Lattice-Based Group Signatures: Achieving Full Dynamicity (and Deniability) with Ease

In this work, we provide the first lattice-based group signature that offers full dynamicity (i.e., users have the flexibility in joining and leaving the group), and thus, resolve a prominent open problem posed by previous works. Moreover, we achieve this non-trivial feat in a relatively simple manner. Starting with Libert et al.'s fully static construction (Eurocrypt 2016) - which is arguably the most efficient lattice-based group signature to date, we introduce simple-but-insightful tweaks that allow to upgrade it directly into the fully dynamic setting. More startlingly, our scheme even produces slightly shorter signatures than the former, thanks to an adaptation of a technique proposed by Ling et al. (PKC 2013), allowing to prove inequalities in zero-knowledge. Our design approach consists of upgrading Libert et al.'s static construction (EUROCRYPT 2016) - which is arguably the most efficient lattice-based group signature to date - into the fully dynamic setting. Somewhat surprisingly, our scheme produces slightly shorter signatures than the former, thanks to a new technique for proving inequality in zero-knowledge without relying on any inequality check. The scheme satisfies the strong security requirements of Bootle et al.'s model (ACNS 2016), under the Short Integer Solution (SIS) and the Learning With Errors (LWE) assumptions. Furthermore, we demonstrate how to equip the obtained group signature scheme with the deniability functionality in a simple way. This attractive functionality, put forward by Ishida et al. (CANS 2016), enables the tracing authority to provide an evidence that a given user is not the owner of a signature in question. In the process, we design a zero-knowledge protocol for proving that a given LWE ciphertext does not decrypt to a particular message

A Code-Based Group Signature Scheme

International audienceIn this work we propose the first code-based group signature. As it will be described below, its security is based on a relaxation of the model of Bel-lare, Shi and Zhang [3] (BSZ model) verifying the properties of anonymity, traceability and non-frameability. Furthermore, it has numerous advantages over all existing post-quantum constructions and even competes (in terms of properties) with pairing based constructions: it allows to dynamically add new members and signature and public key sizes are constant with respect to the number of group members. Last but not least, our scheme can be extended into a traceable signature according to the definition of Kiayias, Tsiounis and Yung [19] (KTY model) and handles membership revocation. The main idea of our scheme consists in building a collision of two syndromes associated to two different matrices: a random one which enables to build a random syndrome from a chosen small weight vector; and a trapdoor matrix for the syndrome decoding problem, which permits to find a small weight preimage of the previous random syndrome. These two small weight vectors will constitute the group member's secret signing key whose knowledge will be proved thanks to a variation of Stern's authentication protocol. For applications , we consider the case of the code-based CFS signature scheme [11] of Courtois, Finiasz and Sendrier

Foundations of Fully Dynamic Group Signatures

Group signatures allow members of a group to anonymously sign on behalf of the group. Membership is administered by a designated group manager. The group manager can also reveal the identity of a signer if and when needed to enforce accountability and deter abuse. For group signatures to be applicable in practice, they need to support fully dynamic groups, i.e., users may join and leave at any time. Existing security definitions for fully dynamic group signatures are informal, have shortcomings, and are mutually incompatible. We fill the gap by providing a formal rigorous security model for fully dynamic group signatures. Our model is general and is not tailored toward a specific design paradigm and can therefore, as we show, be used to argue about the security of different existing constructions following different design paradigms. Our definitions are stringent and when possible incorporate protection against maliciously chosen keys. We consider both the case where the group management and tracing signatures are administered by the same authority, i.e., a single group manager, and also the case where those roles are administered by two separate authorities, i.e., a group manager and an opening authority. We also show that a specialization of our model captures existing models for static and partially dynamic schemes. In the process, we identify a subtle gap in the security achieved by group signatures using revocation lists. We show that in such schemes new members achieve a slightly weaker notion of traceability. The flexibility of our security model allows to capture such relaxation of traceability

SoK: Privacy-Preserving Signatures

Modern security systems depend fundamentally on the ability of users to authenticate their communications to other parties in a network. Unfortunately, cryptographic authentication can substantially undermine the privacy of users. One possible solution to this problem is to use privacy-preserving cryptographic authentication. These protocols allow users to authenticate their communications without revealing their identity to the verifier. In the non-interactive setting, the most common protocols include blind, ring, and group signatures, each of which has been the subject of enormous research in the security and cryptography literature. These primitives are now being deployed at scale in major applications, including Intel\u27s SGX software attestation framework. The depth of the research literature and the prospect of large-scale deployment motivate us to systematize our understanding of the research in this area. This work provides an overview of these techniques, focusing on applications and efficiency

