Cryptology ePrint Archive: Report 2021/1656

Efficient Set Membership Proofs using MPC-in-the-Head

Aarushi Goel and Matthew Green and Mathias Hall-Andersen and Gabriel Kaptchuk

Abstract: Set membership proofs are an invaluable part of privacy preserving systems. These proofs allow a prover to demonstrate knowledge of a witness $w$ corresponding to a secret element $x$ of a public set, such that they jointly satisfy a given NP relation, {\em i.e.} $\mathcal{R}(w,x)=1$ and $x$ is a member of a public set $\{x_1, \ldots, x_\ell\}$. This allows the identity of the prover to remain hidden, eg. ring signatures and confidential transactions in cryptocurrencies.

In this work, we develop a new technique for efficiently adding logarithmic-sized set membership proofs to any MPC-in-the-head based zero-knowledge protocol (Ishai et al. [STOC'07]). We integrate our technique into an open source implementation of the state-of-the-art, post quantum secure zero-knowledge protocol of Katz et al. [CCS'18]. We find that using our techniques to construct ring signatures results in signatures (based only on symmetric key primitives) that are between 5 and 10 times smaller than state-of-the-art techniques based on the same assumptions. We also show that our techniques can be used to efficiently construct post-quantum secure RingCT from only symmetric key primitives.

Category / Keywords: cryptographic protocols / Zero-knowledge, Ring Signatures, Set Membership, Confidential Transactions

Original Publication (with minor differences): Privacy Enhancing Technologies Symposium 2022

Date: received 16 Dec 2021, last revised 22 Dec 2021

Contact author: aarushig at cs jhu edu, mgreen at cs jhu edu, ma at cs au dk, kaptchuk at bu edu

Available format(s): PDF | BibTeX Citation

Version: 20211222:161526 (All versions of this report)

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