Bitcoin mathematical puzzle

Usually in maths — and in life — when you want to prove a statement is true you need to give evidence to back up your claim. With a zero-knowledge proof, however, it is possible to prove a statement is true without revealing any supporting information. For example, just say I have solved an extremely hard Sudoku, and I want to prove to you that I have solved it.

A zero-knowledge proof will convince you that I have solved it without revealing anything at all about my solution. You are in good company. When the zero-knowledge proof first appeared in the s, the wider mathematical community was agog. The whole idea seemed bizarre and counter-intuitive. Ultimately, however, it represented a conceptual revolution in how mathematicians think about proof, and it has found fantastic applications in cryptocurrencies and crypto-systems, where users want to establish trust but keep crucial information confidential.

The stolen paper clip You work in an office of people. One day your favourite paper clip is stolen. You have a pretty good idea of who did it. Your colleague Annabel tells you that she also has a pretty good idea. You want to check with Annabel that you both suspect the same person, but neither of you are willing to identify your suspect just in case you are thinking of different people.

Because of office politics, no one wants to point fingers. Think of a method that allows you and Annabel to check whether your suspect and her suspect are the same person, without either of you revealing any information about your suspects. What the puzzle is asking is this: can you and Annabel agree on a way to compare your information without giving anything away? In the latter case, you will not have leaked any information to Annabel, nor will she have leaked anything to you.

I agree, it sounds impossible! But today is different since I am asking you to contort your brain in a way you have probably never contorted it before. And there are many solutions, each with strengths and weaknesses. Miners try to "guess" the nonce; only way a miner can find the number is by brute-forcing, i. Now, the transaction must be transmitted to the bitcoin network where it will become part of the distributed ledger the blockchain.

We now elaborate hashing in sketchy terms. As of now, the hash of latest block in the blockchain, Block is: afe84da5f0a5aae85f68b1b5 Note the bunch of zero's at the beginning. This difficulty level changes based on how much time, on average, is required to find a block. As the network combined mining capacity increases, difficulty too increases and vice versa. The below figure illustrates block formation: Image credit: Mastering Bitcoin We now take a look at hashes of pending transactions: 2cf24dba5fb0a30e26e83b2ac5b9e29e1be5c1faeb -transaction 1 91efedce94a7f52cd5f48f5ee1afcf0ab -transaction 2 cc2f31fbaea2a9e6ef10dce21ed95e98bdac9c4eea16fe4 -transaction Now miner creates a transaction root aka Merkle root which essentially is hash of all transaction combined.

The process is illustrated below: Image credit: Wikipedia Block 's Merkle root is: d29b40ec75fefba9d5a6a20edf9a0be2aa2a Suppose that we'd like to find the next block Block So we take hash of Block , transaction root of all the transactions waiting to be included in Block , timestamp we'll ignore in illustration. We have scroll right to see entire line : afe84da5f0a5aae85f68b1bea57aadeef1dcffd84f0caaf2afacfce33 Now concatenate 1 to the above string shortened it for the sake of readability : ea57aadeef Run it through SA, and see if it meets difficulty requirement, i.

Try 2, 3, 4, and so on until you find a number that satisfies the difficulty condition. I'm not how computers miners approach this random number guessing. This random number in Block is and was found by F2Pool. Guessing the number is solving the complicated math problem This nonce is not unique,i.

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