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

Fully leakage-resilient signatures revisited: Graceful degradation, noisy leakage, and construction in the bounded-retrieval model

We construct new leakage-resilient signature schemes. Our schemes remain unforgeable against an adversary leaking arbitrary (yet bounded) information on the entire state of the signer (sometimes known as fully leakage resilience), including the random coin tosses of the signing algorithm. The main feature of our constructions is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible

暗号要素技術の一般的構成を介した高い安全性・高度な機能を備えた暗号要素技術の構成

Recent years have witnessed an active research on cryptographic primitives with complex functionality beyond simple encryption or authentication. A cryptographic primitive is required to be proposed together with a formal model of its usage and a rigorous proof of security under that model.This approach has suffered from the two drawbacks: (1) security models are defined in a very specific manner for each primitive, which situation causes the relationship between these security models not to be very clear, and (2) no comprehensive ways to confirm that a formal model of security really captures every possible scenarios in practice.This research relaxes these two drawbacks by the following approach: (1) By observing the fact that a cryptographic primitive A should be crucial for constructing another primitive B, we identify an easy-to-understand approach for constructing various cryptographic primitives.(2) Consider a situation in which there are closely related cryptographic primitives A and B, and the primitive A has no known security requirement that corresponds to some wellknown security requirement (b) for the latter primitive B.We argue that this situation suggests that this unknown security requirement for A can capture some practical attack. This enables us to detect unknown threats for various cryptographic primitives that have been missed bythe current security models.Following this approach, we identify an overlooked security threat for a cryptographic primitive called group signature. Furthermore, we apply the methodology (2) to the “revocable”group signature and obtain a new extension of public-key encryption which allows to restrict a plaintext that can be securely encrypted.通常の暗号化や認証にとどまらず, 複雑な機能を備えた暗号要素技術の提案が活発になっている. 暗号要素技術の安全性は利用形態に応じて, セキュリティ上の脅威をモデル化して安全性要件を定め, 新方式はそれぞれ安全性定義を満たすことの証明と共に提案される.既存研究では, 次の問題があった: (1) 要素技術ごとに個別に安全性の定義を与えているため, 理論的な体系化が不十分であった. (2) 安全性定義が実用上の脅威を完全に捉えきれているかの検証が難しかった.本研究は上記の問題を次の考え方で解決する. (1) ある要素技術(A) を構成するには別の要素技術(B) を部品として用いることが不可欠であることに注目し, 各要素技術の安全性要件の関連を整理・体系化して, 新方式を見通し良く構成可能とする. (2) 要素技術(B)で考慮されていた安全性要件(b) に対応する要素技術(A) の安全性要件が未定義なら, それを(A) の新たな安全性要件(a) として定式化する. これにより未知の脅威の検出が容易になる.グループ署名と非対話開示機能付き公開鍵暗号という2 つの要素技術について上記の考え方を適用して, グループ署名について未知の脅威を指摘する.また, 証明書失効機能と呼ばれる拡張機能を持つグループ署名に上記の考え方を適用して, 公開鍵暗号についての新たな拡張機能である, 暗号化できる平文を制限できる公開鍵暗号の効率的な構成法を明らかにする.電気通信大学201

Short Group Signatures via Structure-Preserving Signatures: Standard Model Security from Simple Assumptions

International audienceGroup signatures are a central cryptographic primitive which allows users to sign messages while hiding their identity within a crowd of group members. In the standard model (without the random oracle idealization), the most efficient constructions rely on the Groth-Sahai proof systems (Euro-crypt'08). The structure-preserving signatures of Abe et al. (Asiacrypt'12) make it possible to design group signatures based on well-established, constant-size number theoretic assumptions (a.k.a. " simple assumptions ") like the Symmetric eXternal Diffie-Hellman or Decision Linear assumptions. While much more efficient than group signatures built on general assumptions, these constructions incur a significant overhead w.r.t. constructions secure in the idealized random oracle model. Indeed, the best known solution based on simple assumptions requires 2.8 kB per signature for currently recommended parameters. Reducing this size and presenting techniques for shorter signatures are thus natural questions. In this paper, our first contribution is to significantly reduce this overhead. Namely, we obtain the first fully anonymous group signatures based on simple assumptions with signatures shorter than 2 kB at the 128-bit security level. In dynamic (resp. static) groups, our signature length drops to 1.8 kB (resp. 1 kB). This improvement is enabled by two technical tools. As a result of independent interest, we first construct a new structure-preserving signature based on simple assumptions which shortens the best previous scheme by 25%. Our second tool is a new method for attaining anonymity in the strongest sense using a new CCA2-secure encryption scheme which is simultaneously a Groth-Sahai commitment

