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What prevents a miner's block from being accepted across the network if the hash checks out when miner forges transactions in the block?

For example, lets say I'm mining and I want to steal money from address A and put it into my address B. So I build a block with the A->B transaction along with some requested transactions. Now if I can compute a hash for the block before anyone else, and send off to peers in the network, how could they reject it? How would they know that's not a real transaction? Their NAT may have blocked that request or something.

I can't think of a good way of fixing this and I didn't find anything about in documentation. Any insight would be appreciated. Thanks.

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While questions about the cryptographic aspects of Bitcoin (or similar money sistems) are fine here, please note that there is a Bitcoin Stack Exchange where other types of question (such like your one) are better left. I'm not moving your question there since it is already duplicated there (and got a good response). –  Paŭlo Ebermann Feb 6 '13 at 20:33
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closed as off topic by Paŭlo Ebermann Feb 13 '13 at 9:18

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up vote 7 down vote accepted

All transactions which transfer money from address A need to be signed by the private key for address A which you don't have. The signature of course also covers the destination address B which stops you changing the transaction to redirect the money. The network does not pay attention to blocks which contain invalid signatures.

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