https://ift.tt/3HOHB2n exactly does Proof-Of-Work help if all transactions are signed by the payers.

If every transaction is signed by the payer, how exactly does the proof-of-work help? No one else (not even the central authority) will be able to modify the transactions into new valid ones, because they don’t have the payers’ secret keys. I don’t get in what scenario the proof of work helps.

The most a central authority can do, is delete the entire database, is that all that proof-of-work protects against?

Thanks in advance, I came here from the [3Blue1Brown video](https://youtu.be/bBC-nXj3Ng4)

Edit: Thank you, I understood now, that the double spending problem is being solved by Proof-Of-Work. To double spend, the person can use the same input to pay two different people (and can sign both transactions).

If I make a transaction to pay for a car, with input transaction x, the car dealership is wise to wait for at least 3 blocks to be mined after the block with our transaction on it (call it B1). He waits, there are 3 blocks AFTER the transaction where I pay the dealership. Now, let’s say I want my money back. How would I do that? I would make my own version of a blockchain where the dealership transaction never happened. I would broadcast another transaction, taking the same input x, and paying it to another one of my accounts. When I publish this transaction, all other miners will reject the transaction and not include it in a block, because the longest chains till now indicate that input x has been spent. What I will have to do, is make a new block B2, which is the same as B1, but does not contain the transaction where I pay the dealership. I will have to work to validate that and every subsequent block. SInce I am the only one doing this work, and no one else is, I am unlikely to outpace everyone else, specially for long periods of time.

As the blockchain gets longer, it gets more and more difficult for me to pretend (and convince the world) that a previous transaction did not happen.

The proof of work is to prevent fraud by a PAYER making a double spend. I can bribe bank officials, and tell them to allow me to double spend. But, I cannot bribe the blockchain.

Also, the distributed blockchain cannot deny service/censor transactions, which a central authority can do easily.

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