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Yes, it's normal practice to generate an ECDSA signature from message $M$ (or it's hash $H(M)$ ), private key $d_U$ and curve parameters, without being given a nonce as input. The nonce $k$ is built as part of the signing process, in one of two ways: It's generated a secret integer $k$ uniformly in $[1,n)$ using a true random number generator with secret ...

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