nostringer 0.1.4

A Rust implementation of the ring signature scheme in the nostringer TypeScript library
Documentation

Nostringer Ring Signatures (Rust)

A blazing fast Rust implementation of the Nostringer unlinkable ring signature scheme for Nostr, compatible with 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.
  • Linkable Option: The BLSAG variant provides linkability through key images to detect when the same key is used multiple times, while still preserving anonymity within the ring.
  • Fast: Implemented in Rust, leveraging efficient and audited cryptographic primitives from the RustCrypto ecosystem (k256, sha2).
  • Optimized API: Provides both hex-string based API and a more efficient binary API that avoids serialization/deserialization overhead.
  • 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::{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(())
}

Optimized Binary API

For applications requiring maximum performance, we provide a binary API that works directly with the native types, avoiding hex conversion overhead:

use nostringer::{sign_binary, verify_binary, KeyPair, RingSignatureBinary, Error};
use k256::{Scalar, ProjectivePoint};

fn main() -> Result<(), Error> {
    // Assuming you have raw binary keys available:
    // (You'd normally get these from elsewhere in your app)
    let private_key = /* Scalar value */;
    let ring_pubkeys = /* Vec<ProjectivePoint> */;
    let message = b"This is a secret message to the group.";

    // Sign using binary API (more efficient)
    let binary_signature = sign_binary(message, &private_key, &ring_pubkeys)?;

    // Verify using binary API (more efficient)
    let is_valid = verify_binary(&binary_signature, message, &ring_pubkeys)?;
    println!("Signature valid: {}", is_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. BLSAG Linkability (examples/blsag_linkability.rs): Demonstrates the linkable BLSAG variant and how to detect when the same key is used for multiple signatures.

    cargo run --example blsag_linkability

  4. 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 for different ring sizes and operations. You can run these benchmarks yourself with:

cargo bench

For detailed information on running and interpreting benchmarks, see BENCHMARKS.md.

The repository also includes a GitHub Actions workflow that automatically runs benchmarks on each push and pull request, with the HTML report available as an artifact in the workflow run.

Performance Results

Below is a summary of the benchmark results, showing median execution times for each operation with different ring sizes:

Operation Ring Size Execution Time
Sign 2 members 204.75 µs
Sign 10 members 897.76 µs
Sign 100 members 13.31 ms
Verify 2 members 166.83 µs
Verify 10 members 847.23 µs
Verify 100 members 12.71 ms
Sign+Verify 2 members 370.41 µs
Sign+Verify 10 members 1.76 ms
Sign+Verify 100 members 25.02 ms

Benchmarking Environment:

  • Model: MacBook Pro (Identifier: MacBookPro18,2)
  • CPU: Apple M1 Max
  • Cores: 10
  • RAM: 64 GB
  • Architecture: arm64
  • Operating System: macOS 14.7 (Build 23H124)

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. This function is a wrapper around the more efficient sign_binary that handles hex conversion.

  • 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. This function is a wrapper around the more efficient verify_binary that handles hex conversion.

  • 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).

sign_binary(message: &[u8], private_key: &Scalar, ring_pubkeys: &[ProjectivePoint]) -> Result<RingSignatureBinary, Error>

Optimized version of sign that works directly with binary types, avoiding hex conversion overhead.

  • message: The message bytes (&[u8]) to sign.
  • private_key: The signer's private key as a k256::Scalar.
  • ring_pubkeys: A slice of public keys as k256::ProjectivePoint representing the ring members.
  • Returns: A Result containing the RingSignatureBinary on success, or an Error on failure.

verify_binary(signature: &RingSignatureBinary, message: &[u8], ring_pubkeys: &[ProjectivePoint]) -> Result<bool, Error>

Optimized version of verify that works directly with binary types, avoiding hex conversion overhead.

  • signature: A reference to the RingSignatureBinary object.
  • message: The original message bytes (&[u8]) that were allegedly signed.
  • ring_pubkeys: A slice of public keys as k256::ProjectivePoint representing the ring.
  • Returns: A Result containing true if the signature is valid, or false if it's invalid.

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

Alias for the original sign function, provided for clarity. Handles hex conversion internally.

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

Alias for the original verify function, provided for clarity. Handles hex conversion internally.

