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Register a new userForward-Secure Group Signatures from Lattices
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Added by
Khoa Nguyen
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Group signature is a fundamental cryptographic primitive, aiming to protect anonymity and ensure accountability of users. It allows group members to anonymously sign messages on behalf of the whole group, while incorporating a tracing mechanism to identify the signer of any suspected signature. Most of the existing group signature schemes, however, do not guarantee security once secret keys are exposed. To reduce potential damages caused by key exposure attacks, Song (ACMCCS 2001) put forward the concept of forward-secure group signature (FSGS), which prevents attackers from forging group signatures pertaining to past time periods even if a secret group signing key is revealed at the current time period. For the time being, however, all known secure FSGS schemes are based on number-theoretic assumptions, and are vulnerable against quantum computers. In this work, we construct the first lattice-based FSGS scheme. Our scheme is proven secure under the Short Integer Solution and Learning With Errors assumptions. At the heart of our construction is a scalable lattice-based key evolving mechanism, allowing users to periodically update their secret keys and to efficiently prove in zero-knowledge that key evolution process is done correctly. To realize this essential building block, we first employ the Bonsai tree structure by Cash et al. (EUROCRYPT 2010) to handle the key evolution process, and then develop Langlois et al.s construction (PKC 2014) to design its supporting zero-knowledge protocol.
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Group signatures allow users of a group to sign messages anonymously in the name of the group, while incorporating a tracing mechanism to revoke anonymity and identify the signer of any message. Since its introduction by Chaum and van Heyst (EUROCRYPT 1991), numerous proposals have been put forward, yielding various improvements on security, efficiency and functionality. However, a drawback of traditional group signatures is that the opening authority is given too much power, i.e., he can indiscriminately revoke anonymity and there is no mechanism to keep him accountable. To overcome this problem, Kohlweiss and Miers (PoPET 2015) introduced the notion of accountable tracing signatures (ATS) - an enhanced group signature variant in which the opening authority is kept accountable for his actions. Kohlweiss and Miers demonstrated a generic construction of ATS and put forward a concrete instantiation based on number-theoretic assumptions. To the best of our knowledge, no other ATS scheme has been known, and the problem of instantiating ATS under post-quantum assumptions, e.g., lattices, remains open to date. In this work, we provide the first lattice-based accountable tracing signature scheme. The scheme satisfies the security requirements suggested by Kohlweiss and Miers, assuming the hardness of the Ring Short Integer Solution (RSIS) and the Ring Learning With Errors (RLWE) problems. At the heart of our construction are a lattice-based key-oblivious encryption scheme and a zero-knowledge argument system allowing to prove that a given ciphertext is a valid RLWE encryption under some hidden yet certified key. These technical building blocks may be of independent interest, e.g., they can be useful for the design of other lattice-based privacy-preserving protocols.
Policy-based signatures (PBS) were proposed by Bellare and Fuchsbauer (PKC 2014) to allow an {em authorized} member of an organization to sign a message on behalf of the organization. The users authorization is determined by a policy managed by the organizations trusted authority, while the signature preserves the privacy of the organizations policy. Signing keys in PBS do not include user identity information and thus can be passed to others, violating the intention of employing PBS to restrict users signing capability. In this paper, we introduce the notion of {em traceability} for PBS by including user identity in the signing key such that the trusted authority will be able to open a suspicious signature and recover the signers identity should the needs arise. We provide rigorous definitions and stringent security notions of traceable PBS (TPBS), capturing the properties of PBS suggested by Bellare-Fuchsbauer and resembling the full traceability requirement for group signatures put forward by Bellare-Micciancio-Warinschi (Eurocrypt 2003). As a proof of concept, we provide a modular construction of TPBS, based on a signature scheme, an encryption scheme and a zero-knowledge proof system. Furthermore, to demonstrate the feasibility of achieving TPBS from concrete, quantum-resistant assumptions, we give an instantiation based on lattices.
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.
On todays Internet, combining the end-to-end security of TLS with Content Delivery Networks (CDNs) while ensuring the authenticity of connections results in a challenging delegation problem. When CDN servers provide content, they have to authenticate themselves as the origin server to establish a valid end-to-end TLS connection with the client. In standard TLS, the latter requires access to the secret key of the server. To curb this problem, multiple workarounds exist to realize a delegation of the authentication. In this paper, we present a solution that renders key sharing unnecessary and reduces the need for workarounds. By adapting identity-based signatures to this setting, our solution offers short-lived delegations. Additionally, by enabling forward-security, existing delegations remain valid even if the servers secret key leaks. We provide an implementation of the scheme and discuss integration into a TLS stack. In our evaluation, we show that an efficient implementation incurs less overhead than a typical network round trip. Thereby, we propose an alternative approach to current delegation practices on the web.
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.
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