feat: Implement comprehensive error handling in verify.cairo

[hexiao-NM]

Error Handling Implementation for Cairo PLONK Verifier

Overview

This PR implements comprehensive error handling for the PLONK verifier in Cairo, transforming the codebase to use Result types and providing detailed error information for debugging and validation.

Key Changes

Error Handling System

• Implemented Result-based error handling throughout verify.cairo
• Added granular error checks for:
  • Curve point validation
  • Field element validation
  • Public input verification
  • Transcript operations
  • Pairing verification

Code Improvements

• Transformed all verification functions to return Result types
• Added detailed error messages for debugging
• Implemented proper error propagation using the ? operator
• Enhanced input validation with specific error cases

Error Types

• InvalidCurvePoint: For curve point validation failures
• InvalidFieldElement: For field element validation issues
• InvalidPublicInput: For public input validation errors
• TranscriptError: For transcript operation failures
• PairingError: For pairing check failures
• VerificationFailed: For general verification failures

Testing

• Verified error propagation works correctly
• Confirmed error messages are helpful for debugging
• Tested all error paths in the verification process