nostringer 0.1.0

A blazing fast Rust implementation of unlinkable ring signatures for Nostr, allowing anonymous group signatures with secp256k1 keys
Documentation

Nostringer Ring Signatures (Rust)

A blazing fast Rust implementation of the unlinkable ring signature scheme in the nostringer TypeScript library.

Built using pure Rust crypto crates, this library allows a signer to prove membership in a group of Nostr accounts (defined by their public keys) without revealing which specific account produced the signature. It uses a Spontaneous Anonymous Group (SAG)-like algorithm compatible with secp256k1 keys used in Nostr.

Nostringer is largely inspired by Monero's Ring Signatures using Spontaneous Anonymous Group signatures (SAG), and beritani/ring-signatures implementation of ring signatures using the elliptic curve Ed25519 and Keccak for hashing.

Table of Contents

Disclaimer

This code is highly experimental. The original author is not a cryptographer, and this Rust port, while aiming for compatibility and correctness using standard libraries, has not been audited or formally verified. Use for educational exploration at your own risk. Production usage is strongly discouraged until thorough security reviews and testing are performed by qualified individuals.

Problem Statement

In many scenarios, you want to prove that "someone among these N credentials produced this signature," but you do not want to reveal which credential or identity. For instance, you might have a set of recognized Nostr pubkeys (e.g., moderators, DAO members, authorized reviewers) who are allowed to perform certain actions, but you want them to remain anonymous within that set when doing so.

A ring signature solves this by letting an individual sign a message on behalf of the group (the ring). A verifier can confirm the message originated from one of the public keys in the ring, without learning the specific signer's identity.

Key Features

  • Unlinkable: Signatures hide the signer's identity. Two signatures from the same signer cannot be linked cryptographically.
  • Fast: Implemented in Rust, leveraging efficient and audited cryptographic primitives from the RustCrypto ecosystem (k256, sha2).
  • Nostr Key Compatibility: Directly supports standard Nostr key formats (hex strings):
    • 32-byte (64-hex) x-only public keys.
    • 33-byte (66-hex) compressed public keys.
    • 65-byte (130-hex) uncompressed public keys.
    • 32-byte (64-hex) private keys.
  • Easy to Use: Simple sign, verify, and generate_keypair_hex functions.
  • Minimal Dependencies: Relies on well-maintained RustCrypto crates.
  • No Trusted Setup: The scheme does not require any special setup ceremony.

Installation

Add this crate to your Cargo.toml dependencies:

[dependencies]
nostringer = "0.1.0" # Replace with the latest version from crates.io

(Note: You might need other crates like hex or rand in your own project depending on how you handle keys and messages.)

Usage

use nostringer_ring::{sign, verify, generate_keypair_hex, RingSignature, Error};

fn main() -> Result<(), Error> {
    // 1. Setup: Generate keys for the ring members
    // Keys can be x-only, compressed, or uncompressed hex strings
    let keypair1 = generate_keypair_hex("xonly");
    let keypair2 = generate_keypair_hex("compressed");
    let keypair3 = generate_keypair_hex("xonly");

    let ring_pubkeys_hex: Vec<String> = vec![
        keypair1.public_key_hex.clone(),
        keypair2.public_key_hex.clone(), // Signer's key must be included
        keypair3.public_key_hex.clone(),
    ];

    // 2. Define the message to be signed (as bytes)
    let message = b"This is a secret message to the group.";

    // 3. Signer (keypair2) signs the message using their private key
    println!("Signing message...");
    let signature = sign(
        message,
        &keypair2.private_key_hex, // Signer's private key hex
        &ring_pubkeys_hex,         // The full ring of public keys
    )?;

    println!("Generated Signature:");
    println!(" c0: {}", signature.c0);
    println!(" s: {:?}", signature.s);

    // 4. Verification: Anyone can verify the signature against the ring and message
    println!("\nVerifying signature...");
    let is_valid = verify(
        &signature,
        message,
        &ring_pubkeys_hex, // Must use the exact same ring (order matters for hashing)
    )?;

    println!("Signature valid: {}", is_valid);
    assert!(is_valid);

    // 5. Tamper test: Verification should fail if the message changes
    println!("\nVerifying with tampered message...");
    let tampered_message = b"This is a different message.";
    let is_tampered_valid = verify(
        &signature,
        tampered_message,
        &ring_pubkeys_hex,
    )?;
    println!("Tampered signature valid: {}", is_tampered_valid);
    assert!(!is_tampered_valid);

    Ok(())
}

Examples

The repository includes several examples that demonstrate different aspects of the library:

  1. Basic Signing (examples/basic_signing.rs): Demonstrates the core signing and verification functionality.

    cargo run --example basic_signing

  2. Key Formats (examples/key_formats.rs): Shows how to work with different key formats (x-only, compressed, uncompressed) and create larger rings.

    cargo run --example key_formats

  3. Error Handling (examples/error_handling.rs): Demonstrates proper error handling for common error scenarios.

    cargo run --example error_handling

These examples provide practical demonstrations of how to use the library in real-world scenarios and handle various edge cases.

