Born and Raised Distributively: Fully Distributed Non-Interactive Adaptively-Secure Threshold Signatures with Short Shares

International audienceThreshold cryptography is a fundamental distributed computational paradigm for enhancing the availability and the security of cryptographic public-key schemes. It does it by dividing private keys into $n$ shares handed out to distinct servers. In threshold signature schemes, a set of at least $t+1 \leq n$ servers is needed to produce a valid digital signature. Availability is assured by the fact that any subset of $t+1$ servers can produce a signature when authorized. At the same time, the scheme should remain robust (in the fault tolerance sense) and unforgeable (cryptographically) against up to $t$ corrupted servers; {\it i.e.}, it adds quorum control to traditional cryptographic services and introduces redundancy. Originally, most practical threshold signatures have a number of demerits: They have been analyzed in a static corruption model (where the set of corrupted servers is fixed at the very beginning of the attack), they require interaction, they assume a trusted dealer in the key generation phase (so that the system is not fully distributed), or they suffer from certain overheads in terms of storage (large share sizes). In this paper, we construct practical {\it fully distributed} (the private key is born distributed), non-interactive schemes -- where the servers can compute their partial signatures without communication with other servers -- with adaptive security ({\it i.e.}, the adversary corrupts servers dynamically based on its full view of the history of the system). Our schemes are very efficient in terms of computation, communication, and scalable storage (with private key shares of size $O(1)$, where certain solutions incur $O(n)$ storage costs at each server). Unlike other adaptively secure schemes, our schemes are erasure-free (reliable erasure is a hard to assure and hard to administer property in actual systems). To the best of our knowledge, such a fully distributed highly constrained scheme has been an open problem in the area. In particular, and of special interest, is the fact that Pedersen's traditional distributed key generation (DKG) protocol can be safely employed in the initial key generation phase when the system is born -- although it is well-known not to ensure uniformly distributed public keys. An advantage of this is that this protocol only takes one round optimistically (in the absence of faulty player)

Efficient public-key cryptography with bounded leakage and tamper resilience

We revisit the question of constructing public-key encryption and signature schemes with security in the presence of bounded leakage and tampering memory attacks. For signatures we obtain the first construction in the standard model; for public-key encryption we obtain the first construction free of pairing (avoiding non-interactive zero-knowledge proofs). Our constructions are based on generic building blocks, and, as we show, also admit efficient instantiations under fairly standard number-theoretic assumptions. The model of bounded tamper resistance was recently put forward by Damgård et al. (Asiacrypt 2013) as an attractive path to achieve security against arbitrary memory tampering attacks without making hardware assumptions (such as the existence of a protected self-destruct or key-update mechanism), the only restriction being on the number of allowed tampering attempts (which is a parameter of the scheme). This allows to circumvent known impossibility results for unrestricted tampering (Gennaro et al., TCC 2010), while still being able to capture realistic tampering attack

A Domain Transformation for Structure-Preserving Signatures on Group Elements

We present a generic transformation that allows us to use a large class of pairing-based signatures to construct schemes for signing group elements in a structure preserving way. As a result of our transformation we obtain a new efficient signature scheme for signing a vector of group elements that is based only on the well established decisional linear assumption (DLIN). Moreover, the public keys and signatures of our scheme consist of group elements only, and a signature is verified by evaluating a set of pairing-product equations. In combination with the Groth-Sahai proof system, such a signature scheme is an ideal building block for many privacy-enhancing protocols. To do this, we start by proposing a new stateful signature scheme for signing vectors of exponents that is F-unforgeable under weak chosen message attacks. This signature scheme is of independent interest as it is compatible with Groth-Sahai proofs and secure under a computational assumption implied by DLIN. Then we give a general transformation for signing group elements based on signatures (for signing exponents) with efficient non-interactive zero-knowledge proofs. This transform also removes any dependence on state in the signature used to sign exponents. Finally, we obtain our result by instantiating this transformation with the above signature scheme and Groth-Sahai proofs

Group Signatures with Message-Dependent Opening: Formal Definitions and Constructions

This paper introduces a new capability for group signatures called message-dependent opening. It is intended to weaken the high trust placed on the opener; i.e., no anonymity against the opener is provided by an ordinary group signature scheme. In a group signature scheme with message-dependent opening (GS-MDO), in addition to the opener, we set up an admitter that is not able to extract any user’s identity but admits the opener to open signatures by specifying messages where signatures on the specified messages will be opened by the opener. The opener cannot extract the signer’s identity from any signature whose corresponding message is not specified by the admitter. This paper presents formal definitions of GS-MDO and proposes a generic construction of it from identity-based encryption and adaptive non-interactive zero-knowledge proofs. Moreover, we propose two specific constructions, one in the standard model and one in the random oracle model. Our scheme in the standard model is an instantiation of our generic construction but the message-dependent opening property is bounded. In contrast, our scheme in the random oracle model is not a direct instantiation of our generic construction but is optimized to increase efficiency and achieves the unbounded message-dependent opening property. Furthermore, we also demonstrate that GS-MDO implies identity-based encryption, thus implying that identity-based encryption is essential for designing GS-MDO schemes

