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Private and Public Keys A bitcoin wallet contains a collection of key pairs, each consisting of a private key and a public key. The private key (k) is a number, usually picked at random. From the private key, we use elliptic curve multiplication, a one-way cryptographic function, to generate a public key (K). From the public key (K), we use a one-way cryptographic hash function to generate a bitcoin address (A). In this section we will start with generating the private key, look at the elliptic curve math that is used to turn that into a public key, and finally, generate a bitcoin address from the public key. The relationship between private key, public key and bitcoin address is shown below: Figure 4-1. Private Key, Public Key and Bitcoin Address Private Keys A private key is simply a number, picked at random. Ownership and control over the private key is the root of user control over all funds associated with the corresponding bitcoin address. The private key is used to create signatures that are required to spend bitcoins by proving ownership of funds used in a transaction. The private key must remain secret at all times, as revealing it to a third party is equivalent to giving them control over the bitcoins secured by that key. The private key must also be backed up and protected from accidental loss, since if lost it cannot be recovered and the funds secured by it are forever lost too. The bitcoin private key is just a number. You can pick your private keys randomly using just a coin, pencil and paper: Toss a coin 256 times and you have the binary digits of a random private key you can use in a bitcoin wallet. The public key can be then generated from the private key. Generating a private key from a random number The first and most important step in generating keys is to find a secure source of entropy, or randomness. Creating a bitcoin key is essentially the same as “Pick a number between 1 and 2256“. The exact method you use to pick that number does not matter as long as it Introduction | 63PDF Image | Mastering Bitcoin
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