Provably Secure Group Signature Schemes from Code-Based Assumptions

We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise problem, and a variant of the Syndrome Decoding problem. The construction produces smaller key and signature sizes than the previous group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed $2^{24}$, which is roughly comparable to the current population of the Netherlands. We develop the basic scheme further to achieve the strongest anonymity notion, i.e., CCA-anonymity, with a small overhead in terms of efficiency. The feasibility of two proposed schemes is supported by implementation results. Our two schemes are the first in their respective classes of provably secure groups signature schemes. Additionally, the techniques introduced in this work might be of independent interest. These are a new verifiable encryption protocol for the randomized McEliece encryption and a novel approach to design formal security reductions from the Syndrome Decoding problem.Comment: Full extension of an earlier work published in the proceedings of ASIACRYPT 201

A Revocable Group Signature Scheme with Scalability from Simple Assumptions and Its Application to Identity Management

Group signatures are signatures providing signer anonymity where signers can produce signatures on behalf of the group that they belong to. Although such anonymity is quite attractive considering privacy issues, it is not trivial to check whether a signer has been revoked or not. Thus, how to revoke the rights of signers is one of the major topics in the research on group signatures. In particular, scalability, where the signing and verification costs and the signature size are constant in terms of the number of signers N, and other costs regarding signers are at most logarithmic in N, is quite important. In this paper, we propose a revocable group signature scheme which is currently more efficient compared to previous all scalable schemes. Moreover, our revocable group signature scheme is secure under simple assumptions (in the random oracle model), whereas all scalable schemes are secure under q-type assumptions. We implemented our scheme by employing Barreto-Lynn-Scott curves of embedding degree 12 over a 455-bit prime field (BLS-12-455), and Barreto-Naehrig curves of embedding degree 12 over a 382-bit prime field (BN-12-382), respectively, by using the RELIC library. We showed that the online running times of our signing algorithm were approximately 14 msec (BLS-12-455) and 11 msec (BN-12-382), and those of our verification algorithm were approximately 20 msec (BLS-12-455) and 16 msec (BN-12-382), respectively. Finally, we showed that our scheme is applied to an identity management system proposed by Isshiki et al

Revocable Hierarchical Attribute-based Signatures from Lattices

Attribute-based Signatures (ABS) allow users to obtain attributes from issuing authorities, and sign messages whilst simultaneously proving compliance of their attributes with a verification policy. ABS demands that both the signer and the set of attributes used to satisfy a policy remain hidden to the verifier. Hierarchical ABS (HABS) supporting roots of trust and delegation were recently proposed to alleviate scalability issues in centralised ABS schemes. An important yet challenging property for privacy-preserving ABS is revocation, which may be applied to signers or some of the attributes they possess. Existing ABS schemes lack efficient revocation of either signers or their attributes, relying on generic costly proofs.Moreover, in HABS there is a further need to support revocation of authorities on the delegation paths, which is not provided by existing HABS constructions. This paper proposes a direct HABS scheme with a Verifier-Local Revocation (VLR) property. We extend the original HABS security model to address revocation and develop a new attribute delegation technique with appropriate VLR mechanism for HABS, which also implies the first ABS scheme to support VLR. Moreover, our scheme supports inner-product signing policies, offering a wider class of attribute relations than previous HABS schemes, and is the first to be based on lattices, which are thought to offer post-quantum security

Shortening the Libert-Peters-Yung Revocable Group Signature Scheme by Using the Random Oracle Methodology

At EUROCRYPT 2012, Libert, Peters and Yung (LPY) proposed the first scalable revocable group signature (R-GS) scheme in the standard model which achieves constant signing/verification costs and other costs regarding signers are at most logarithmic in N, where N is the maximum number of group members. However, although the LPY R-GS scheme is asymptotically quite efficient, this scheme is not sufficiently efficient in practice. For example, the signature size of the LPY scheme is roughly 10 times larger than that of an RSA signature (for 160-bit security). In this paper, we propose a compact R-GS scheme secure in the random oracle model that is efficient not only in the asymptotic sense but also in practical parameter settings. We achieve the same efficiency as the LPY scheme in an asymptotic sense, and the signature size is nearly equal to that of an RSA signature (for 160-bit security). It is particularly worth noting that our R-GS scheme has the smallest signature size compared to those of previous R-GS schemes which enable constant signing/verification costs. Our technique, which we call parallel Boneh–Boyen–Shacham group signature technique, helps to construct an R-GS scheme without following the technique used in LPY, i.e., we directly apply the Naor–Naor–Lotspiech framework without using any identity-based encryption