user82945: I've learned that OP_CHECKMULTISIG is a Bitcoin builtin opcode to validate Multisig transactions. Can I write Bitcoin script to validate the Multisig transactions without invoking OP_CHECKMULTISIG? If so, what do I need to change in the redeemScript?

user48884: Yes, you can use a redeemScript that has a lot of OP_CHECKSIGs and boolean operations. You would have to enumerate all possible combinations of signatures however.
As a simple example, if you used a 2-of-2 multisig, traditionally your redeemScript would be
OP_2 <pubkey1> <pubkey2> OP_2 OP_CHECKMULTISIG

and the scriptSig is then
OP_0 <sig1> <sig2> <redeemScript>

Without OP_CHECKMULTISIG, your redeemScript would be
<pubkey1> OP_CHECKSIG OP_SWAP <pubkey2> OP_CHECKSIG OP_BOOLAND

and the scriptSig would be
<sig2> <sig1> <redeemScript>

For more complex multisigs with more keys and m-of-n, the scripts will be much more complicated with more OP_SWAPs, OP_BOOLORs, and OP_BOOLANDs.

82945: <p>I've learned that OP_CHECKMULTISIG is a Bitcoin builtin opcode to validate Multisig transactions. Can I write Bitcoin script to validate the Multisig transactions without invoking OP_CHECKMULTISIG? If so, what do I need to change in the redeemScript?</p>
 48884: <p>Yes, you can use a redeemScript that has a lot of OP_CHECKSIGs and boolean operations. You would have to enumerate all possible combinations of signatures however.</p>

<p>As a simple example, if you used a 2-of-2 multisig, traditionally your redeemScript would be</p>

<pre><code>OP_2 &lt;pubkey1&gt; &lt;pubkey2&gt; OP_2 OP_CHECKMULTISIG
</code></pre>

<p>and the scriptSig is then</p>

<pre><code>OP_0 &lt;sig1&gt; &lt;sig2&gt; &lt;redeemScript&gt;
</code></pre>

<p>Without OP_CHECKMULTISIG, your redeemScript would be</p>

<pre><code>&lt;pubkey1&gt; OP_CHECKSIG OP_SWAP &lt;pubkey2&gt; OP_CHECKSIG OP_BOOLAND
</code></pre>

<p>and the scriptSig would be</p>

<pre><code>&lt;sig2&gt; &lt;sig1&gt; &lt;redeemScript&gt;
</code></pre>

<p>For more complex multisigs with more keys and m-of-n, the scripts will be much more complicated with more OP_SWAPs, OP_BOOLORs, and OP_BOOLANDs.</p>
