Proof of Work in Go

This is a simple implementation of a proof of work algorithm in Go.

The algorithm implemented solves the following problem:

Given a difficulty level y where y is the number of leading zeros bits in the resulting hash, find a nonce x such that the hash of the nonce concatenated with the input block has y leading zeros.

As y grows the probability of finding x by picking a random nonce decreases exponentially on every independent try.

To estimate the number of tries needed to find a valid nonce, we start by computing the probability of finding a valid nonce on an independent try:

The probability is equal to the number of valid hashes divided by the total number of possible hashes.

$$p = \frac{2^{n-y}}{2^n} = \frac{1}{2^y}$$

The cumulative probability $\delta$ of finding the nonce after $k$ tries is given by the formula¹:

$$\delta = 1 - (1 - p)^k$$

By solving for $k$ we get:

$$k = \lceil\frac{\log(1 - \delta)}{\log(1 - p)}\rceil$$

Which we can easily put into a spreadsheet and compute some numbers:

So for a difficulty level of 20 leading zeros, the probability of finding a valid nonce is 80% after 1.687.618 tries.