International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Xiaohui Liang

Publications

Year
Venue
Title
2021
CRYPTO
Towards a Unified Approach to Black-Box Constructions of Zero-Knowledge Proofs 📺
Xiao Liang Omkant Pandey
General-purpose zero-knowledge proofs for all $\NP$ languages greatly simplify secure protocol design. However, they inherently require the code of the underlying relation. If the relation contains black-box calls to a cryptographic function, the code of that function must be known to use the ZK proof, even if both the relation and the proof require only black-box access to the function. Rosulek (Crypto'12) shows that non-trivial proofs for even simple statements, such as membership in the range of a one-way function, require non-black-box access. We propose an alternative approach to bypass Rosulek's impossibility result. Instead of asking for a ZK proof directly for the given one-way function $f$, we seek to construct a {\em new} one-way function $F$ given only black-box access to $f$, {\em and} an associated ZK protocol for proving non-trivial statements, such as range membership, over its output. We say that $F$, along with its proof system, is a {\em proof-based} one-way function. We similarly define proof-based versions of other primitives, specifically pseudo-random generators and collision-resistant hash functions. We show how to construct proof-based versions of each of the primitives mentioned above from their ordinary counterparts under mild but necessary restrictions over the input. More specifically, \begin{itemize} \item We first show that if the prover entirely chooses the input, then proof-based pseudo-random generators cannot be constructed from ordinary ones in a black-box manner, thus establishing that some restrictions over the input are necessary. \item We next present black-box constructions handling inputs of the form $(x,r)$ where $r$ is chosen uniformly by the verifier. This is similar to the restrictions in the widely used Goldreich-Levin theorem. The associated ZK proofs support range membership over the output as well as arbitrary predicates over prefixes of the input. \end{itemize} Our results open up the possibility that general-purpose ZK proofs for relations that require black-box access to the primitives above may be possible in the future without violating their black-box nature by instantiating them using proof-based primitives instead of ordinary ones.
2021
CRYPTO
Compact Ring Signatures from Learning With Errors 📺
Ring signatures allow a user to sign a message on behalf of a ``ring'' of signers, while hiding the true identity of the signer. As the degree of anonymity guaranteed by a ring signature is directly proportional to the size of the ring, an important goal in cryptography is to study constructions that minimize the size of the signature as a function of the number of ring members. In this work, we present the first compact ring signature scheme (i.e., where the size of the signature grows logarithmically with the size of the ring) from the (plain) learning with errors (LWE) problem. The construction is in the standard model and it does not rely on a trusted setup or on the random oracle heuristic. In contrast with the prior work of Backes \etal~[EUROCRYPT'2019], our scheme does not rely on bilinear pairings, which allows us to show that the scheme is post-quantum secure assuming the quantum hardness of LWE. At the heart of our scheme is a new construction of compact and statistically witness-indistinguishable ZAP arguments for NP $\cap$ coNP, that we show to be sound based on the plain LWE assumption. Prior to our work, statistical ZAPs (for all of NP) were known to exist only assuming \emph{sub-exponential} LWE. We believe that this scheme might find further applications in the future.
2007
EPRINT
Fully Secure Proxy Re-Encryption without Random Oracles
In a proxy re-encryption scheme, a semi-trusted proxy, with some additional information, can transform a ciphertext under Alice's public key into a new ciphertext under Bob's public key on the same message, but cannot learn any information about the messages encrypted under the public key of either Alice or Bob. In this paper, we propose two new unidirectional proxy re-encryption schemes, where a proxy can transform a ciphertext for Alice into a new ciphertext for Bob, but not vice versa. Note that, unidirectional proxy re-encryption is more powerful than bidirectional one, since a bidirectional scheme can always be implemented by an unidirectional one. Furthermore, these two schemes can be proved \emph{in the standard model}, chosen-ciphertext secure based on Decisional Bilinear Inverse Diffie-Hellman assumption and master key secure based on Extended Discrete Logarithm assumption. To our best knowledge, our proposals are the first fully secure (CCA-secure and master key secure) proxy re-encryption schemes in the standard model.
2007
EPRINT
Proxy Re-Signature Schemes without Random Oracles
To construct a suitable and secure proxy re-signature scheme is not an easy job, up to now, there exist only three schemes, one is proposed by Blaze et al. at EUROCRYPT 1998, and the others are proposed by Ateniese and Hohenbergerat ACM CCS 2005. However, none of these schemes is proved in the standard model (i.e., do not rely on the random oracle heuristic). In this paper, based on Waters' approach, we first propose a multi-use bidirectional proxy re-signature scheme, denoted as $S_{mb}$, which is existentially unforgeable in the standard model. And then, we extend $S_{mb}$ to be a multi-use bidirectional ID-based proxy re-signature scheme, denoted by $S_{id-mb}$, which is also existentially unforgeable in the standard model. Both of these two proposed schemes are computationally efficient, and their security bases on the Computational Diffie-Hellman (CDH) assumption.
2007
EPRINT
Short Group Signature without Random Oracles
Xiaohui Liang Zhenfu Cao Jun Shao Huang Lin
We construct a short group signature which is proven secure without random oracles. By making certain reasonable assumptions and applying the technique of non-interactive proof system, we prove that our scheme is full anonymity and full traceability. Compared with other related works, such as BW06, BW07, ours is more practical due to the short size of both public key and group signature.