The +dumpprivkey+ command opens the wallet and extracts the private key that was generated by the +getnewaddress+ command. It is not otherwise possible for bitcoind to know the private key from the public key, unless they are both stored in the wallet.
The +dumpprivkey+ command is not generating a private key from a public key, as this is impossible. The command simply reveals the private key that is already known to the wallet and which was generated by the getnewaddress command.
You can also use the command-line sx tools (see <<sx_tools>>) to generate and display private keys with the sx command +newkey+: (((range="endofrange", startref="ix_ch04-asciidoc3")))(((range="endofrange", startref="ix_ch04-asciidoc2")))(((range="endofrange", startref="ix_ch04-asciidoc1")))