Public key signature and verification process

Set

Private key: k,
public key: K,
elliptic curve base point: G,
and satisfy K = k * G, private key k → Public key K, the process is irreversible
Temporary random private key: r,
temporary public key: R = r * G
Message to be encrypted: Message
The message after the hash: hash
Message Digest: Digest
Digital Signature: Signature
Random number: x

一、The process of signature

1. Calculate the temporary public key: $$R=r\ast G$$
2. calculate the signture: $$Signature=\frac{hash+k\ast x}{r}$$
3. Send the temporary public key R, Message and Signature to the message receiver

二、The process of verifying

The principle of check is to calculate the temporary public key r *G according to the public key K, Message and digital signature,
$$\begin{gathered} V=\frac{hash+k\ast x}{s}\cdot \times G \\ =\frac{hash}{s}\times G+\frac{k\ast x}{s}\cdot \times G \\ =\frac{hash}{s}\times G+\frac{x}{s}\cdot \times K \end{gathered}$$

then verify whether it is consistent with the received message R.
If V == R, the signature is valid; if v ≠ r, the signature is invalid.