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I suppose that you address the question to a signature scheme, in which the signature is still the pair $(r,s)$ with $r=g^k \bmod p$ as the exponentiated nonce and $$s = H(m)\cdot x + k \mod q,$$ where $h = H(m)$ depends solely on the message $m$ being signed. Here $x$ denotes the secret signing key and $q$ the order of the generator $g$ of a prime ...

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