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Section 3.1.2 of the Lightning paper (Version 0.5.9.2, last modified 14 January 2016) discusses ways to fix the transaction malleability issue, which prevented Bitcoin transactions from spending UTXO from yet unconfirmed transactions. Specifically, it mentioned SIGHASH_NOINPUT transaction type.

As far as I know, the malleability issue was fixed with the Segwit soft fork in August 2017. Was the malleability issue fixed with SIGHASH_NOINPUT or with some other method? How does it affect the Lightning network design as described in the paper?

A related (very old) question, another one.

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As far as I know, the malleability issue was fixed with the Segwit soft fork in August 2017.

Yes.

Was the malleability issue fixed with SIGHASH_NOINPUTor with some other method?

No, using SegWit.

SegWit stands for segregated witness. It's a generic and backward compatible change that results in signatures no longer contributing to txids. As the txids of previous transaction outputs being spent are included in what transactions sign, this indirectly results in malleation no longer resulting in the invalidation on descendant transactions.

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