Benchmarks

The library includes comprehensive benchmarks using the Criterion framework:

  • Signing with different ring sizes (3, 5, 10, 20 members)
  • Verification with different ring sizes
  • Combined signing and verification
  • Performance with different key formats (x-only, compressed, uncompressed)

To run the benchmarks:

cargo bench

This will generate detailed reports showing the performance of each operation across different parameters.

API Reference

sign(message: &[u8], private_key_hex: &str, ring_pubkeys_hex: &[String]) -> Result<RingSignature, Error>

Signs a message using the SAG-like ring signature scheme.

  • message: The message bytes (&[u8]) to sign.
  • private_key_hex: The signer's private key as a 64-character hex string.
  • ring_pubkeys_hex: A slice of public key hex strings representing the ring members. The signer's corresponding public key (or the key corresponding to the negated private key) must be present in this ring. The order of keys matters for verification.
  • Returns: A Result containing the RingSignature on success, or an Error on failure (e.g., signer not in ring, invalid keys, ring too small).

verify(signature: &RingSignature, message: &[u8], ring_pubkeys_hex: &[String]) -> Result<bool, Error>

Verifies a ring signature against a message and the ring of public keys.

  • signature: A reference to the RingSignature object ({ c0, s }).
  • message: The original message bytes (&[u8]) that were allegedly signed.
  • ring_pubkeys_hex: A slice of public key hex strings representing the ring. Must be identical (including order) to the ring used during signing.
  • Returns: A Result containing true if the signature is valid for the message and ring, or false if it's invalid. Returns an Error if inputs are malformed (e.g., wrong signature length, invalid hex).

generate_keypair_hex(format: &str) -> KeyPairHex

Generates a new random secp256k1 key pair.

  • format: A string slice specifying the desired public key format:
    • "xonly": 64-hex (32 bytes), guaranteed even-Y point.
    • "compressed": 66-hex (33 bytes), starts with 02 or 03.
    • "uncompressed": 130-hex (65 bytes), starts with 04.
    • Defaults to "compressed" if an unrecognized format is provided.
  • Returns: A KeyPairHex struct containing private_key_hex (String) and public_key_hex (String). Note: The returned private_key_hex is the original randomly generated scalar, even if internal negation was required to produce an even-Y public key for the "xonly" format.

RingSignature Struct

pub struct RingSignature {
  pub c0: String, // Initial challenge scalar (64-char hex)
  pub s: Vec<String>, // Array of response scalars (64-char hex strings)
}

KeyPairHex Struct

pub struct KeyPairHex {
  pub private_key_hex: String, // 64-char hex
  pub public_key_hex: String,  // Hex format depends on generation option
}

Error Enum

An enum representing possible errors during signing or verification, such as invalid key formats, signer not found in the ring, ring too small, hex decoding errors, or internal cryptographic errors.

Signature Size

The size of the generated ring signature depends directly on the number of members (n) in the ring. It consists of:

  • One initial challenge (c0) scalar (32 bytes binary / 64 hex chars).
  • n response scalars (s array) (each 32 bytes binary / 64 hex chars).

The total binary size follows the formula: Size (bytes) = 32 * (n + 1)

This means the signature size grows linearly with the ring size. A larger ring provides more anonymity but results in a larger signature.

Security Considerations

  • Anonymity Set: The level of anonymity depends on the size (n) and plausibility of the chosen ring members. Ensure the ring containskeys that could realistically be the signer in the given context.
  • No Trusted Setup: This scheme does not require any trusted setup procedure.
  • Unlinkability: Signatures produced by the same signer for different messages (using the same or different rings) should be cryptographically unlinkable.
  • No Traceability: This specific SAG implementation does not produce linkability tags (like key images used in Monero's MLSAG/CLSAG) which would allow detecting if the same key was used to sign twice within different rings for the same message. This enhances privacy but means double-spending prevention requires other mechanisms if used for voting/claiming.
  • Implementation Security: This library relies on the correctness of the underlying k256 crate. While k256 is well-regarded, this specific ring signature implementation has not been independently audited.

License

This project is licensed under the MIT License.

References

Built with love by AbdelStark 🧡

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