Clarification on the script P2SH, how is executed to Bitcoin core?

Question

This question is a continuation of the my post yesterday.

Today I have a question on P2SH execution so, an example of the script should be this

OP_0 <A Signature> <B Signature> OP_2 <Public key A> <Public key B> 
<Public key C> OP_3 OP_CHECKMULTISIG
OP_HASH160 <ScriptSig Hash> OP_EQUAL

or if used the P2SH key should be is this (I think in this script left-hand something to convert the hash160 inside the P2SH key, right?)

OP_0 <A Signature> <B Signature> OP_2 <Public key A> <Public key B> 
<Public key C> OP_3 OP_CHECKMULTISIG
OP_HASH160 <P2SH key> OP_EQUAL

Now if I have understood well the simulation of the execution is divided into two phases

1. The hash scriptSig is equal to hash inside the scriptPubKey

Simulation

• Put on the scriptSig on the stack, so the stack now is <A sig> <B sig> <A pubkey> <B pubkey> <C pubkey>
• Calculate the hash160 with the data inside the stack, so now the stack status is <scriptSig hash>
• Put on the scriptSig hash expected, now the stack status is <hash scriptsig> <hash scriptsigexpected>
• return the result of the operator OP_EQUAL (true or false)

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2. the scriptSig will execute such as the script multi-signature

Simulation

• put on the stack the scriptSig, the stack status is <A Signature> <B Signature>
• push the public keys, that stack status is <A Signature> <B Signature> <Public key A> <Public key B> <Public key C>
• apply the OP_CHECKMULTISIG operator and get the result

My questions are:

• With the P2SH key, the execution is the same? if not, what is the form of the P2SH with the P2SH key?

Also, I read this post but I don't think contains this answer.

If my example script is wrong, I'm sorry to give me a corrections

Answer 1

Let's go over this step by step. Suppose say you want to lock some bitcoins in a 2-of-3 multi-sig.

Locking steps

1. Create a multi-sig script: OP_2 <pub_key 1> <pub_key2> <pub_key3> OP_3 OP_CHECKMULTISIG.
2. Hash the multi-sig script with HASH160 which gives you multi-sig_scripthash.
3. Base58Check the multi-sig_scripthash with version 0x05 giving you an address starting with 3....
4. The scriptPubKey will be OP_HASH160 <multi-sig_scripthash> OP_EQUAL.

Unlocking Steps

1. Your stack will start at <signatures><redeemScript>. The signature is OP_0 <sig_A> <sig_B> and redeemScript is OP_2 <pub_key 1> <pub_key2> <pub_key3> OP_3 OP_CHECKMULTISIG.

2. Since v0.3.7, Bitcoin Core executes the unlocking script first and looks at the resulting stack. So your <signatures> and <redeemScript> are evaluated together first. This would result in a multi-signature evaluation.

3. In normal cases the above step should just return 1 as signatures satisfy the redeemScript. But with P2SH there is a caveat added by BIP-16. Whenever you have a OP_HASH160 <hash> OP_EQUAL locking script, it serves as a P2SH identifier. So before the evaluation of <signatures> with <redeemScript> the redeemScript is copied from the stack to another one. Then the evaluation is done with what is on stack (<signatures><redeemScript> in our case). If successful, replace the current stack with the just redeemScript. Hence, instead of 1 you have <redeemScript> at the top of the stack.

4. You run OP_HASH160 on the redeemScript. Stack is now <hash160_of_redeemScript>

5. You push <expectedredeemScripthash>. Stack is now <hash160_of_redeemScript><expectedredeemScripthash>

6. You run OP_EQUAL resulting in evaluation and returning 1 to the top of the stack.