Signatures with Flexible Public Key: Introducing Equivalence Classes for Public Keys

We introduce a new cryptographic primitive called signatures with flexible public key (SFPK). We divide the key space into equivalence classes induced by a relation R. A signer can efficiently change his or her key pair to a different representative of the same class, but without a trapdoor it is hard to distinguish if two public keys are related. Our primitive is motivated by structure-preserving signatures on equivalence classes (SPSEQ), where the partitioning is done on the message space. Therefore, both definitions are complementary and their combination has various applications. We first show how to efficiently construct static group signatures and self-blindable certificates by combining the two primitives. When properly instantiated, the result is a group signature scheme that has a shorter signature size than the current state-of-the-art scheme by Libert, Peters, and Yung from Crypto'15, but is secure in the same setting. In its own right, our primitive has stand-alone applications in the cryptocurrency domain, where it can be seen as a straightforward formalization of so-called stealth addresses. Finally, it can be used to build the first ring signature scheme in the plain model without trusted setup, where signature size depends only sub-linearly on the number of ring members. Thus, solving an open problem stated by Malavolta and Schroeder at ASIACRYPT'2017

Constant-Size Structure-Preserving Signatures: Generic Constructions and Simple Assumptions

This paper presents efficient structure-preserving signature schemes based on assumptions as simple as Decision-Linear. We first give two general frameworks for constructing fully secure signature schemes from weaker building blocks such as variations of one-time signatures and random-message secure signatures. They can be seen as refinements of the Even-Goldreich-Micali framework, and preserve many desirable properties of the underlying schemes such as constant signature size and structure preservation. We then instantiate them based on simple (i.e., not q-type) assumptions over symmetric and asymmetric bilinear groups. The resulting schemes are structure-preserving and yield constant-size signatures consisting o

New approaches to privacy preserving signatures

In this thesis we advance the theory and practice of privacy preserving digital signatures. Privacy preserving signatures such as group and ring signatures enable signers to hide in groups of potential signers. We design a cryptographic primitive called signatures with flexible public keys, which allows for modular construction of privacy preserving signatures. Its core is an equivalence relation between verification keys, such that key representatives can be transformed in their class to obscures their origin. The resulting constructions are more efficient than the state of the art, under the same or weaker assumptions. We show an extension of the security model of fully dynamic group signatures, which are those where members may join and leave the group over time. Our contribution here, which is facilitated by the new primitive, is the treatment of membership status as potentially sensitive information. In the theory of ring signatures, we show a construction of ring signatures which is the first in the literature with logarithmic signature size in the size of the ring without any trusted setup or reliance on non-standard assumptions. We show how to extend our techniques to the derived setting of linkable ring signatures, where different signatures of the same origin may be publicly linked. Here, we further revisit the notion of linkable anonymity, offering a significant strengthening compared to previous definitions.Diese Arbeit treibt die Theorie und Praxis der privatsphärewahrenden digitalen Signa- turen voran. Privatsphärewahrende Signaturen, wie Gruppen- oder Ringsignaturen erlauben es Zeichnern sich in einer Gruppe potenzieller Zeichner zu verstecken. Wir entwerfen mit Signatures with Flexible Public Keys einen kryptografischen Baustein zur modularen Konstruktion von privatsphärewahrenden Signaturen. Dessen Kern ist eine Äquivalenzrelation zwischen den Schlüsseln, sodass ein Schlüsselvertreter in seiner Klasse bewegt werden kann, um seinen Ursprung zu verschleiern. Darauf auf- bauende Konstruktionen sind effizienter als der Stand der Technik, unter gleichen oder schwächeren Annahmen. Wir erweitern das Sicherheitsmodell vollständig dynami- scher Gruppensignaturen, die es Mitgliedern erlauben der Gruppe beizutreten oder sie zu verlassen: Durch das neue Primitiv, wird die Behandlung der Mitgliedschaft als potenziell sensibel ermöglicht. In der Theorie der Ringsignaturen geben wir die erste Konstruktion, welche über eine logarithmische Signaturgröße verfügt, ohne auf eine Vorkonfiguration oder unübliche Annahmen vertrauen zu müssen. Wir übertragen unsere Ergebnisse auf das Feld der verknüpfbaren Ringsignaturen, die eine öffentliche Verknüpfung von zeichnergleichen Signaturen ermöglichen. Unsere Neubetrachtung des Begriffs der verknüpfbaren Anonymität führt zu einer signifikanten Stärkung im Vergleich zu früheren Definitionen

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