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Possible Duplicate:
How are public & private keys in an address created?
If I lost my public key, but still have the private key, is it possible to recreate the public keys.
How many public keys can be made from one private key?
Is it a computationally expensive process to create all the public keys from one private key?
Sincerely,
Joe.
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Relation is one private key generates one public key and it is possible to recreate the public key. You can't recreate the private key though, so if you lose them, you lose all coins associated with that key.
It is not computationally expensive to generate or recover keypairs, but you need specific programs for that support secp256k1 elliptic curve cryptography.
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bitaddress.org allows you to recreate your public key from a private key. Go to the "Wallet Details" tab, paste in the private key and click 'view details'.
The page is a single large javascript program, and works entirely offline. If you don't trust it, you could disconnect from the Internet before pasting in your private key.
If you really don't trust it, try a random private key I just generated:
5KZAueujixZWLhhRZXejQUBVUsz4ighKd7gwsb4yjAKs6PhKEAD
The corresponding Bitcoin address is:
11CywWGeviZVmcHnNMm2oxrH4RhTU4YTe
