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0x1000000000000000000000000000000000000000000000000000000000000000. We call this threshold the target and the goal is to find a hash that is numerically less than the target. If we decrease the target, the task of finding a hash that is less than the target becomes more and more difficult. To give a simple analogy, imagine a game where players throw a pair of dice repeatedly, trying to throw less than a specified target. In the first round, the target is 12. Unless you throw double-six, you win. In the next round the target is 11. Players must throw 10 or less to win, again an easy task. Let’s say a few rounds later the target is down to 5. Now, more than half the dice throws will add up to more than 5 and therefore be invalid. It takes exponentially more dice throws to win, the lower the target gets. Eventually, when the target is 2 (the minimum possible), only one throw out of every 36, or 2% of them will produce a winning result. In the hashing example above, the winning “nonce” is 13 and this result can be confirmed by anyone independently. Anyone can add the number 13 as a suffix to the phrase “I am Satoshi Nakamoto” and compute the hash, verifying that it is less than the target. The successful result is also proof-of-work, as it proves we did the work to find that nonce. While it only takes one hash computation to verify, it took us 13 hash compu‐ tations to find a nonce that worked. If we had a lower target (higher difficulty) it would take many more hash computations to find a suitable nonce, but only one hash com‐ putation for anyone to verify. Furthermore, by knowing the target, anyone can estimate the difficulty using statistics and therefore know how much work was needed to find such a nonce. Bitcoin’s Proof-of-Work is very similar to the problem above. The miner constructs a candidate block filled with transactions. Next, the miner calculates the hash of this block’s header and see if it is smaller than the current target. If the hash is not less than the target, the miner will modify the nonce (usually just incrementing it by one) and try again. At the current difficulty in the bitcoin network, miners have to try quadrillions of times before finding a nonce that results in a low enough block header hash. A very simplified Proof-of-Work algorithm is implemented in Python here: Example 8-11. Simplified Proof-Of-Work Implementation #!/usr/bin/env python # example of proof-of-work algorithm import hashlib import time max_nonce = 2 ** 32 # 4 billion def proof_of_work(header, difficulty_bits): # calculate the difficulty target target = 2 ** (256-difficulty_bits) Mining the Block | 195PDF Image | Mastering Bitcoin
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