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I am new to Bitcoin and this question is based on 3 assumptions that may be incorrect.
Assumption 1: If I understand correctly, the Bitcoin address is generated algorithmically independent of the network, so I should be able to create a public address and private key offline correct?
Assumption 2: I can receive funds through the network using my public address without ever having to make my private key known to anyone correct?
Assumption 3: Now when it's time to spend my funds, offline I can create a Bitcoin transaction authorizing the transfer from my address to another location and sign it with my private key entirely offline. I can then transfer that transaction to a separate computer with internet access and then publish that transaction to the Bitcoin network to be mined/verified in the blockchain?
Conclusion: If all 3 points are true then I should be able to keep my private key from the internet for it's entire life correct?
3Yep, only nitpick is on assumption 3, the transaction is not just "pay from my address to other address(es)", but "pay from transaction(s) xyz to other address(es)". What this means in practice is that you'll get the transaction ready on an online computer, sign it on the offline computer, then publish it from the online computer. – Tim S. – 2015-01-14T18:02:05.480