COMET-MPC: Commitment-Oriented Multi-Party Computation with Equality Testing — A Dealerless, One-Round Framework for Privacy-Preserving Verification

We present COMET-MPC (Commitment-Oriented Multi-Party Computation with Equality Testing), a novel MPC framework that fundamentally reimagines multi-party computation as a commitment verification problem rather than a traditional secret-sharing problem. COMET-MPC achieves dealerless, one-round setup by reducing all MPC coordination tasks—input binding, consistency verification, and replay prevention—to homomorphic equality testing over elliptic-curve commitments. Unlike classical MPC protocols (Shamir’s secret sharing, FROST) that require multi-round polynomial verification or interactive zero-knowledge proofs, COMET-MPC performs verification through a single algebraic check: testing whether a group element equals the identity. This zero-detection paradigm exploits the structural identity between EC-Pedersen commitments and EC-ElGamal ciphertexts, enabling decrypt-free verification with perfect correctness and computational hiding under the Decisional Diffie-Hellman (DDH) assumption. We provide complete algorithmic specifications, formal security proofs including binding, hiding, replay resistance, and a rigorous security level analysis demonstrating ≈ 128-bit security for standard 256-bit elliptic curves. COMET-MPC is particularly suited for real-world ledger systems, authentication protocols, confidential databases, and privacy-preserving regulatory compliance where minimal interaction, minimal trust, and minimal leakage are paramount.