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I am looking at the BIP143 P2WPKH example. I am kind of following until the generation of the sigHash: c37af31116d1b27caf68aae9e3ac82f1477929014d5b917657d0eb49478cb670 but then that is used to generate the signature 304402203609e17b84f6a7d30c80bfa610b5b4542f32a8a0d5447a12fb1366d7f01cc44a0220573a954c4518331561406f90300e8f3358f51928d43c212a8caed02de67eebee. Given that this transaction comprises two inputs I would somehow expect both corresponding private keys to generate a signature. So how is that signature in the example obtained?

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Only the private key for the second input is used in this signature as this signature is only for the second input. The first input is P2PK and is ignored in this example as it is non-segwit so the standard non-segwit sighash algorithm is used for it.

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