Improved Security for Linearly Homomorphic Signatures: A Generic Framework

We propose a general framework that converts (ordinary) signature schemes having certain properties into linearly homomorphic signature schemes, i.e., schemes that allow authentication of linear functions on signed data. The security of the homomorphic scheme follows from the same computational assumption as is used to prove security of the underlying signature scheme. We show that the following signature schemes have the required properties and thus give rise to secure homomorphic signatures in the standard model: - The scheme of Waters (Eurocrypt 2005), secure under the computational Diffie-Hellman asumption in bilinear groups. - The scheme of Boneh and Boyen (Eurocrypt 2004, J. Cryptology 2008), secure under the $q$-strong Diffie-Hellman assumption in bilinear groups. - The scheme of Gennaro, Halevi, and Rabin (Eurocrypt 1999), secure under the strong RSA assumption. - The scheme of Hohenberger and Waters (Crypto 2009), secure under the RSA assumption. Our systems not only allow weaker security assumptions than were previously available for homomorphic signatures in the standard model, but also are secure in a model that allows a stronger adversary than in other proposed schemes. Our framework also leads to efficient linearly homomorphic signatures that are secure against our stronger adversary under weak assumptions (CDH or RSA) in the random oracle model; all previous proofs of security in the random oracle model break down completely when faced with our stronger adversary

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

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

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 UC Commitment Extension with Homomorphism for Free (and Applications)

Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment. We obtain amortized linear computational complexity in the length of the input messages and rate 1. Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters. While the previously best constructions use UC oblivious transfer as the main building block, our constructions only require extractable commitments and PRGs, achieving better concrete efficiency and offering new insights into the sufficient conditions for obtaining homomorphic UC commitments. Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic. These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments. Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge

Quasi-Adaptive NIZK for Linear Subspaces Revisited

Non-interactive zero-knowledge (NIZK) proofs for algebraic relations in a group, such as the Groth-Sahai proofs, are an extremely powerful tool in pairing-based cryptography. A series of recent works focused on obtaining very efficient NIZK proofs for linear spaces in a weaker quasi-adaptive model. We revisit recent quasi-adaptive NIZK constructions, providing clean, simple, and improved constructions via a conceptually different approach inspired by recent developments in identity-based encryption. We then extend our techniques also to linearly homomorphic structure-preserving signatures, an object both of independent interest and with many applications

Linearly Homomorphic Structure-Preserving Signatures and Their Applications

Structure-preserving signatures (SPS) are signature schemes where messages, signatures and public keys all consist of elements of a group over which a bilinear map is efficiently computable. This property makes them useful in cryptographic protocols as they nicely compose with other algebraic tools (like the celebrated Groth-Sahai proof systems). In this paper, we consider SPS systems with homomorphic properties and suggest applications that have not been provided before (in particular, not by employing ordinary SPS). We build linearly homomorphic structure-preserving signatures under simple assumptions and show that the primitive makes it possible to verify the calculations performed by a server on outsourced encrypted data (i.e., combining secure computation and authenticated computation to allow reliable and secure cloud storage and computation, while freeing the client from retaining cleartext storage). Then, we give a generic construction of non-malleable (and actually simulation-sound) commitment from any linearly homomorphic SPS. This notably provides the first constant-size non-malleable commitment to group elements