"Once you download and run the Bitcoin client software, it connects over the Internet to the decentralized network of all Bitcoin users and also generates a pair of unique, mathematically linked keys, which you'll need to exchange bitcoins with any other client. One key is private and kept hidden on your computer. The other is public and a version of it dubbed a Bitcoin address is given to other people so they can send you bitcoins. Crucially, it is practically impossible—even with the most powerful supercomputer—to work out someone's private key from their public key. This prevents anyone from impersonating you. Your public and private keys are stored in a file that can be transferred to another computer, for example if you upgrade."
http://www.technologyreview.com/computing/37619/?p1=A1&a=f
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