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How is a Bitcoin transaction signed using ECDSA?

You say you are familiar with how secp256k1 and ECDSA works but from what you say later I'm unsure whether you are. SegWit v0 didn't change the signing algorithm (ECDSA) nor the curve (secp256k1). ...
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How does ECDSA work when generating the public key?

What is secp256k1, is it the curve that is always used Indeed the elliptic curve used in Bitcoin is secp256k1 which is the curve defined using a=0 and b=7 in your equation mod p. But other curves are ...
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