International Association
for Cryptologic Research

Secure computation is a cornerstone of modern cryptography and a rich body of research is devoted to understanding its round complexity. In this work, we consider two-party computation (2PC) protocols (where both parties receive output) that remain secure in the realistic setting where many instances of the protocol are executed in parallel (concurrent security). We obtain a two-round concurrent-secure 2PC protocol based on a single, standard, post-quantum assumption: The subexponential hardness of the learning-with-errors (LWE) problem. Our protocol is in the plain model, i.e., it has no trusted setup, and it is secure in the super-polynomial simulation framework of Pass (EUROCRYPT 2003). Since two rounds are minimal for (concurrent) 2PC, this work resolves the round complexity of concurrent 2PC from standard assumptions. As immediate applications, our work establishes feasibility results for interesting cryptographic primitives such as the first two-round password authentication key exchange (PAKE) protocol in the plain model and the first two-round concurrent secure computation protocol for quantum circuits (2PQC).

We revisit the well-studied problem of preventing steganographic communication in multi-party communications. While this is known to be a provably impossible task, we propose a new model that allows circumventing this impossibility. In our model, the parties first publish a single message during an honest \emph{non-interactive} pre-processing phase and then later interact in an execution phase. We show that in this model, it is indeed possible to prevent any steganographic communication in zero-knowledge protocols. Our solutions rely on standard cryptographic assumptions.

While NIZK arguments in the CRS model are widely studied, the question of what happens when the CRS is subverted has received little attention. In ASIACRYPT 2016, Bellare, Fuchsbauer, and Scafuro showed the first negative and positive results, proving also that it is impossible to achieve subversion soundness and (even non-subversion) zero knowledge at the same time. On the positive side, they constructed a sound and subversion-zero knowledge (Sub-ZK) non-succinct NIZK argument for NP. We consider the practically very relevant case of zk-SNARKs. We make Groth’s zk-SNARK for Circuit-SAT from EUROCRYPT 2016 computationally knowledge-sound and perfectly composable Sub-ZK with minimal changes. We only require the CRS trapdoor to be extractable and the CRS to be publicly verifiable. To achieve the latter, we add some new elements to the CRS and construct an efficient CRS verification algorithm. We also provide a definitional framework for knowledge-sound and Sub-ZK SNARKs.

Recently, Bellare et al. defined subversion-resistance (security in the case the CRS creator may be malicious) for NIZK. In particular, a Sub-ZK NIZK is zero-knowledge, even in the case of subverted CRS. We study Sub-ZK QA-NIZKs, where the CRS can depend on the language parameter. First, we observe that subversion zero-knowledge (Sub-ZK) in the CRS model corresponds to no-auxiliary-string non-black-box NIZK in the Bare Public Key model, and hence, the use of non-black-box techniques is needed to obtain Sub-ZK. Second, we give a precise definition of Sub-ZK QA-NIZKs that are (knowledge-)sound if the language parameter but not the CRS is subverted and zero-knowledge even if both are subverted. Third, we prove that the most efficient known QA-NIZK for linear subspaces by Kiltz and Wee is Sub-ZK under a new knowledge assumption that by itself is secure in (a weaker version of) the algebraic group model. Depending on the parameter setting, it is (knowledge-)sound under different non-falsifiable assumptions, some of which do not belong to the family of knowledge assumptions.