Subject: [bitcoindev] Re: [BIP Proposal] Elliptic Curve Operations for Bitcoin Script

From: jeremy <[email-masked]>
Date: Mon, 25 Aug 2025 09:45:44 -0700 (PDT)

Interesting proposal and a great contrast of options v.s. OP_TWEAKADD. I 
have a few notes which might strengthen this proposal:

I would suggest adding an operation *OP_EC_LIFT_X_EVEN* which "undos" 
OP_EC_POINT_X_COORD (not perfectly because of parity). This is helpful if 
OP_IKEY is used.

I would also suggest adding *OP_EC_GENERATOR* which pushes G onto the 
stack, rather than taking a 0 to mean G. This is more composable, as 
presently you have:

<x: [u8;32]> <y : Either<0, [u8;33]> OP_EC_POINT_MUL -> Either<0, [u8;33]>

therefore scripts like:

<blah> SHA256 <[0; 32]> <0> OP_EC_POINT_MUL OP_EC_POINT_MUL

will return: h(blah) G

rather than more straightforwardly carrying the point at infinity onwards.

If you instead had OP_G:

<blah> SHA256 <[0; 32]> OP_EC_GENERATOR OP_EC_POINT_MUL OP_EC_POINT_MUL

will return: point at infinity

then you'd get more correct multiplication chaining.

This lets you implement OP_TWEAKADD as:

<H> OP_EC_GENERATOR OP_EC_POINT_MUL OP_INTERNALKEY OP_EC_LIFT_X_EVEN 
OP_EC_POINT_ADD
v.s.
<H> OP_IKEY OP_TWEAKADD

Note: The BIP incorrectly gives:

<tweak> <empty_vector> OP_EC_POINT_MUL  # tweak*G (33-byte)
<internal_key> OP_EC_POINT_ADD           # P + tweak*G (33-byte)
OP_EC_POINT_X_COORD                      # Extract x-coordinate (32-byte)

the internal key, as specified, must be lifted first before adding.

On Sunday, August 24, 2025 at 8:52:36 PM UTC-4 Olaoluwa Osuntokun wrote:

> Hi y'all,
>
> I've just published a draft of a BIP to add Elliptic Curve operation op 
> codes
> as a soft fork utilizing the existing Taproot infrastructure and current 
> tap
> leaf version.
>
> My primary motivation is enabling the commutation of the top level Taproot
> output public key within Bitcoin Script. Alongside introspection enabling 
> op
> codes, this enables the creation of a new flavor of on-chain state machine
> within Bitcoin Script. The set of op codes is also generic enough to enable
> several other use cases related to (optimized DLCs, partial musig2 
> signature
> verification, EC based sigma protocols, etc).
>
> A total of 4 op codes are proposed (each allocated from the existing
> OP_SUCCESS) range:
>   * `OP_EC_POINT_ADD`
>   * `OP_EC_POINT_MUL`
>   * `OP_EC_POINT_NEGATE`
>   * `OP_EC_POINT_X_COORD`
>
> The full BIP text can be found here: 
>  * https://github.com/bitcoin/bips/pull/1945
>
> A reference implementation in `btcd` can be found here:
>   * https://github.com/btcsuite/btcd/pull/2413
>
> --Laolu
>

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