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I am learning about how Bitcoin works under the hood. I am unable to understand why consensus is needed if digital signature is already being used. By my understanding, consensus is used by nodes to achieve same state of the blockchain, where same state means the chain with no tampering(theoretically). But doesn't digital signature achieve the same thing? What is the need of achieving same state if the transactions which are not authentic are already being declared invalid.

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    there bitcoin stack exchange, and this is answered on wikipedia, and this is answered in the original 10 page bitcoin whitepaper. – Z.T. May 11 '19 at 19:39

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There are two thigs you need to achieve with cryptocurrency. You must ensure that only the owner of the money can spend it. That is achieved by his signature. The owner has to sign that he is transfering the money. You can obviously trust the owner not to sign transfers he does not want.

The second thing you need to ensure is that the money is only spent once! Make sure the owner does not sign two transfers of the same currency. You can't trust the owner here as he would love to have the cake and eat it too. Spend the same money twice and get more things. So the owners signature is worthless here, as the owner can not be trusted. That is where consensus comes in. Consensus of which of the two transactions should actually happen and only allow one of them.

In other words, the owner can sign 100 orders to transfer the money to 100 different people, but the bitcoin miners will only pick and include one of them in the blockchain. So only one of the 100 people will get the money.

Peter Harmann
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