International Association
for Cryptologic Research

Recently, significant progress has been made toward quantumly secure multi-party computation (MPC) in the stand-alone setting. In sharp contrast, the picture of concurrently secure MPC (or even 2PC), for both classical and quantum functionalities, still remains unclear. Quantum information behaves in a fundamentally different way, making the job of adversary harder and easier at the same time. Thus, it is unclear if the positive or negative results from the classical setting still apply. This work initiates a systematic study of concurrent secure computation in the quantum setting. We obtain a mix of positive and negative results. We first show that assuming the existence of post-quantum one-way functions (PQ-OWFs), concurrently secure 2PC (and thus MPC) for quantum functionalities is impossible. Next, we focus on the bounded-concurrent setting, where we obtain simulation-sound zero-knowledge arguments for both NP and QMA, assuming PQ-OWFs. This is obtained by a new design of simulation-sound gadget, relying on the recent post-quantum non-malleable commitments by Liang, Pandey, and Yamakawa [arXiv:2207.05861], and the quantum rewinding strategy recently developed by Ananth, Chung, and La Placa [CRYPTO'21] for bounded-concurrent post-quantum ZK. Moreover, we show that our technique is general enough---It also leads to quantum-secure bounded-concurrent coin-flipping protocols, and eventually general-purpose 2PC and MPC, for both classical and quantum functionalities. All these constructions can be based on the quantum hardness of Learning with Errors.

This work revisits the security of classical signatures and ring signatures in a quantum world. For (ordinary) signatures, we focus on the arguably preferable security notion of {\em blind-unforgeability} recently proposed by Alagic et al.\ (Eurocrypt'20). We present two {\em short} signature schemes achieving this notion: one is in the quantum random oracle model, assuming quantum hardness of SIS; and the other is in the plain model, assuming quantum hardness of LWE with super-polynomial modulus. Prior to this work, the only known blind-unforgeable schemes are Lamport's one-time signature and the Winternitz one-time signature, and both of them are in the quantum random oracle model. For ring signatures, the recent work by Chatterjee et al.\ (Crypto'21) proposes a definition trying to capture adversaries with quantum access to the signer. However, it is unclear if their definition, when restricted to the classical world, is as strong as the standard security notion for ring signatures. They also present a construction that only {\em partially} achieves (even) this seeming weak definition, in the sense that the adversary can only conduct superposition attacks over the messages, but not the rings. We propose a new definition that does not suffer from the above issue. Our definition is an analog to the blind-unforgeability in the ring signature setting. Moreover, assuming the quantum hardness of LWE, we construct a compiler converting any blind-unforgeable (ordinary) signatures to a ring signature satisfying our definition.

Non-malleable zero-knowledge, originally introduced in the context of man-in-the-middle attacks, serves as an important building block to protect against concurrent attacks where different protocols may coexist and interleave. While this primitive admits almost optimal constructions in the plain model, they are several orders of magnitude slower in practice than standalone zero-knowledge. This is in sharp contrast to non-malleable commitments where practical constructions (under the DDH assumption) have been known for a while. We present a new approach for constructing efficient non-malleable zero-knowledge for all languages in NP, based on a new primitive called instance-based non-malleable commitment (IBNMC). We show how to construct practical IBNMC by leveraging the fact that simulators of sub-linear zero-knowledge protocols can be much faster than the honest prover algorithm. With an efficient implementation of IBNMC, our approach yields the first general-purpose non-malleable zero-knowledge protocol that achieves practical efficiency in the plain model. All of our protocols can be instantiated from symmetric primitives such as block-ciphers and hash functions, have reasonable efficiency in practice, and are general-purpose. Our techniques also yield the first efficient non-malleable commitment scheme without public-key assumptions.

From the minimal assumption of post-quantum semi-honest oblivious transfers, we build the first $\epsilon$-simulatable two-party computation (2PC) against quantum polynomial-time (QPT) adversaries that is both constant-round and black-box (for both the construction and security reduction). A recent work by Chia, Chung, Liu, and Yamakawa (FOCS'21) shows that post-quantum 2PC with standard simulation-based security is impossible in constant rounds, unless either $NP \subseteq BQP$ or relying on non-black-box simulation. The $\epsilon$-simulatability we target is a relaxation of the standard simulation-based security that allows for an arbitrarily small noticeable simulation error $\epsilon$. Moreover, when quantum communication is allowed, we can further weaken the assumption to post-quantum secure one-way functions (PQ-OWFs), while maintaining the constant-round and black-box property. Our techniques also yield the following set of constant-round and black-box two-party protocols secure against QPT adversaries, only assuming black-box access to PQ-OWFs: - extractable commitments for which the extractor is also an $\epsilon$-simulator; - $\epsilon$-zero-knowledge commit-and-prove whose commit stage is extractable with $\epsilon$-simulation; - $\epsilon$-simulatable coin-flipping; - $\epsilon$-zero-knowledge arguments of knowledge for $NP$ for which the knowledge extractor is also an $\epsilon$-simulator; - $\epsilon$-zero-knowledge arguments for $QMA$. At the heart of the above results is a black-box extraction lemma showing how to efficiently extract secrets from QPT adversaries while disturbing their quantum state in a controllable manner, i.e., achieving $\epsilon$-simulatability of the after-extraction state of the adversary.

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.

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.