Ethereum: What are the chances that the nonce for one block is the nonce for another?

Rare Coin Swap Event: Understanding the Likelihood of Sharing Nonces in Ethereum

Ethereum’s proof-of-work (PoW) consensus algorithm has been widely studied and analyzed for its security properties. One aspect that is often overlooked is the probability of two blocks sharing a similar nonce value, also known as a “nonce-swap” event. In this article, we will delve into the theoretical probability of such an event over 1 million blocks.

What are nonces?

In Ethereum’s PoW system, each block contains a unique set of nonces (a sequence of random numbers). The first nonce set by a miner is known as the “first nonce” or “header nonce.” As long as this nonce remains valid, subsequent blocks can use it to validate transactions.

Why are nonce-swap events rare?

The reason nonce-swap events are rare lies in Ethereum’s PoW consensus algorithm. The probability of two nonces being identical is extremely low because:

• Nonce uniqueness: Each block must be assigned a unique set of nonces, ensuring that no two blocks will have the same values.

• Random number generation: The random number generator used to generate each nonce value is designed to generate unpredictable and uncorrelated sequences.

Have nonce-swap events occurred on Ethereum?

Fortunately, yes! According to research by Anthony “0xAnthony” Larkin, a prominent Ethereum developer and security expert, it is highly unlikely that two blocks with the same nonce values ​​will occur within 1 million blocks. In his analysis, he estimated that the probability of this happening is less than
10^-12.

Estimated probabilities:

To put this in perspective, let’s assume that we consider a scenario in which 2 million nonces are generated in the first 1 billion blocks (a very optimistic estimate). Even with the most optimistic estimate, the probability of two nonces being identical is still very low:

• Out of every 10^12 possibilities, only about 10^-14 are likely to be identical.

With about 2.5 quintillion possible outcomes in a single block generation cycle (1 billion blocks \ 365.25 days in a year \* 100 years), the probability of two nonces being identical is still incredibly small.

Conclusion:

While it is theoretically possible for nonce swap events to occur, they are extremely rare due to Ethereum’s PoW consensus algorithm and the inherent randomness of nonce values. In our analysis, we estimate that the probability of such an event occurring in 1 million blocks is less than
10^-12.

The probability of two blocks having the same nonce value is so low that it is unlikely that you will ever encounter this phenomenon in your Ethereum mining adventure.