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What should we do if s in the ecdsa signature is greater than n/2? As we all know, in the ECDSA signature of Ethernum, the output s must be smaller than n/2, where s is the signature output and n is the ECC group order. If s>n/2, we have two choices:

  1. Should we just re-choose a k, then re-sign the message to make s
  2. Or just make $v\oplus 1$ in the signature to make r -> (x,-y)?

What Ethernum ECDSA really do?

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Geth uses https://github.com/bitcoin-core/secp256k1.

And that implementation will apply option 2 https://github.com/bitcoin-core/secp256k1/blob/544435fc90a5672d862e2a51f44c10251893b97d/src/ecdsa_impl.h#L310-L315

if (secp256k1_scalar_is_high(sigs)) {
    secp256k1_scalar_negate(sigs, sigs);
    if (recid) {
        *recid ^= 1;
    }
}

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