checksum mainly protects against transmission errors.). To create this bitcoin im umlauf block, a miner uses a Merkle tree of hashes, which refer the individual transactions included in this block, the previous block, and some other data. I'm not sure if we could in fact include bogus transactions this way (or by other SHA-2 breaks means) in our Merkle tree - I think the receivers of a blocks should still check if its transactions have actually a valid signature. So, how could we cheat here?
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In one of the blocks consisting this chain. (But this would be off-topic here.). The Block chain, for a transaction to be deemed valid, it has to be included in the block chain,.g. By finding a faster way to get the right nonce than trying many of them, we can generate the blocks faster than everyone else. This can be reached by manipulating one part of the block, the nonce value, calculating the hash, and repeating until one is lucky hitting the right nonce to make this block valid. Accounts/Transactions, to move money from one account to another, you need to collect some data (the previous transaction(s) which got you the money, the target account, the amount you want to transfer) and sign them, using the private key which belongs to your account. The (public) addresses of the accounts are given as address version hash checksum, where version 0 (one byte hash and checksum first 4 bytes of SHA-256(SHA-256(version hash). There are several uses of cryptographic algorithms in the protocol.
It is much easier for now to use a trojan or such to steal the actual private key of the owner. This tree uses SHA-256, too. If there are several valid blocks running around (which are not descendants of each other "good" miners will usually build on the one with the longest chain. If I can fake your signature, I can also steal your money. For now, no such break of SHA-2 is known. Having a monopole, we can also effectively decide which transactions to include and which ones not (this could be a denial-of-service for competitors who want to transmit money). This would mean that we will get all of the mined coins, at first. If I can create a fitting private key for your public key, this is also possible.
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