Feature/13 fq field u384

[twliu-dorian]

Refactor Fq Type from fq c0:u256 to fq c0:u384

Description

This pull request refactors the entire codebase to replace the existing fq type definition from c0: u256 to c0: u384. This change is aimed at improving the precision and compatibility of the finite field operations for the application.

Details of the Change

• Updated all instances of the fq type and associated operations from u256 to u384.
• Adjusted the related arithmetic operations and utility functions to handle the larger data type.
• Ensured compatibility with the modular arithmetic constraints used in PLONK proof verification.

Benchmarking Update

The current end-to-end PLONK verification process benchmark stands at 7,924,389 steps. No significant performance optimizations have been applied yet, but future iterations may focus on improving efficiency.

Testing

• All unit tests have been updated to reflect the type change and pass successfully.
• Benchmarking tools were run to ensure the correctness of the PLONK verification after the refactor.

Next Steps

• Monitor for any edge cases or regressions introduced due to the change in type.
• Optimize arithmetic operations if performance becomes a bottleneck.

Please review the changes and let me know if there are any issues or suggestions.