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If I understand it correctly, I could generate a valid Bitcoin address (key pair) following this algorithm.
With an address generated in such a way I would be able to receive Bitcoin without ever having to install a Bitcoin client. Is this correct?
How could I follow this algorithm with common (command-line) tools, i.e. those typically available on (even older) GNU/Linux systems? (they don’t have to be installed by default, but they should be part of the distributor’s package archive)
Would there be any risks/problems using such a key instead of one generated by a Bitcoin client?
You should keep in mind that computers are not very good in creating randomness. Many applications that require a lot of randomness, get it from user input. Just make sure your private key is random enough :) You could use Vanitygen to create keypairs. – Steven Roose – 2013-05-12T14:39:34.270
Users be aware that typically you want a wallet program to manage your addresses and make sure you're monitoring the blockchain for any funds sent to your address. Generating them as described in the current answers means that no wallet software is monitoring your address to alert you when you receive your coins. – morsecoder – 2015-12-14T12:53:23.377