We introduce ESC (Encrypted Sequential Context) Commitment, a novel commitment scheme designed for decrypt-free equality verification of encrypted data in asymmetric on-chain/off-chain execution models. Unlike classical commitment schemes that require explicit opening for verification, ESC enables blockchain-based verifiers to check equality between stored encrypted ledger values and user-provided inputs using only elliptic curve group operations, without access to secret keys or decryption oracles. ESC is inspired by Pedersen-style commitments but incorporates sequential nonce evolution and pairwise commitment contexts to ensure replay resistance and prevent correlation attacks across multiple verification sessions. The scheme separates commitment generation into two phases: the blockchain derives a pre-commitment from stored encrypted data, while the off-chain system constructs a matching commitment from user input under the same sequential context. Verification reduces to a simple group equality check. We formalize ESC’s security through rigorous game-based proofs, demonstrating computational hiding, binding, and our novel equality soundness property under standard elliptic curve assumptions (DDH, collision-resistant hashing). ESC achieves minimal on-chain leakage, single-use commitment semantics, and algebraic compatibility with EC-ElGamal partial homomorphic encryption, making it particularly suitable for vault-based ledger verification systems and privacy-preserving blockchain applications. Our concrete instantiation using elliptic curve groups achieves practical performance: commitment generation requires one scalar multiplication, verification requires one group operation (subtraction), and the on-chain footprint is a single elliptic curve point. We demonstrate ESC’s applicability to encrypted ledger verification, regulatory compliance systems, and privacy-preserving payment protocols.
Lee et al. (Tue,) studied this question.