International Association
for Cryptologic Research

Multi-signatures allow a set of parties to produce a single signature for a common message by combining their individual signatures. The result can be verified using the aggregated public key that represents the group of signers. Very recent work by Lehmann and Özbay (PKC '24) studied the use of multi-signatures for ad-hoc privacy-preserving group signing, formalizing the notion of multi-signatures with probabilistic yet verifiable key aggregation. Moreover, they proposed new BLS-type multi-signatures, allowing users holding a long-term key pair to engage with different groups, without the aggregated key leaking anything about the corresponding group. This enables key-reuse across different groups in a privacy-preserving way. Unfortunately, their technique cannot be applied to Schnorr-type multi-signatures, preventing state-of-the-art multi-signatures to benefit from those privacy features. In this work, we revisit the privacy framework from Lehmann and Özbay. Our first contribution is a generic lift that adds privacy to any multi-signature with deterministic key aggregation. As our second contribution, we study two concrete multi-signatures, and give dedicated transforms that take advantage of the underlying structures for improved efficiency. The first one is a slight modification of the popular MuSig2 scheme, achieving the strongest privacy property for free compared to the original scheme. The second is a variant of the lattice-based multi-signature scheme DualMS, making our construction the first post-quantum secure multi-signature for ad-hoc privacy-preserving group signing. The light overhead incurred by the modifications in our DualMS variant still allow us to benefit from the competitiveness of the original scheme.

Mercurial signatures are an extension of equivalence class signatures that allow malleability for the public keys, messages, and signatures within the respective classes. Unfortunately, the most efficient construction to date suffers from a weak public key class-hiding property, where the original signer with the signing key can link the public keys in the same class. This is a severe limitation in their applications, where the signer is often considered untrustworthy of privacy. This paper presents two-party and multi-party interactive threshold mercurial signatures that overcome the above limitation by eliminating the single entity who knows the signing key. For the general case, we propose two constructions. The first follows the same interactive structure as the two-party case, avoiding complex distributed computations such as randomness generation, inversion, and multiplication, and even eliminates the need for private communication between parties. The second is based on a blueprint for general multi-party computation using verifiable secret sharing, but adopting optimizations. We show applications in anonymous credential systems that individually fit the two-party and multi-party constructions. In particular, in the two-party case, our approach provides stronger privacy by completely removing the trust in the authorities. We also discuss more applications, from blind signatures to multi-signatures and threshold ring signatures. Finally, to showcase the practicality of our approach, we implement our interactive constructions and compare them against related alternatives.

Delegatable anonymous credentials (DACs) enable a root issuer to delegate credential-issuing power, allowing a delegatee to take a delegator role. To preserve privacy, credential recipients and verifiers should not learn anything about intermediate issuers in the delegation chain. One particularly efficient approach to constructing DACs is due to Crites and Lysyanskaya (CT-RSA '19). In contrast to previous approaches, it is based on mercurial signatures (a type of equivalence-class signature), offering a conceptually simple design that does not require extensive use of zero-knowledge proofs. Unfortunately, current constructions of ``CL-type'' DACs only offer a weak form of privacy-preserving delegation: if an adversarial issuer (even an honest-but-curious one) is part of a user's delegation chain, they can detect when the user shows its credential. This is because the underlying mercurial signature schemes allows a signer to identify his public key in a delegation chain. We propose CL-type DACs that overcome the above limitation based on a new mercurial signature scheme that provides adversarial public key class hiding which ensures that adversarial signers who participate in a user's delegation chain cannot exploit that fact to trace users. We achieve this introducing structured public parameters for each delegation level. Since the related setup produces critical trapdoors, we discuss techniques from updatable structured reference strings in zero-knowledge proof systems (Groth et al. CRYPTO '18) to guarantee the required privacy needs. In addition, we propose a simple way to realize revocation for CL-type DACs via the concept of revocation tokens. While we showcase this approach to revocation using our DAC scheme, it is generic and can be applied to any CL-type DAC system. Revocation is a vital feature that is largely unexplored and notoriously hard to achieve for DACs, thus providing it can help to make DAC schemes more attractive in practical applications.

Anonymous attribute-based credentials (ABCs) are a powerful tool allowing users to authenticate while maintaining privacy. When instantiated from structure-preserving signatures on equivalence classes (SPS-EQ) we obtain a controlled form of malleability, and hence increased functionality and privacy for the user. Existing constructions consider equivalence classes on the message space, allowing the joint randomization of credentials and the corresponding signatures on them. In this work, we additionally consider equivalence classes on the signing-key space. In this regard, we obtain a \emph{signer hiding} notion, where the issuing organization is not revealed when a user shows a credential. To achieve this, we instantiate the ABC framework of Fuchsbauer, Hanser, and Slamanig (FHS, Journal of Cryptology '19) with a recent SPS-EQ scheme (ASIACRYPT '19) modified to support a fully adaptive NIZK from the framework of Couteau and Hartmann (CRYPTO '20). We also show how to obtain Mercurial Signatures (CT-RSA, 2019), extending the application of our construction to anonymous delegatable credentials. To further increase functionality and efficiency, we augment the set-commitment scheme of FHS19 to support openings on attribute sets disjoint from those possessed by the user, while integrating a proof of exponentiation to allow for a more efficient verifier. Instantiating in the CRS model, we obtain an efficient credential system, anonymous under malicious organization keys, with increased expressiveness and privacy, proven secure in the standard model.