In the evolving landscape of cryptography, multi-party Schnorr signatures stand out for their robustness and versatility. This article will guide you through implementing different Schnorr multi-signature schemes using Rust, along with troubleshooting tips to smoothen your journey.

Understanding Multi-Party Schnorr Signatures

Multi-party Schnorr signatures serve two main purposes:

• n,n-Multi-Signature Scheme: All parties involved must cooperate to issue the signature.
• t,n-Threshold-Signature Schemes (TSS): Any group of at least t+1 parties can successfully issue a valid signature.

Think of these schemes as a locked vault. For the n,n scheme, all the key holders need to be present to unlock it. In the t,n scheme, if the vault has several key holders, a minimum number can unlock it, as long as they meet the required threshold.

Choosing the Right Protocol Implementation

This library offers several implementations of Schnorr multi-signature schemes. Below is a summary of the protocols available:

Protocol                     | Type  | Rounds | Assumptions              | Comments
-----------------------------|-------|--------|--------------------------|--------------------------------
Boneh, et al. (MuSig)       | n,n   | 3      | DLP, ROM                 | Fixes security proof of [1]
Nick, et al. (MuSig2)       | n,n   | 2      | DLP, ROM, AGM            | Improvement on [2]
Micali, et al.              | n,n   | 3      | DLP, ROM                 | 
Stinson-Strobl              | t,n   | 3      | DLP, ROM                 | See (*)(*)

Additional efficiency can be gained by implementing Distributed Key Generation (DKG) from the resource on Fast Multiparty Threshold ECDSA with Fast Trustless Setup. However, if any party is malicious during the DKG, the protocol will stop for security reasons.

Getting Started

To start implementing Schnorr signatures, refer to the following test vectors:

• schnorr_bip_test_vector_2
• schnorr_two_party_signing
• threshold 3 out of 5 with 4 parties in signing

Troubleshooting Tips

As you embark on your journey to implement multi-party Schnorr signatures, you might encounter some hurdles. Here are some troubleshooting ideas:

• Ensure all dependencies are correctly installed and up to date in your Rust environment.
• Check for any typographical errors in the code or links to external documents.
• If you encounter security concerns, refer to the implementation notes and consider alternatives until the library is production-ready.

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Important Disclaimers

– This code should not be used for production at the moment.

– The code is not secure against side-channel attacks.

– The library does not contain a networking layer. For more exploration, check out the ongoing efforts at white-city.

References

For further reading and verification, you may want to refer to these resources:

• Simple Schnorr Multi-Signatures
• Compact Multi-Signatures
• MuSig2: Two-Round Schnorr Multi-Signatures
• Accountable Subgroups Multi-signatures
• Provably Secure Distributed Schnorr Signatures

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