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DualRing: Generic Construction of Ring Signatures with Efficient Instantiations

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Advances in Cryptology – CRYPTO 2021 (CRYPTO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12825))

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Abstract

We introduce a novel generic ring signature construction, called DualRing, which can be built from several canonical identification schemes (such as Schnorr identification). DualRing differs from the classical ring signatures by its formation of two rings: a ring of commitments and a ring of challenges. It has a structural difference from the common ring signature approaches based on accumulators or zero-knowledge proofs of the signer index. Comparatively, DualRing has a number of unique advantages.

Considering the DL-based setting by using Schnorr identification scheme, our DualRing structure allows the signature size to be compressed into logarithmic size via an argument of knowledge system such as Bulletproofs. We further improve on the Bulletproofs argument system to eliminate about half of the computation while maintaining the same proof size. We call this Sum Argument and it can be of independent interest. This DL-based construction, named DualRing-EC, using Schnorr identification with Sum Argument has the shortest ring signature size in the literature without using trusted setup.

Considering the lattice-based setting, we instantiate DualRing by a canonical identification based on M-LWE and M-SIS. In practice, we achieve the shortest lattice-based ring signature, named DualRing-LB, when the ring size is between 4 and 2000. DualRing-LB is also 5\(\times \) faster in signing and verification than the fastest lattice-based scheme by Esgin et al. (CRYPTO’19).

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Notes

  1. 1.

    Here, we do not require the zero-knowledge property since the anonymity of DualRing is provided by the ring structure.

  2. 2.

    A ring signature of n users has some inherent limitations such that it requires at least n operations in signing and verification and storage of n public keys. These two limitations restrict the ring size to go up a lot for many practical applications. On the other hand, for very small ring sizes of, say, 2–5, the anonymity guarantee is very weak. For example, there has been attacks against Monero (cf. [26, 34]) that exploit the earlier use of very small rings of size \(<6\). Hence, one may argue that the most relevant range in practice falls inside 10–2000.

  3. 3.

    E.g., a DL-based public key \(g^x\) is a Pedersen commitment to zero.

  4. 4.

    The condition \(|\varDelta _c| > 8 q_h/\epsilon _b\) is not needed if we use the forking lemma in [7] with a looser security bound.

  5. 5.

    Which implicitly implies all users should use the same set of security parameters including the same group and generator for their \(\mathsf{sk}\) and \(\mathsf{pk}\).

  6. 6.

    For simplicity, we compare the schemes by assuming that a multi-exponentiation of size \(\ell \) is the same as \(\ell \) exponentiation in \(\mathbb {G}\).

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Authors and Affiliations

  1. The University of Hong Kong, Pok Fu Lam, Hong Kong

    Tsz Hon Yuen & Man Ho Au

  2. Department of Software Systems and Cybersecurity, Faculty of Information Technology, Monash University, Melbourne, Australia

    Muhammed F. Esgin & Joseph K. Liu

  3. CSIRO’s Data61, Melbourne, Australia

    Muhammed F. Esgin

  4. Rice University, Houston, USA

    Zhimin Ding

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Correspondence to Tsz Hon Yuen .

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Editors and Affiliations

  1. Columbia University, New York City, NY, USA

    Tal Malkin

  2. University of Michigan, Ann Arbor, MI, USA

    Chris Peikert

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Yuen, T.H., Esgin, M.F., Liu, J.K., Au, M.H., Ding, Z. (2021). DualRing: Generic Construction of Ring Signatures with Efficient Instantiations. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12825. Springer, Cham. https://doi.org/10.1007/978-3-030-84242-0_10

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