Non-interactive Witness Indistinguishable Proofs Research Articles

Wildcarded identity-based ring signatures based on linearly homomorphic signatures

In identity-based ring signatures (IBRS) (Zhang and Kim, 2002), a binary string ID∈{0,1}L for L∈N, representing a unique information about a signer (e.g., e-mail address, telephone number), is associated with a secret-key. Its owner can anonymously signs a message under a set of IDs called ring including the signer’s ID. Wildcarded IBRS (WIBRS) (Ishizaka&Kiyomoto, ISC’20) is a generalization of IBRS, in which the ring consists of wildcarded IDs. The signer correctly signs iff her ID matches at least one of the wildcarded IDs. To the best of our knowledge, the only one known WIBRS scheme adaptively secure under standard assumptions is obtained as an instantiation of the attribute-based signatures scheme by Sakai et al. (PKC’16). It has signatures of length O(kL) and secret-keys of (constant) length O(1), where k denotes cardinality of the ring. In this paper, we propose a generic WIBRS construction, built by linearly homomorphic signatures and non-interactive witness-indistinguishable proof. We instantiate it to obtain a concrete WIBRS scheme secure under standard assumptions, whose length of signatures (resp. secret-keys) O(k+L) (resp. O(L)).

An Adaptively Secure Functional Encryption for Randomized Functions

Abstract Functional encryption (FE) can provide a fine-grained access control on the encrypted message. Therefore, it has been applied widely in security business. The previous works about functional encryptions most focused on the deterministic functions. The randomized algorithm has wide application, such as securely encryption algorithms against chosen ciphertext attack, privacy-aware auditing. Based on this, FE for randomized functions was proposed. The existing constructions are provided in a weaker selective security model, where the adversary is forced to output the challenge message before the start of experiment. This security is not enough in some scenes. In this work, we present a novel construction for FE, which supports the randomized functionalities. We use the technology of key encapsulated mechanism to achieve adaptive security under the simulated environment, where the adversary is allowed to adaptively choose the challenge message at any point in time. Our construction is built based on indistinguishability obfuscation, non-interactive witness indistinguishable proofs and perfectly binding commitment scheme.

Verifiable Random Functions from Non-interactive Witness-Indistinguishable Proofs

Verifiable random functions (VRFs) are pseudorandom functions where the owner of the seed, in addition to computing the function’s value y at any point x, can also generate a non-interactive proof $$\pi $$ that y is correct, without compromising pseudorandomness at other points. Being a natural primitive with a wide range of applications, considerable efforts have been directed toward the construction of such VRFs. While these efforts have resulted in a variety of algebraic constructions (from bilinear maps or the RSA problem), the relation between VRFs and other general primitives is still not well understood. We present new constructions of VRFs from general primitives, the main one being non-interactive witness-indistinguishable proofs (NIWIs). This includes: (1) a selectively secure VRF assuming NIWIs and non-interactive commitments. As usual, the VRF can be made adaptively secure assuming subexponential hardness of the underlying primitives. (2) An adaptively secure VRF assuming (polynomially hard) NIWIs, non-interactive commitments, and (single-key) constrained pseudorandom functions for a restricted class of constraints. The above primitives can be instantiated under various standard assumptions, which yields corresponding VRF instantiations, under different assumptions than were known so far. One notable example is a non-uniform construction of VRFs from subexponentially hard trapdoor permutations, or more generally, from verifiable pseudorandom generators (the construction can be made uniform under a standard derandomization assumption). This partially answers an open question by Dwork and Naor (FOCS ’00). The construction and its analysis are quite simple. Both draw from ideas commonly used in the context of indistinguishability obfuscation.

Fully adaptive attribute-based group signature in standard model

Attribute-based group signatures (ABGS) allow a signer to anonymously prove her membership in a group and her ownership of certain attributes, thus can find many applications where both privacy and authentication are required. In this paper, we present a new construction of ABGS based on Fuchsbauer’s automorphic signatures and the Groth and Sahai’s non-interactive witness-indistinguishable proof system. Compared with other ABGS in the literature, our construction is proved secure against fully adaptive adversaries in the standard model, instead of against selected adversaries in the random oracle model. In addition, it admits any signing policies if they can be described as monotone Boolean formulas, and the size of a signature is independent of the number of signers in the group.

Identity Traceable Attribute-Based Signature Scheme

In an attribute-based signature(ABS) scheme,the signer's identity keeps anonymous.To prevent the signer from abusing this property,Escala,Herranz,and Morillo proposed an identity traceable attribute-based signature scheme(EHM-ABS).Their scheme used an automorphic signature,and applied the non-interactive witness indistinguishable(NIWI) proofs many times.Inspired by Boyen,and Waters' identity-based compact group signature scheme,the study presents an identity traceable ABS scheme in the standard model.When issuing the attribute private key,the signer's identity is embedded.By using the NIWI proof of encrypting each bit of identity,this scheme achieves the traceability.To compare with EHM-ABS,this scheme reduces the number of applying the NIWI proofs when the order of the claimed attributes set is bigger than the quarter of the bit length of identity,and do not need to use automorphic signature.The security of this proposed scheme is based on the subgroup dicision and the computational diffie-Hellman assumptions.

Efficient Noninteractive Proof Systems for Bilinear Groups

Noninteractive zero-knowledge proofs and noninteractive witness-indistinguishable proofs have played a significant role in the theory of cryptography. However, lack of efficiency has prevented them from being used in practice. One of the roots of this inefficiency is that noninteractive zero-knowledge proofs have been constructed for general NP-complete languages such as Circuit Satisfiability, causing an expensive blowup in the size of the statement when reducing it to a circuit. The contribution of this paper is a general methodology for constructing very simple and efficient noninteractive zero-knowledge proofs and noninteractive witness-indistinguishable proofs that work directly for a wide class of languages that are relevant in practice (namely, ones involving the satisfiability of equations over bilinear groups), without needing a reduction to Circuit Satisfiability. Groups with bilinear maps have enjoyed tremendous success in the field of cryptography in recent years and have been used to construct a plethora of protocols. This paper provides noninteractive witness-indistinguishable proofs and noninteractive zero-knowledge proofs that can be used in connection with these protocols. Our goal is to spread the use of noninteractive cryptographic proofs from mainly theoretical purposes to the large class of practical cryptographic protocols based on bilinear groups.