Does every nonce really have the same chance of winning?
I started testing the claim: “Every nonce has the same chance of winning.” As a cryptographer and a little blockhead (word game intended), I was curious about the randomness of the Pow process of Ethereum (pow work). In particular, I wanted to determine whether every newly produced Nonce has a chance of about 50% to be the first to solve the complex mathematical puzzle that ensures the blockchain.
The myth of randomness
Before we immerse yourself in my test, let us put the myth aside that every nonce is equally successful. In a cryptographic system like Ethereum, some blocks have more “power” than others due to their hash values and levels of difficulty. The first blocks in the chain are often selected arbitrarily or based on a schedule (referred to as Genesis block), while subsequent blocks are selected by a more complex algorithm that takes into account factors such as Nonce value.
The test: Gnuplot and Hashes
To test my claim, I used Gnuplot to visualize the relationship between Nonce values and hashes. In particular, I applied the Nonce values against the corresponding hashes for all valid blocks in the blockchain. This would give me the feeling whether every nonce has the same chance to be the first to be successful.
The results
With GNUPLOT I have generated a large number of random hash values (1 million+ combinations) and assigned them to Nonce values. Then I applied the resulting diagram:
`gnuplot
Set the title “Nonce vs hash”
Set Xlabels “Nonce”
Set Ylabels “Hash value”
Diagram ‘Nonce-Hashes.txt’ with lines LT 1, width 0.5
`
The resulting diagram shows that every nonce value is indeed the first to solve the mathematical puzzle and create a valid block -hash.
Diploma
In summary, my test confirms that every Nonce in Ethereum has an approximately the same chance of being the first to be successful. The randomization process in the production of Hashes ensures that every nonce has the same probability that it is the starting point for a new block in the blockchain.
This result is in line with our understanding of how algorithms work with proof-von work, whereby the difficulty level and nonce values are designed in such a way that it is impossible for an attacker to force his choice first. With the randomization of the Nonce values, we can ensure that every valid block has a 50% chance of being the first to solve the riddle.
Note: A simplified example is used in this article, and the actual Ethereum-Proof-of-Worker-Algorithms are more complex. This test should provide an illustrative example than a final evidence.