This proposal defines a new transaction digest algorithm for signature verification in version 0 witness program, in order to minimize redundant data hashing in verification, and to cover the input value by the signature.
There are 4 ECDSA signature verification codes in the original Bitcoin script system: CHECKSIG, CHECKSIGVERIFY, CHECKMULTISIG, CHECKMULTISIGVERIFY (“sigops”). According to the sighash type (ALL, NONE, SINGLE, ANYONECANPAY), a transaction digest is generated with a double SHA256 of a serialized subset of the transaction, and the signature is verified against this digest with a given public key. The detailed procedure is described in a Bitcoin Wiki article. <ref name=wiki>[https://en.bitcoin.it/wiki/OP_CHECKSIG]</ref>
Unfortunately, there are at least 2 weaknesses in the original transaction digest algorithm:
* For the verification of each signature, the amount of data hashing is proportional to the size of the transaction. Therefore, data hashing grows in O(n<sup>2</sup>) as the number of sigops in a transaction increases. While a 1 MB block would normally take 2 seconds to verify with an average computer in 2015, a 1MB transaction with 5569 sigops may take 25 seconds to verify. This could be fixed by optimizing the digest algorithm by introducing some reusable “midstate”, so the time complexity becomes O(n). <ref>[https://web.nvd.nist.gov/view/vuln/detail?vulnId=CVE-2013-2292 CVE-2013-2292]</ref><ref>[https://bitcointalk.org/?topic=140078 New Bitcoin vulnerability: A transaction that takes at least 3 minutes to verify]</ref><ref>[http://rusty.ozlabs.org/?p=522 The Megatransaction: Why Does It Take 25 Seconds?]</ref>
* The algorithm does not involve the amount of Bitcoin being spent by the input. This is usually not a problem for online network nodes as they could request for the specified transaction to acquire the output value. For an offline transaction signing device ("cold wallet"), however, the unknowing of input amount makes it impossible to calculate the exact amount being spent and the transaction fee. To cope with this problem a cold wallet must also acquire the full transaction being spent, which could be a big obstacle in the implementation of lightweight, air-gapped wallet. By including the input value of part of the transaction digest, a cold wallet may safely sign a transaction by learning the value from an untrusted source. In the case that a wrong value is provided and signed, the signature would be invalid and no funding might be lost. <ref>[https://bitcointalk.org/index.php?topic=181734.0 SIGHASH_WITHINPUTVALUE: Super-lightweight HW wallets and offline data]</ref>
Deploying the aforementioned fixes in the original script system is not a simple task. That would be either a hardfork, or a softfork for new sigops without the ability to remove or insert stack items. However, the introduction of segregated witness softfork offers an opportunity to define a different set of script semantics without disrupting the original system, as the unupgraded nodes would always consider such a transaction output is spendable by arbitrary signature or no signature at all. <ref>[https://github.com/bitcoin/bips/blob/master/bip-0141.mediawiki BIP141: Segregated Witness (Consensus layer)]</ref>
1. nVersion of the transaction (4-byte little endian)
2. hashPrevouts (32-byte hash)
3. hashSequence (32-byte hash)
4. outpoint (32-byte hash + 4-byte little endian)
5. scriptCode of the input (varInt for the length + script)
6. value of the output spent by this input (8-byte little endian)
7. nSequence of the input (4-byte little endian)
8. hashOutputs (32-byte hash)
9. nLocktime of the transaction (4-byte little endian)
10. sighash type of the signature (4-byte little endian)
The items 1, 4, 7, 9, 10 have the same meaning as the original algorithm. <ref name=wiki></ref>
The item 5:
*For P2WPKH witness program, the scriptCode is <code>0x1976a914{20-byte-pubkey-hash}88ac</code>.
*For P2WSH witness program,
**if the <code>witnessScript</code> does not contain any <code>OP_CODESEPERATOR</code>, the <code>scriptCode</code> is a <code>varInt</code> for the length of the <code>witnessScript</code>, followed by the <code>witnessScript</code>.
**if the <code>witnessScript</code> contains any <code>OP_CODESEPERATOR</code>, the <code>scriptCode</code> is the evaluated script, with all <code>OP_CODESEPARATOR</code> and everything up to the last <code>OP_CODESEPARATOR</code> before the signature checking opcode being executed removed, and prepended by a <code>varInt</code> for the length of the truncated script.
*If the sighash type is neither SINGLE nor NONE, hashOutputs is the double SHA256 of the serialization of all output value (8-byte little endian) with scriptPubKey (<code>varInt</code> for the length + script);
*If sighash type is SINGLE and the input index is not greater than the number of outputs, <code>hashOutputs</code> is the double SHA256 of the output value with <code>scriptPubKey</code> of the same index as the input;
*Otherwise, <code>hashOutputs</code> is a <code>uint256</code> of <code>0x0000......0000</code>.
The <code>hashPrevouts</code>, <code>hashSequence</code>, and <code>hashOutputs</code> calculated in an earlier verification may be reused in other inputs of the same transaction, so that the time complexity of the whole hashing process reduces from O(n<sup>2</sup>) to O(n).
The serialized signed transaction is: 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
As a soft fork, older software will continue to operate without modification. Non-upgraded nodes, however, will not see nor validate the witness data and will consider all witness programs, inculding the redefined sigops, as anyone-can-spend scripts.