Zero-Knowledge Arguments for Matrix-Vector Relations and Lattice-Based Group Encryption

International audienceGroup encryption (GE) is the natural encryption analogue of group signatures in that it allows verifiably encrypting messages for some anonymous member of a group while providing evidence that the receiver is a properly certified group member. Should the need arise, an opening authority is capable of identifying the receiver of any ciphertext. As introduced by Kiayias, Tsiounis and Yung (Asiacrypt'07), GE is motivated by applications in the context of oblivious retriever storage systems, anonymous third parties and hierarchical group signatures. This paper provides the first realization of group encryption under lattice assumptions. Our construction is proved secure in the standard model (assuming interaction in the proving phase) under the Learning-With-Errors (LWE) and Short-Integer-Solution (SIS) assumptions. As a crucial component of our system, we describe a new zero-knowledge argument system allowing to demonstrate that a given ciphertext is a valid encryption under some hidden but certified public key, which incurs to prove quadratic statements about LWE relations. Specifically, our protocol allows arguing knowledge of witnesses consisting of X ∈ Z m×n q , s ∈ Z n q and a small-norm e ∈ Z m which underlie a public vector b = X · s + e ∈ Z m q while simultaneously proving that the matrix X ∈ Z m×n q has been correctly certified. We believe our proof system to be useful in other applications involving zero-knowledge proofs in the lattice setting

ClaimChain: Improving the Security and Privacy of In-band Key Distribution for Messaging

The social demand for email end-to-end encryption is barely supported by mainstream service providers. Autocrypt is a new community-driven open specification for e-mail encryption that attempts to respond to this demand. In Autocrypt the encryption keys are attached directly to messages, and thus the encryption can be implemented by email clients without any collaboration of the providers. The decentralized nature of this in-band key distribution, however, makes it prone to man-in-the-middle attacks and can leak the social graph of users. To address this problem we introduce ClaimChain, a cryptographic construction for privacy-preserving authentication of public keys. Users store claims about their identities and keys, as well as their beliefs about others, in ClaimChains. These chains form authenticated decentralized repositories that enable users to prove the authenticity of both their keys and the keys of their contacts. ClaimChains are encrypted, and therefore protect the stored information, such as keys and contact identities, from prying eyes. At the same time, ClaimChain implements mechanisms to provide strong non-equivocation properties, discouraging malicious actors from distributing conflicting or inauthentic claims. We implemented ClaimChain and we show that it offers reasonable performance, low overhead, and authenticity guarantees.Comment: Appears in 2018 Workshop on Privacy in the Electronic Society (WPES'18

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

Signature Schemes with Efficient Protocols and Dynamic Group Signatures from Lattice Assumptions

International audienceA recent line of works – initiated by Gordon, Katz and Vaikuntanathan (Asiacrypt 2010) – gave lattice-based realizations of privacy-preserving protocols allowing users to authenticate while remaining hidden in a crowd. Despite five years of efforts, known constructions remain limited to static populations of users, which cannot be dynamically updated. For example, none of the existing lattice-based group signatures seems easily extendable to the more realistic setting of dynamic groups. This work provides new tools enabling the design of anonymous authen-tication systems whereby new users can register and obtain credentials at any time. Our first contribution is a signature scheme with efficient protocols, which allows users to obtain a signature on a committed value and subsequently prove knowledge of a signature on a committed message. This construction, which builds on the lattice-based signature of Böhl et al. (Eurocrypt'13), is well-suited to the design of anonymous credentials and dynamic group signatures. As a second technical contribution, we provide a simple, round-optimal joining mechanism for introducing new members in a group. This mechanism consists of zero-knowledge arguments allowing registered group members to prove knowledge of a secret short vector of which the corresponding public syndrome was certified by the group manager. This method provides similar advantages to those of structure-preserving signatures in the realm of bilinear groups. Namely, it allows group members to generate their public key on their own without having to prove knowledge of the underlying secret key. This results in a two-round join protocol supporting concurrent enrollments, which can be used in other settings such as group encryption