An Anonymous Credential System with Constant-Size Attribute Proofs for CNF Formulas with Negations

Okishima, Ryo; Nakanishi, Toru

doi:10.1587/transfun.2020tap0003

Cited by 2 publications

(8 citation statements)

References 16 publications

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“…As an immediate contribution, we rigorously define the necessary and stronger security notions for ABC systems. Our notions for security of impersonation resilience and unlinkability under adaptive active and concurrent attacks are stronger than those of the state-of-the-art ABC systems [16,20,31,40]. We prove the security of our construction with respect to the security against impersonation and linkability in the standard model, especially offering a tight reduction for impersonation resilience under the q-(co-)SDH assumption.…”

Section: Introductionmentioning

confidence: 92%

“…There were some attempts to apply Camenisch et al's accumulator [19] and its variants on P-signatures [35], LRSW-CL signature [34] and structure preserving signatures [6,40,43] to support complex non-interactive zero-knowledge (NIZK) show proofs. Among all, Sadiah et al's ABC system [43] offers the most expressive show proofs.…”

Section: Introductionmentioning

confidence: 99%

“…Considering only S = S F , their ABC system allows constant-size and constant-complexity NIZK show proofs for monotone formulas at the cost of issuing |P(A F )| credentials to every user where P(A F ) is the power set of the user attribute set A F . Instead of performing this expensive process during the issuing protocol, Okishima and Nakanishi's ABC system [40] generates P(S F ) during key generation and inflates the public key size with |P(S F )| signatures to enable constant-size non-interactive witnessindistinguishable (NIWI) show proofs for conjunctive composite formulas. There are also ABC systems [7,9] that were built on Pointcheval and Sanders' signature [41].…”

Section: Introductionmentioning

confidence: 99%

“…The security models in the two works, however, are not designed to cover expressive show proofs. Other frameworks [9,20] that formalized the commit-and-sign technique and even those [7,40,43] support show proofs on complex statements also fall short in this aspect.…”

Section: Introductionmentioning

confidence: 99%

“…Research Gap. Existing constructions yield considerable restrictions when expressive show proofs are concerned: The SRSA-based CG scheme [17] as well as accumulator-based schemes [6,34,35,40,43,45] constrain the attribute space to finite-set attributes (A F ∈ S F ) and require a trusted setup that inflates either the public-key size or the credential size. Their expressiveness and the computational complexity are no better than the pairing-based constructions [2,4,7,31,48] and the general ABC frameworks [9,16,20] alike, when only string attributes (A S ∈ S S ) are considered.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

MoniPoly—An Expressive q-SDH-Based Anonymous Attribute-Based Credential System

Tan

Groß

2020

Advances in Cryptology – ASIACRYPT 2020

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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 an 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, but 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, building upon the the q-(co-)SDH assumption, we prove the security against impersonation 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.

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Section: Introductionmentioning

confidence: 92%