How proof of work and mining work

Proof of work is a rule that a block counts only if somebody did a lot of trying to make it. Finding the answer is slow, but checking it takes one hash.

This is what makes an old block costly to change. You will mine a block yourself and see how the work grows.

A block's hash depends on its contents. To get a different hash without changing the records, the block carries one more field, the nonce. It is just a whole number.

Mining means trying nonce 0, then 1, then 2, and so on. After each try you work out the hash. You stop when it starts with enough zeros.

docker exec jupyter python3 steps/mine.py

A hash is written in hexadecimal. Each hex digit has 16 possible values, and only one of them is a zero. So one chance in 16 gives a first zero, and one in 256 gives two zeros.

Each extra zero multiplies the average work by 16. Real tries vary. The lab needed 835 for two zeros where the average is 256, which is luck, not a fault.

import hashlib

def mine(data, difficulty):
    nonce = 0
    while True:
        text = data + str(nonce)
        digest = hashlib.sha256(text.encode()).hexdigest()
        if digest.startswith("0" * difficulty):
            return nonce, digest
        nonce = nonce + 1

nonce, digest = mine("Asha pays Ben 5", 3)
print("nonce:", nonce)
print("tries:", nonce + 1)
print("hash starts:", digest[:8])
# Change 3 to 2 and run again, then to 4.

Finding a good nonce took thousands of tries. Checking one takes a single hash: work the hash out from the block and the nonce, then look at its first characters.

This difference is the whole idea. Mining is slow for the one who adds a block. Checking is quick for everybody else, so everybody can afford to verify.

import hashlib

def good(data, nonce, difficulty):
    digest = hashlib.sha256((data + str(nonce)).encode()).hexdigest()
    return digest.startswith("0" * difficulty)

print(good("Asha pays Ben 5", 1864, 3))
print(good("Asha pays Ben 5", 1865, 3))
# One hash decides each answer. Try nonce 1863.

When a block is edited, its hash changes, so it no longer starts with zeros. You must mine it again. That also changes its hash, which breaks the link in the next block, so that one must be mined again too.

A block that is ten places back means ten blocks to mine again, while everybody else keeps adding new ones.