Recover ECDSA pub key from signature

Question

I am trying to recover a ecdsa pub key from the given signature and data. But returned pubkey does not match with the signer. Is there something that is missing or wrong?

let pair = ecdsa::Pair::from_string(&format!("//{}",1), None).unwrap();
let t_hash = keccak_256(b"Hello");
let new_signature = pair.sign(&t_hash);
if let Ok(recover_pub_key) = sp_io::crypto::secp256k1_ecdsa_recover(&new_signature.0, &t_hash) {
    print!("This is recovered key : {:?}",recover_pub_key);
    } else {
        print!("recovery failed ...!");
    }

Output:

signer publicKey : [3, 51, 2, 40, 152, 20, 6, 98, 223, 234, 132, 126, 60, 191, 229, 233, 137, 132, 90, 198, 118, 110, 131, 71, 47, 139, 12, 101, 13, 133, 231, 123, 174]

Recovered PublicKey : [81, 75, 231, 120, 203, 190, 133, 220, 74, 33, 169, 246, 87, 80, 28, 196, 89, 171, 118, 173, 174, 27, 147, 176, 42, 53, 71, 229, 36, 36, 0, 90, 52, 165, 231, 253, 187, 118, 225, 90, 140, 119, 23, 194, 231, 252, 99, 207, 211, 84, 179, 184, 245, 248, 243, 215, 56, 53, 26, 252, 92, 230, 14, 218]

Answer 1

Making your code work required:

• Using sign_prehashed instead of sign
• secp256k1_ecdsa_recover_compressed instead of secp256k1_ecdsa_recover
• Using ecdsa::Public::from_raw to construct the recovered PK

use sp_core::{ecdsa, keccak_256, Pair};
use sp_io::crypto::secp256k1_ecdsa_recover_compressed;

let pair = ecdsa::Pair::from_string(&format!("//{}",1), None).unwrap();
let hash = keccak_256(b"Hello");
let signature = pair.sign_prehashed(&hash);

if let Ok(recovered_raw) = secp256k1_ecdsa_recover_compressed(&signature.0, &hash) {
    let recovered = ecdsa::Public::from_raw(recovered_raw);
    // Assert that we recovered the correct PK.
    assert_eq!(pair.public(), recovered);
} else {
    panic!("recovery failed ...!");
}

There are much better ways to do this than directly using the low-level primitives.
Maybe this question better fits your use-case.