feat: ecdsa on BabyJubJub

[YashBit]

Implement ECDSA Signature Generation and Verification in Noir

Overview

This PR introduces a comprehensive ECDSA (Elliptic Curve Digital Signature Algorithm) implementation in Noir, utilizing the Baby JubJub curve. The implementation includes functions for signature generation, verification, and related utility operations.

Key Features

• ECDSA signature generation and verification
• Modular inverse calculation
• Public key derivation from private key
• Conversion of byte arrays to field elements

Function Definitions

calculate_signature

Generates an ESDSA signature for a given message using a private key and random nonce.

verify_signature

Verifies an ECDSA signature against a given message hash and public key.

mod_inv

Computes the modular inverse of a field element with respect to a given modulus.

field_from_bytes

Converts a byte array to a field element, supporting both big-endian and little-endian formats.

derive_public_key

Computes a public key from a private key using the Baby JubJub curve.

derive_public_key_optimized

Provides an optimized version of public key derivation using pre-computed curve parameters.

Usage

This implementation can be used for secure digital signature generation and verification in Noir projects. It's particularly useful for blockchain and cryptographic applications requiring ECDSA functionality.

Notes

• The implementation uses the Baby JubJub curve, which is well-suited for zero-knowledge proofs.
• Random nonce generation is not included and should be handled externally for security reasons.
• The code includes comprehensive error checking and assertions for robustness.

Future Improvements

• Consider adding more extensive testing, especially for edge cases.
• Explore further optimizations for performance-critical operations.
• Evaluate the possibility of implementing additional signature schemes.

[YashBit]

@signorecello

I am still working on the integration test, but the code for ECDSA is complete. Compiles without any errors. Please can you comment on the logic, etc?

[signorecello]

Can we have a test and a proper README with instructions on how to use, import, test, and with a benchmark? Seems like this library would benefit from using noir-edwards too.

A lot of this code is AI-generated.

[YashBit]

On it.

Yes, AI Generated.

[YashBit]

Optimised version of BabyJubJub already implements noir-edwards I believe.

[signorecello]

Closing this PR as we have significant evidence of you asking community members to do the remaining work on your behalf.

[YashBit]

@signorecello

Hi,

Implementing ECDSA was not a part of the work for the grant that I received. So I have not asked people to complete work that is "on my behalf", but I wanted to collaborate further with the community and add value.

Moreover, I merely asked you to comment on the logic. Hence, I believe closing this PR signals poor judgement.