## Cryptology ePrint Archive: Report 2022/142

Efficient Verifiable Partially-Decryptable Commitments from Lattices and Applications

Muhammed F. Esgin and Ron Steinfeld and Raymond K. Zhao

Abstract: We introduce verifiable partially-decryptable commitments (VPDC), as a building block for constructing efficient privacy-preserving protocols supporting auditability by a trusted party. A VPDC is an extension of a commitment along with an accompanying proof, convincing a verifier that (i) the given commitment is well-formed and (ii) a certain part of the committed message can be decrypted using a (secret) trapdoor known to a trusted party.

We first formalize VPDCs and then introduce a general decryption feasibility result that overcomes the challenges in relaxed proofs arising in the lattice setting. Our general result can be applied to a wide class of Fiat-Shamir based protocols and may be of independent interest.

Next, we show how to extend the commonly used lattice-based Hashed-Message Commitment' (HMC) scheme into a succinct and efficient VPDC. In particular, we devise a novel gadget'-based Regev-style (partial) decryption method, compatible with efficient relaxed lattice-based zero-knowledge proofs. We prove the soundness of our VPDC in the setting of adversarial proofs, where a prover tries to create a valid VPDC output that fails in decryption.

To demonstrate the effectiveness of our results, we extend a private blockchain payment protocol, MatRiCT, by Esgin et al. (ACM CCS '19) into a formally auditable construction, which we call MatRiCT-Au, with very low communication and computation overheads over MatRiCT.

Category / Keywords: cryptographic protocols / Lattice, Zero Knowledge, Verifiable Partially-Decryptable Commitment, Auditable RingCT, Accountable Ring Signature

Original Publication (with major differences): IACR-PKC-2022

Contact author: muhammed esgin at monash edu, ron steinfeld at monash edu, raymond zhao at monash edu

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2022/142

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