[BIP Proposal] Elliptic Curve Operations for Bitcoin Script

This initiative paves the way for the computation of the top-level Taproot output public key using Bitcoin Script, enabling a more dynamic approach to creating smart contracts on the Bitcoin blockchain. The integration of these op codes, including OP_EC_POINT_ADD, OP_EC_POINT_MUL, OP_EC_POINT_NEGATE, and OP_EC_POINT_X_COORD, is designed to broaden the range of functional operations available to developers, thereby fostering the development of versatile smart contracts and innovative applications such as optimized Discreet Log Contracts (DLCs), partial musig2 signature verifications, and EC-based sigma protocols.

A specific aspect of the proposal highlights the introduction of an operation named OP_EC_LIFT_X_EVEN, which seeks to counteract the effects of OP_EC_POINT_X_COORD with some limitations due to parity considerations, useful in conjunction with OP_IKEY. Moreover, the proposal suggests the addition of OP_EC_GENERATOR to simplify script composability by pushing the generator point G onto the stack directly, which addresses the ambiguity associated with representing G as 0 and facilitates a more intuitive execution of operations involving the point at infinity. This modification is expected to streamline processes like OP_TWEAKADD by enabling a more coherent sequence of generating a point, multiplication, lifting, and adding points together.

These proposed changes aim to rectify and clarify the procedures for elliptic curve operations within Bitcoin's scripting language, addressing current shortcomings and inaccuracies. By doing so, they set the stage for more accurate and efficient implementations of elliptic curve operations in Bitcoin scripts. For those interested in the technical specifics or contributing to the ongoing discussion, comprehensive details can be accessed through the Bitcoin Improvement Proposal (BIP) here, alongside a reference implementation for btcd available here. Through these enhancements, Bitcoin's scripting language is poised for significant advancements in its ability to support complex and secure on-chain logic implementations, marking a substantial step forward in the evolution of Bitcoin's scripting functionalities.