With the private key, we can use the one-way encryption function of elliptic curve multiplication to generate the public key (K).

With the public key (K), we can use the one-way cryptographic hash function to generate the bitcoin address (A).

H3

Private key

The private key is just a randomly selected number. The control of all funds in a bitcoin address depends on the ownership and control of the corresponding private key. In bitcoin transactions, the private key is used to generate the signature needed to pay bitcoin to prove the ownership of funds. The private key must always be kept secret, because once it is leaked to a third party, it is equivalent to giving away the bitcoin protected by the private key. The private key must also be backed up to prevent accidental loss, because once the private key is lost, it will be difficult to recover and the bitcoin it protects will be lost forever.

Bitcoin private key is just a number. You can randomly generate your private key with coins, pencils and paper: toss a coin 256 times, record the front and back with paper and pen and convert it into 0 and 1. The randomly obtained 256-bit binary number can be used as the private key of Bitcoin wallet. The private key can further generate the public key.

H3

Public key

The public key can be calculated from the private key by elliptic curve algorithm, which is an irreversible process: k = k * g, where k is the private key, g is an invariant point called the generating point, and k is the obtained public key. Its reverse operation, called "finding discrete logarithm"-finding private key K from known public key K-is very difficult, just like trying all possible K values, that is, brute force search.

H3

Bitcoin address

A bitcoin address is a string of numbers and letters that can be shared with anyone who wants to give you bitcoin. The bitcoin address generated by the public key (a string of numbers and letters) starts with the number "1". The following is an example of a bitcoin address:

1j 7 MDG 5 rbqyuhenydx 39 wvwk 7 fslpeoxzy

In a transaction, the bitcoin address usually appears as the payee. If the bitcoin transaction is compared to a check, the bitcoin address is the payee, which is what we want to write in the payee column. The payee of a check can be a bank account, a company, an institution or even a cash check. Checks do not need to specify a specific account, but use a common name as the payee, which makes it a quite flexible payment tool. Similarly, the use of bitcoin addresses also makes bitcoin transactions very flexible. A bitcoin address can represent the owner of a pair of public keys and private keys, or something else, such as "P2SH".

(Pay-to-Script-Hash) "payment script.