# ECDSA verify signature

The algorithm to **verify a ECDSA signature** takes as input the signed message ***msg*** + the signature {***r***, ***s***} produced from the signing algorithm + the public key ***pubKey***, corresponding to the signer's private key. The output is boolean value: ***valid*** or ***invalid*** signature. The **ECDSA signature verify** algorithm works as follows (with minor simplifications):

1. Calculate the message **hash**, with the same cryptographic hash function used during the signing: ***h*** = hash(***msg***)
2. Calculate the modular inverse of the signature proof: ***s1*** = $$s^{-1} \pmod n$$
3. Recover the random point used during the signing: ***R'*** = (***h*** \* **s1**) \* **G** + (***r*** \* ***s1***) \* ***pubKey***
4. Take from ***R'*** its x-coordinate: ***r'*** = ***R'*****.x**
5. Calculate the signature validation **result** by comparing whether ***r'*** == ***r***

The general idea of the signature verification is to **recover the point** ***R'*** using the public key and check whether it is same point ***R***, generated randomly during the signing process.

[Source](https://cryptobook.nakov.com/digital-signatures/ecdsa-sign-verify-messages)


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