I hear that each address has one private key. Is it possible generate three public key address by only one private key?
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You need at least two private keys to get three addresses: you can get one address from each private key (in two formats) plus a 3rd multisig address if you combine the two. – May 02 '14 at 19:28
3 Answers
What do you mean by "public key address" ?
From one private key, you can generate:
- A pay-to-pubkey hash address that uses the uncompressed form of the public key.
- Pay-to-script hash address, where the script is (1)
- Pay-to-script hash address, with a OP_CHECKSIG script
- Pay-to-script hash addresses, paying to 1-of-1 OP_CHECKMULTISIG with uncompressed pubkey.
And all of the above could use the compressed form of the pubkey to get another 4 addresses.
So one private key can be represented by eight different addresses.

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Not directly, no. Each private key corresponds to exactly one public key. This public key can be represented in two ways that give different addresses: uncompressed and compressed. This gives you two addresses for a private key.
You could, however, use the private key as a seed to generate more private keys, much like Electrum's 128-bit seed. For example, if your seed were the 24-bit 6B8ABC in hex, use the following numbers as private keys
- SHA256(6B8ABC00)
- SHA256(6B8ABC01)
- SHA256(6B8ABC02)
(note: do not use a 24-bit seed or private key, as someone could easily steal your bitcoins)

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You could create 2: one address using the public key in compressed form and a second using the public key in uncompressed form.

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