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Formats” on page 76. Here’s an example of generating and displaying a private key using these two commands: $ bitcoind getnewaddress 1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy $ bitcoind dumpprivkey 1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy KxFC1jmwwCoACiCAWZ3eXa96mBM6tb3TYzGmf6YwgdGWZgawvrtJ The dumpprivkey command opens the wallet and extracts the private key that was gen‐ erated by thegetnewaddresscommand. It is not otherwise possible for bitcoind to know the private key from the public key, unless they are both stored in the wallet. You can also use the command-line sx tools (see “Libbitcoin and sx tools” on page 56) to generate and display private keys: New key with sx tools $ sx newkey 5J3mBbAH58CpQ3Y5RNJpUKPE62SQ5tfcvU2JpbnkeyhfsYB1Jcn Public Keys The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: K = k * G where k is the private key, G is a constant point called the Generator Point and K is the resulting public key. The reverse operation, known as “finding the discrete logarithm" — calculating k if you know K — is as difficult as trying all possible values of k, i.e., a brute-force search. Before we demonstrate how to generate a public key from a private key, let’s look at Elliptic Curve Cryptography in a bit more detail. Elliptic Curve Cryptography Explained Elliptic Curve Cryptography is a type of asymmetric or public-key cryptography based on the discrete logarithm problem as expressed by addition and multiplication on the points of an elliptic curve. Below we see an example of an elliptic curve, similar to that used by bitcoin: Introduction | 65PDF Image | Mastering Bitcoin
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