Improve the MillerLoopResult type.

[carloskiki]

This fixes a few issues with MillerLoopResult.

• It makes it more usable. Currently, the type cannot be converted into a Gt element with final_exponentiation, which makes the type quite useless otherwise.

• It makes it coherent. The type documentation states that it can't be compared. However, the type still implements PartialEq and Eq which is contradictory. Moreover, the implementation of Eq and PartialEq was wrong. It is known that two MillerLoopResults are not numerically equivalent. This fixes the type by adding a final_verify method, and implementing Eq and ParitalEq based on it.

• Allows for trivial construction. A MillerLoopResult can now be constructed using the top level miller_loop function.

[Copilot]

Pull Request Overview

This PR refactors the pairing operations by extracting the Miller loop into a separate public function and adds new equality comparison capabilities to MillerLoopResult. It also removes the rust-toolchain file, allowing the MSRV specified in Cargo.toml to take precedence.

• Refactored pairing() to use the new miller_loop() function
• Added final_verify() method and PartialEq/Eq implementations for MillerLoopResult
• Removed rust-toolchain file to rely on rust-version in Cargo.toml

Reviewed Changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 4 comments.

File	Description
src/pairing.rs	Extracts Miller loop into separate function, adds final_verify method and equality traits to MillerLoopResult, improves documentation
rust-toolchain	Removes toolchain specification file to use Cargo.toml MSRV

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.