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)
}

RingSignatureBinary Struct

pub struct RingSignatureBinary {
  pub c0: Scalar, // Initial challenge scalar in binary form
  pub s: Vec<Scalar>, // Array of response scalars in binary form
}

BlsagSignature Struct

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

BlsagSignatureBinary Struct

pub struct BlsagSignatureBinary {
  pub c0: Scalar, // Initial challenge scalar in binary form
  pub s: Vec<Scalar>, // Array of response scalars in binary form
}

KeyImage Struct

pub struct KeyImage(pub ProjectivePoint);

A struct representing a key image for linkable signatures. Key images uniquely identify the signer's private key without revealing it. Provided with methods to convert to/from hex strings and compare for equality.

KeyPairHex Struct

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

KeyPair Struct

pub struct KeyPair {
  pub private_key: Scalar,
  pub public_key: ProjectivePoint,
}

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.

sign_blsag_binary(message: &[u8], private_key: &Scalar, ring_pubkeys: &[ProjectivePoint]) -> Result<(BlsagSignatureBinary, KeyImage), Error>

Creates a BLSAG (linkable) signature using binary inputs.

  • message: The message bytes (&[u8]) to sign.
  • private_key: The signer's private key as a k256::Scalar.
  • ring_pubkeys: A slice of public keys as k256::ProjectivePoint representing the ring members.
  • Returns: A Result containing a tuple of (BlsagSignatureBinary, KeyImage) on success, or an Error on failure. The KeyImage can be used to detect when the same key is used for multiple signatures.

verify_blsag_binary(signature: &BlsagSignatureBinary, key_image: &KeyImage, message: &[u8], ring_pubkeys: &[ProjectivePoint]) -> Result<bool, Error>

Verifies a BLSAG (linkable) signature using binary inputs.

  • signature: The binary BLSAG signature to verify.
  • key_image: The key image associated with the signature.
  • message: The message bytes that were allegedly signed.
  • ring_pubkeys: A slice of public keys as k256::ProjectivePoint representing the ring.
  • Returns: A Result containing true if the signature is valid, or false if it's invalid.

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

Creates a BLSAG (linkable) signature using hex inputs.

  • 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.
  • Returns: A Result containing a tuple of (BlsagSignature, String) on success, or an Error on failure. The second element is the key image as a hex string.

verify_blsag_hex(signature_hex: &BlsagSignature, key_image_hex: &str, message: &[u8], ring_pubkeys_hex: &[String]) -> Result<bool, Error>

Verifies a BLSAG (linkable) signature using hex inputs.

  • signature_hex: The hex BLSAG signature to verify.
  • key_image_hex: The key image hex string associated with the signature.
  • message: The message bytes that were allegedly signed.
  • ring_pubkeys_hex: A slice of public key hex strings representing the ring.
  • Returns: A Result containing true if the signature is valid, or false if it's invalid.

key_images_match(image1: &KeyImage, image2: &KeyImage) -> bool

Compares two key images to determine if they were created by the same signer.

  • image1: The first key image to compare.
  • image2: The second key image to compare.
  • Returns: true if the key images match (same signer), false otherwise.

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 contains keys that could realistically be the signer in the given context.
  • No Trusted Setup: This scheme does not require any trusted setup procedure.
  • Unlinkability vs. Linkability:
    • SAG: The default SAG implementation provides complete unlinkability. Signatures produced by the same signer for different messages (using the same or different rings) are cryptographically unlinkable.
    • BLSAG: The BLSAG variant intentionally provides linkability through key images. These key images allow detecting when the same key signed multiple messages, while still preserving anonymity (not revealing which specific ring member is the signer).
  • 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.

Signature Variants

The library offers two main variants of ring signatures:

1. SAG (Spontaneous Anonymous Group)

The default variant that provides:

  • Complete unlinkability (no way to tell if two signatures came from the same signer)
  • Maximum privacy within the ring
  • Suitable for anonymous voting, whistleblowing, or any scenario requiring maximum privacy

2. BLSAG (Back's Linkable Spontaneous Anonymous Group)

A linkable variant that:

  • Produces a key image along with the signature to enable linkability
  • Can detect when the same key signs multiple times (via the key image)
  • Still doesn't reveal which specific ring member signed (preserves anonymity within the ring)
  • Suitable for preventing double-spending, duplicate voting, or tracking usage of a credential
  • Similar to the linkable ring signature scheme used in Monero

Choose the variant that best suits your privacy and security requirements.

License

This project is licensed under the MIT License.

References

Built with love by AbdelStark 🧡

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