Montgomery Multiplication Implementation Notes

Status

Montgomery multiplication has been partially implemented in field.go. The current implementation provides the API structure but uses standard multiplication internally.

Current Implementation

• ToMontgomery(): Converts to Montgomery form using R² multiplication
• FromMontgomery(): Converts from Montgomery form (currently uses standard multiplication)
• MontgomeryMul(): Multiplies two Montgomery-form elements (currently uses standard multiplication)
• montgomeryReduce(): REDC algorithm implementation (partially complete)

Issues

1. The FromMontgomery() implementation needs proper R⁻¹ computation
2. The MontgomeryMul() should use the REDC algorithm directly instead of standard multiplication
3. The R² constant may need verification
4. Tests are currently failing due to incomplete implementation

Next Steps

1. Compute R⁻¹ mod p correctly
2. Implement proper REDC algorithm in MontgomeryMul
3. Verify R² constant against reference implementation
4. Add comprehensive tests

References

• Montgomery reduction: https://en.wikipedia.org/wiki/Montgomerymodularmultiplication
• secp256k1 field implementation: src/field_5x52.h