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Public key

There are pairs of keys in the public key cryptographic algorithm, which is an asymmetric algorithm that is required for a digital signature to verify the transactions: public keys and private keys. A public key is composed with number of 32 bytes, which is calculated from a private key using the elliptic curve digital signature algorithm.

The elliptic curve equation satisfies the equation below.

The public keys are calculated from private keys by the calculation as follows.

(K: public key, k: private key, G: generate point)

From the value above, because G stands for the constant value which Bitcoin appointed, when multiplying G by private key, the constant value of public key is returned.

When creating public keys from private keys, Bitcoin uses 'secp256k1', which is an elliptic curve and a constant value by the standard. Also with this value, when finding x-coordinate by modular arithmetic, the property to calculate y-coordinate can be used on verification, and reduce the size of the public keys.