Fully-Adaptive Two-Round Threshold Schnorr Prototype

This repository contains a prototype implementation accompanying the paper

Fully-Adaptive Two-Round Threshold Schnorr Signatures from DDH
Paul Gerhart, Davide Li Calsi, Luigi Russo, and Dominique Schröder
EUROCRYPT 2026

⚠️ Prototype Disclaimer
This code is intended solely for research and benchmarking. It is a proof of concept and has not been audited, is not hardened against side-channel attacks,
and must not be used in production systems. Please use only in controlled, research, or testing environments.

Overview

We implement the cryptographic core of our threshold signature scheme, which combines:

• Polynomial evaluation: signing randomness is derived by evaluating a secret polynomial at a given point.
• Proof of correct evaluation: a polynomial commitment scheme ensures that the evaluation was done honestly.
• Well-formedness of the first-round message: proved by combining the polynomial commitment with a Chaum–Pedersen style proof.

Cryptographic building blocks

• Polynomial commitment scheme

  • Commitments: Pedersen commitments (C_f) to the polynomial coefficients.
  • Proofs: logarithmic-size inner-product arguments (from the dalek-cryptography/bulletproofs crate) for proving correct evaluation.

• Chaum–Pedersen proof
  For showing correctness of the first-round message (R) with respect to a signer’s public key
  [ pk = (g^x h^w v^u, C_f) ] and the evaluation point (z).

Code structure

• sig_setup.rs / sig_keygen.rs
  Parameter setup and partial public key generation.

• rand_eval.rs
  Core RelEval protocol: prover (rel_eval_prove) and verifier (rel_eval_verify).

• benches/bench_com.rs
  Criterion benchmarks for proving and verifying correctness of the first-round message at different polynomial degrees.

• main.rs
  A simple round-trip example: generate a proof, evaluate, and verify.

Requirements

• Rust ≥ 1.75
• Cargo
• criterion (for benchmarks)

Usage

Build the project:

cargo build

Run the round-trip demo (from main.rs):

cargo run 

Run benchmarks:

cargo bench