Constant-size dynamic k-times anonymous authentication

Dynamic k-times anonymous authentication (k-TAA) schemes allow members of a group to be authenticated anonymously by application providers for a bounded number of times, where application providers can independently and dynamically grant or revoke access right to members in their own group. In this paper, we construct a dynamic k-TAA scheme with space and time complexities of O(log(k)) and a variant, in which the authentication protocol only requires constant time and space complexities at the cost of O(k) -sized public key. We also describe some tradeoff issues between different system characteristics. We detail all the zero-knowledge proof-of-knowledge protocols involved and show that our construction is secure in the random oracle model under the q-strong Diffie-Hellman assumption and q-decisional Diffie-Hellman inversion assumption. We provide a proof-of-concept implementation, experiment on its performance, and show that our scheme is practical

Improved Structure Preserving Signatures under Standard Bilinear Assumptions

We show that the recent structure-preserving signature (SPS) scheme of Kiltz, Pan and Wee [CRYPTO 2015], provably secure under the standard bilinear pairings group assumption SXDH, can be improved to have one less group element and one less pairing product equation in the signature verification step. Our improved SPS scheme only requires six group elements (five in one group, and one in the other), and two pairing product equations for verification. The number of pairing product equations is optimal, as it matches a known lower bound of Abe et al [CRYPTO 2011]. The number of group elements in the signature also approaches the known lower bound of four for SXDH assumption. Further, while the earlier scheme had a security reduction which incurred a security loss that is quadratic in number of queries $Q$, our novel security reduction incurs only a $Q \log{Q}$ factor loss in security. Structure-preserving signatures are used pervasively in group signatures, group encryptions, blind signatures, proxy signatures and many other anonymous credential applications. Our work directly leads to improvements in these schemes. Moreover, the improvements are usually of a higher multiplicative factor order, as these constructions use Groth-Sahai NIZK proofs for zero-knowledge verification of pairing-product equations. We also give our construction under the more general and standard \D_k-MDDH (Matrix-DDH) assumption. The signature size in our scheme is $3k+2$ elements in one group, and one element in the other. The number of pairing product equations required for verification is only $2k$, whereas the earlier schemes required at least $2k+1$ equations

Improved (Almost) Tightly-Secure Structure-Preserving Signatures

Structure Preserving Signatures (SPS) allow the signatures and the messages signed to be further encrypted while retaining the ability to be proven valid under zero-knowledge. In particular, SPS are tailored to have structure suitable for Groth-Sahai NIZK proofs. More precisely, the messages, signatures, and verification keys are required to be elements of groups that support efficient bilinear-pairings (bilinear groups), and the signature verification consists of just evaluating one or more bilinear-pairing product equations. Since Groth-Sahai NIZK proofs can (with zero-knowledge) prove the validity of such pairing product equations, it leads to interesting applications such as blind signatures, group signatures, traceable signatures, group encryption, and delegatable credential systems. In this paper, we further improve on the SPS scheme of Abe, Hofheinz, Nishimaki, Ohkubo and Pan (CRYPTO 2017) while maintaining only an $O(\lambda)$-factor security reduction loss to the SXDH assumption. In particular, we compress the size of the signatures by almost 40%, and reduce the number of pairing-product equations in the verifier from fifteen to seven. Recall that structure preserving signatures are used in applications by encrypting the messages and/or the signatures, and hence these optimizations are further amplified as proving pairing-product equations in Groth-Sahai NIZK system is not frugal. While our scheme uses an important novel technique introduced by Hofheinz (EuroCrypt 2017), i.e., structure-preserving adaptive partitioning, our approach to building the signature scheme is different and this leads to the optimizations mentioned. Thus we make progress towards an open problem stated by Abe et al (CRYPTO 2017) to design more compact SPS-es with smaller number of group elements

Efficient Tightly-Secure Structure-Preserving Signatures and Unbounded Simulation-Sound QA-NIZK Proofs

