How much does the weight of 2-of-3 multisignature inputs change between P2SH and P2SH-P2WSH?

Question

I'm trying to calculate the weight of a 2-of-3 multisignature P2SH-P2WSH input. I found the related question Predict multi signature transaction size, which I've calculated out with m=2, n=3 here:

pubkeySize=33
sigSize=72

SizeOfRedeemScript = 1+n*(1+pubkeySize)+1+1
// 2-of-3: SizeOfRedeemScript = 1+3*(1+33)+1+1 = 105

SizeOfScriptSig = 1+m*(1+sigSize)+SizeOfPushDataFor(RedeemScript)+SizeOfRedeemScript
// 2-of-3: SizeOfScriptSig = 1+2*(1+72)+2+105 = 1 + 146 + 2 + 105 = 254

sizeOf(input) = 32+4+SizeOfCsuintFor(SizeOfScriptSig) + SizeOfScriptSig + 4
// 2-of-3: sizeOf(input) = 32+4+3+254+4 = 297

The size of 2-of-3 input in P2SH has 293 to 297 bytes¹. Thus, this would correspond to up to 297*4 = 1188 bytes weight (BW).

How would I calculate the same BW for a 2-of-3 multisignature P2SH-P2WSH input?

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¹_{Correction: Note that if both signatures are 71 bytes, the scriptSig is 252 bytes which as a length can be encoded in 1 byte, but in the worst case both signatures are 72 bytes and the length of the scriptSig needs 3 bytes.}

Answer 1

To calculate the block weight, you need to know the size in bytes of the non-witness data and the size in bytes of the witness data.

With a P2SH-P2WSH input, your scriptSig will always be 35 bytes. This makes the size in bytes of the inputs to be 36 + 35 + 4 = 75. The witnesses contain your signatures and scripts, so the witness for that input will be 1+m*(1 + sigSize) + SizeOfVarIntFor(RedeemScript) + SizeOfRedeemScript. For a 2-of-3 multsig input, you will thus have 1 + 2*(1 + 72) + 2 + 105 = 254 as the size in bytes of your witness.

The formula for calculating block weight is base size * 3 + total size. The base size is the size of all non-witness data, so your base size is 75 bytes. The total size is the size of all data, including witnesses, so your total size will be 75 + 254 = 329. Plugging this into the formula gets 75 * 3 + 329 = 554. Thus the weight of the P2SH-P2WSH 2-of-3 multisig is 554.

*Note that SizeOfVarIntFor(RedeemScript) is actually two bytes because you need to use OP_PUSHDATA1 since the length of the redeemscript is longer than 75 bytes.