Structure-preserving Signature Scheme Research Articles

Compact Structure-Preserving Signatures with Almost Tight Security

In structure-preserving cryptography, every building block shares the same bilinear groups. These groups must be generated for a specific, a priori fixed security level, and thus, it is vital that the security reduction in all involved building blocks is as tight as possible. In this work, we present the first generic construction of structure-preserving signature schemes whose reduction cost is independent of the number of signing queries. Its chosen-message security is almost tightly reduced to the chosen-plaintext security of a structure-preserving public-key encryption scheme and the security of Groth–Sahai proof system. Technically, we adapt the adaptive partitioning technique by Hofheinz (Eurocrypt 2017) to the setting of structure-preserving signature schemes. To achieve a structure-preserving scheme, our new variant of the adaptive partitioning technique relies only on generic group operations in the scheme itself. Interestingly, however, we will use non-generic operations during our security analysis. Instantiated over asymmetric bilinear groups, the security of our concrete scheme is reduced to the external Diffie–Hellman assumption with linear reduction cost in the security parameter, independently of the number of signing queries. The signatures in our schemes consist of a larger number of group elements than those in other non-tight schemes, but can be verified faster, assuming their security reduction loss is compensated by increasing the security parameter to the next standard level.

Efficient Fully Structure-Preserving Signatures and Shrinking Commitments

In structure-preserving signatures, public keys, messages, and signatures are all collections of source group elements of some bilinear groups. In this paper, we introduce fully structure-preserving signature schemes, with the additional requirement that even secret keys are group elements. This strong property allows efficient non-interactive proofs of knowledge of the secret key, which is useful in designing cryptographic protocols under simulation-based security where online extraction of the secret key is needed. We present efficient constructions under simple standard assumptions and pursue even more efficient constructions with the extra property of randomizability based on the generic bilinear group model. An essential building block for our efficient standard model construction is a shrinking structure-preserving trapdoor commitment scheme, which is by itself an important primitive and of independent interest as it appears to contradict a known impossibility result that structure-preserving commitments cannot be shrinking. We argue that a relaxed binding property lets us circumvent the impossibility while still retaining the usefulness of the primitive in important applications as mentioned above.

Black-Box Accumulation: Collecting Incentives in a Privacy-Preserving Way

Abstract We formalize and construct black-box accumulation (BBA), a useful building block for numerous important user-centric protocols including loyalty systems, refund systems, and incentive systems (as, e.g., employed in participatory sensing and vehicle-to-grid scenarios). A core requirement all these systems share is a mechanism to let users collect and sum up values (call it incentives, bonus points, reputation points, etc.) issued by some other parties in a privacy-preserving way such that curious operators may not be able to link the different transactions of a user. At the same time, a group of malicious users may not be able to cheat the system by pretending to have collected a higher amount than what was actually issued to them. As a first contribution, we fully formalize the core functionality and properties of this important building block. Furthermore, we present a generic and non-interactive construction of a BBA system based on homomorphic commitments, digital signatures, and non-interactive zero-knowledge proofs of knowledge. For our construction, we formally prove security and privacy properties. Finally, we propose a concrete instantiation of our construction using Groth-Sahai commitments and proofs as well as the optimal structure-preserving signature scheme of Abe et al. and analyze its efficiency.

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

This paper presents efficient structure-preserving signature schemes based on simple assumptions such as decisional 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 of 11---14 group elements, which compares favorably to existing schemes whose security relies on q-type assumptions.

Non-Interactive Anonymous Credential Based on Structure-Preserving Signature

ABSTRACTStructure-preserving signature, as a special kind of digital signature, provides a way to construct modular cryptographic protocols with reasonable efficiency while retaining conceptual simplicity. This feature makes it suitable to be applied in the construction of non-interactive anonymous credential systems, which allows the user to convince a verifier of the possession of a certificate issued by the trusted authority anonymously and efficiently without interaction. In this paper, we design a secure and efficient structure-preserving signature scheme (SPSIG), and combine the scheme with Groth–Sahai non-interactive zero-knowledge (GSNIZK) proof system to construct a non-interactive anonymous credential scheme. The SPSIG is based on q-ADH-SDH assumption and can resist existential forgery in the chosen message attack. The message, signature, and verification keys are group elements, which are fully compatible with the GSNIZK system. The SXDH assumption is employed to instantiate the certificate-proving process, which is considered to be the most efficient instantiation at the moment. We analyze the efficiency and formally prove the security in the standard model. The result shows that our scheme satisfies correctness, zero knowledge, and unforgeability, and achieves identity authentication in the way of anonymity. Besides, our scheme has stronger anonymity, traceability, and non-interaction, and has lower communication cost compared with the conventional schemes.

Tightly secure signatures and public-key encryption

We construct the first public-key encryption (PKE) scheme whose chosen-ciphertext (i.e., IND-CCA) security can be proved under a standard assumption and does not degrade in either the number of users or the number of ciphertexts. In particular, our scheme can be safely deployed in settings in which no a-priori bound on the number of encryptions and/or users is known. As a central technical building block, we devise the first structure-preserving signature scheme with a tight security reduction. (This signature scheme may be of independent interest.) Combining this scheme with Groth---Sahai proofs yields a tightly simulation-sound non-interactive zero-knowledge proof system for group equations. If we use this proof system in the Naor---Yung double encryption scheme, we obtain a tightly IND-CCA secure PKE scheme from the decision linear assumption. We point out that our techniques are not specific to PKE security. Rather, we view our signature scheme and proof system as general building blocks that can help to achieve a tight security reduction.

Structure-Preserving Signatures and Commitments to Group Elements

A modular approach to constructing cryptographic protocols leads to simple designs but often inefficient instantiations. On the other hand, ad hoc constructions may yield efficient protocols at the cost of losing conceptual simplicity. We suggest a new design paradigm, structure-preserving cryptography, that provides a way to construct modular protocols with reasonable efficiency while retaining conceptual simplicity. A cryptographic scheme over a bilinear group is called structure-preserving if its public inputs and outputs consist of elements from the bilinear groups and their consistency can be verified by evaluating pairing-product equations. As structure-preserving schemes smoothly interoperate with each other, they are useful as building blocks in modular design of cryptographic applications. This paper introduces structure-preserving commitment and signature schemes over bilinear groups with several desirable properties. The commitment schemes include homomorphic, trapdoor and length-reducing commitments to group elements, and the structure-preserving signature schemes are the first ones that yield constant-size signatures on multiple group elements. A structure-preserving signature scheme is called automorphic if the public keys lie in the message space, which cannot be achieved by compressing inputs via a cryptographic hash function, as this would destroy the mathematical structure we are trying to preserve. Automorphic signatures can be used for building certification chains underlying privacy-preserving protocols. Among a vast number of applications of structure-preserving protocols, we present an efficient round-optimal blind-signature scheme and a group signature scheme with an efficient and concurrently secure protocol for enrolling new members.