We show how to construct structure-preserving signatures (SPS) and unbounded quasi-adaptive non-interactive zero-knowledge (USS QA-NIZK) proofs with a tight security reduction to simple assumptions, being the first with a security loss of $\mathcal{O}(1)$. Specifically, we present a SPS scheme which is more efficient than existing tightly secure SPS schemes and from an efficiency point of view is even comparable with other non-tight SPS schemes. In contrast to existing work, however, we only have a lower security loss of $\mathcal{O}(1)$, resolving an open problem posed by Abe et al. (CRYPTO 2017). In particular, our tightly secure SPS scheme under the SXDH assumption requires 11 group elements. Moreover, we present the first tightly secure USS QA-NIZK proofs with a security loss of $\mathcal{O}(1)$ which also simultaneously have a compact common reference string and constant size proofs (5 elements under the SXDH assumption, which is only one element more than the best non-tight USS QA-NIZK). From a technical perspective, we present a novel randomization technique, inspired by Naor-Yung paradigm and adaptive partitioning, to obtain a randomized pseudorandom function (PRF). In particular, our PRF uses two copies under different keys but with shared randomness. Then we adopt ideas of Kiltz, Pan and Wee (CRYPTO 2015), who base their SPS on a randomized PRF, but in contrast to their non-tight reduction our approach allows us to achieve tight security. Similarly, we construct the first compact USS QA-NIZK proofs adopting techniques from Kiltz and Wee (EUROCRYPT 2015). We believe that the techniques introduced in this paper to obtain tight security with a loss of $\mathcal{O}(1)$ will have value beyond our proposed constructions

Practical Group-Signatures with Privacy-Friendly Openings

Group signatures allow creating signatures on behalf of a group, while remaining anonymous. To prevent misuse, there exists a designated entity, named the opener, which can revoke anonymity by generating a proof which links a signature to its creator. Still, many intermediate cases have been discussed in the literature, where not the full power of the opener is required, or the users themselves require the power to claim (or deny) authorship of a signature and (un-)link signatures in a controlled way. However, these concepts were only considered in isolation. We unify these approaches, supporting all these possibilities simultaneously, providing fine-granular openings, even by members. Namely, a member can prove itself whether it has created a given signature (or not), and can create a proof which makes two created signatures linkable (or unlinkable resp.) in a controlled way. Likewise, the opener can show that a signature was not created by a specific member and can prove whether two signatures stem from the same signer (or not) without revealing anything else. Combined, these possibilities can make full openings irrelevant in many use-cases. This has the additional benefit that the requirements on the reachability of the opener are lessened. Moreover, even in the case of an involved opener, our framework is less privacy-invasive, as the opener no longer requires access to the signed message. Our provably secure black-box CCA-anonymous construction with dynamic joins requires only standard building blocks. We prove its practicality by providing a performance evaluation of a concrete instantiation, and show that our non-optimized implementation is competitive compared to other, less feature-rich, notions

Threshold Structure-Preserving Signatures

Structure-preserving signatures (SPS) are an important building block for privacy-preserving cryptographic primitives, such as electronic cash, anonymous credentials, and delegatable anonymous credentials. In this work, we introduce the first threshold structure-preserving signature scheme (TSPS). This enables multiple parties to jointly sign a message, resulting in a standard, single-party SPS signature, and can thus be used as a replacement for applications based on SPS. We begin by defining and constructing SPS for indexed messages, which are messages defined relative to a unique index. We prove its security in the random oracle model under a variant of the generalized Pointcheval-Sanders assumption (PS). Moreover, we generalize this scheme to an indexed multi-message SPS for signing vectors of indexed messages, which we prove secure under the same assumption. We then formally define the notion of a TSPS and propose a construction based on our indexed multi-message SPS. Our TSPS construction is fully non-interactive, meaning that signers simply output partial signatures without communicating with the other signers. Additionally, signatures are short: they consist of 2 group elements and require 2 pairing product equations to verify. We prove the security of our TSPS under the security of our indexed multi-message SPS scheme. Finally, we show that our TSPS may be used as a drop-in replacement for UC-secure Threshold-Issuance Anonymous Credential (TIAC) schemes, such as Coconut, without the overhead of the Fischlin transform