and have no concrete evidence.
Conclusion: 6 confirmations, but why?
Although mathematical explanations can give an insight into the consensus mechanism of Ethereum, they do not completely explain why six are viewed as the optimal number of confirmations. The answer lies in a combination of a historical context, practical considerations and design decisions of the development team.
For securing the future and scalability, it is important to compensate for computing power with difficulty. While higher numbers can offer greater security, increasing the too high level of difficulty Ethereum may be less suitable for certain applications.
