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Can two signatures based on the elliptic curve secp256k1 be compared to determine if they use the same public key without recovering the public keys?

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    $\begingroup$ The signature and message are given $\endgroup$ Commented Apr 26 at 6:53
  • $\begingroup$ Don't use secp256k1, it's not widely supported. Use P-256 (a.k.a. secp256r1, prime256v1). $\endgroup$
    – DannyNiu
    Commented Apr 26 at 6:56

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You haven't specified which digital signature scheme to use. ECDSA will be assumed in this answer.

SEC#1 v2.0 section 4.1.6 specifies a procedure that recovers the public key from a message and its signature. Using this, you can compare whether 2 public keys from 2 msg-sig pair are same, additively complementary, or otherwise distinct.

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