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Non-interactive Keyed-Verification Anonymous Credentials

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Public-Key Cryptography – PKC 2019 (PKC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11442))

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Abstract

Anonymous credential (\(\mathsf {AC}\)) schemes are protocols which allow for authentication of authorized users without compromising their privacy. Of particular interest are non-interactive anonymous credential (\(\mathsf {NIAC}\)) schemes, where the authentication process only requires the user to send a single message that still conceals its identity. Unfortunately, all known \(\mathsf {NIAC}\) schemes in the standard model require pairing based cryptography, which limits them to a restricted set of specific assumptions and requires expensive pairing computations. The notion of keyed-verification anonymous credential (\(\mathsf {KVAC}\)) was introduced in (Chase et al., CCS’14) as an alternative to standard anonymous credential schemes allowing for more efficient instantiations; yet, making existing \(\mathsf {KVAC}\) non-interactive either requires pairing-based cryptography, or the Fiat-Shamir heuristic.

In this work, we construct the first non-interactive keyed-verification anonymous credential (\(\mathsf {NIKVAC}\)) system in the standard model, without pairings. Our scheme is efficient, attribute-based, supports multi-show unlinkability, and anonymity revocation. We achieve this by building upon a combination of algebraic \(\mathsf {MAC}\) with the recent designated-verifier non-interactive zero-knowledge (\(\mathsf {DVNIZK}\)) proof of knowledge of (Couteau and Chaidos, Eurocrypt’18). Toward our goal of building \(\mathsf {NIKVAC}\), we revisit the security analysis of a \(\mathsf {MAC}\) scheme introduced in (Chase et al., CCS’14), strengthening its guarantees, and we introduce the notion of oblivious non-interactive zero-knowledge proof system, where the prover can generate non-interactive proofs for statements that he cannot check by himself, having only a part of the corresponding witness, and where the proof can be checked efficiently given the missing part of the witness. We provide an efficient construction of an oblivious \(\mathsf {DVNIZK}\), building upon the specific properties of the \(\mathsf {DVNIZK}\) proof system of (Couteau and Chaidos, Eurocrypt’18).

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Notes

  1. 1.

    In [11], the size of the group must be equal to the size of the plaintext space of a \(\mathsf {DVNIZK}\)-friendly encryption scheme, such as Paillier.

  2. 2.

    The protocol depends highly on the chosen \(\mathsf {MAC}\) scheme. Thus, we omit details in abstract instantiation.

  3. 3.

    The parameters \(({\mathsf {crs}},\mathsf {pk},\mathsf {ipp} _M)\) are fixed for all \(\Phi \in \varvec{\Phi } \), since they do not depend on the particular choice of \(\Phi \).

  4. 4.

    In this proof, this refers to the first property of definition 14.

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Correspondence to Geoffroy Couteau .

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Couteau, G., Reichle, M. (2019). Non-interactive Keyed-Verification Anonymous Credentials. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11442. Springer, Cham. https://doi.org/10.1007/978-3-030-17253-4_3

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