MoniPoly---An Expressive qq-SDH-Based Anonymous Attribute-Based Credential System

Modern attribute-based anonymous credential (ABC) systems benefit from special encodings that yield expressive and highly efficient show proofs on logical statements. The technique was first proposed by Camenisch and Groß, who constructed an SRSA-based ABC system with prime-encoded attributes that offers efficient AND, OR and NOT proofs. While other ABC frameworks have adopted constructions in the same vein, the Camenisch-Groß ABC has been the most expressive and asymptotically most efficient proof system to date, even if it was constrained by the requirement of a trusted message-space setup and an inherent restriction to finite-set attributes encoded as primes. In this paper, combining a new set commitment scheme and a SDH-based signature scheme, we present a provably secure ABC system that supports show proofs for complex statements. This construction is not only more expressive than existing approaches, it is also highly efficient under unrestricted attribute space due to its ECC protocols only requiring a constant number of bilinear pairings by the verifier; none by the prover. Furthermore, we introduce strong security models for impersonation and unlinkability under adaptive active and concurrent attacks to allow for the expressiveness of our ABC as well as for a systematic comparison to existing schemes. Given this foundation, we are the first to comprehensively formally prove the security of an ABC with expressive show proofs. Specifically, we prove the security against impersonation under the $q$-(co-)SDH assumption with a tight reduction. Besides the set commitment scheme, which may be of independent interest, our security models can serve as a foundation for the design of future ABC systems

Attribute-based Anonymous Credential: Optimization for Single-Use and Multi-Use

User attributes can be authenticated by an attribute-based anonymous credential while keeping the anonymity of the user. Most attribute-based anonymous credential schemes are designed specifically for either multi-use or single-use. In this paper, we propose a unified attribute-based anonymous credential system, in which users always obtain the same format of credential from the issuer. The user can choose to use it for an efficient multi-use or single-use show proof. It is a more user-centric approach than the existing schemes. Technically, we propose an interactive approach to the credential issuance protocol using a two-party computation with an additive homomorphic encryption. At the same time, it keeps the security property of impersonation resilience, anonymity, and unlinkability. Apart from the interactive protocol, we further design the show proofs for efficient single-use credentials which maintain the user anonymity

Non-Interactive Zero-Knowledge Functional Proofs

In this paper, we consider to generalize NIZK by empowering a prover to share a witness in a fine-grained manner with verifiers. Roughly, the prover is able to authorize a verifier to obtain extra information of witness, i.e., besides verifying the truth of the statement, the verifier can additionally obtain certain function of the witness from the accepting proof using a secret functional key provided by the prover. To fulfill these requirements, we introduce a new primitive called \emph{non-interactive zero-knowledge functional proofs (fNIZKs)}, and formalize its security notions. We provide a generic construction of fNIZK for any $\textsf{NP}$ relation $\mathcal{R}$, which enables the prover to share any function of the witness with a verifier. For a widely-used relation about set membership proof (implying range proof), we construct a concrete and efficient fNIZK, through new building blocks (set membership encryption and dual inner-product encryption), which might be of independent interest