Round Optimal Concurrent Non-Malleability from Polynomial Hardness

Non-malleable commitments are a central cryptographic primitive that guarantee security against man-in-the-middle adversaries, and their exact round complexity has been a subject of great interest. Pass (TCC 2013, CC 2016) proved that non-malleable commitments with respect to commitment are impossible to construct in less than three rounds, via black-box reductions to polynomial hardness assumptions. Obtaining a matching positive result has remained an open problem so far. While three-round constructions of non-malleable commitments have been achieved, beginning with the work of Goyal, Pandey and Richelson (STOC 2016), current constructions require super-polynomial assumptions. In this work, we settle the question of whether three-round non-malleable commitments can be based on polynomial hardness assumptions. We give constructions based on polynomial hardness of Decisional Diffie-Hellman assumption or Quadratic Residuosity or Nth Residuosity, together with ZAPs. Our protocols also satisfy concurrent non-malleability

Statistically Sender-Private OT from LPN and Derandomization

We construct a two-message oblivious transfer protocol with statistical sender privacy (SSP OT) based on the Learning Parity with Noise (LPN) Assumption and a standard Nisan-Wigderson style derandomization assumption. Beyond being of interest on their own, SSP OT protocols have proven to be a powerful tool toward minimizing the round complexity in a wide array of cryptographic applications from proofs systems, through secure computation protocols, to hard problems in statistical zero knowledge (SZK). The protocol is plausibly post-quantum secure. The only other constructions with plausible post quantum security are based on the Learning with Errors (LWE) Assumption. Lacking the geometric structure of LWE, our construction and analysis rely on a different set of techniques. Technically, we first construct an SSP OT protocol in the common random string model from LPN alone, and then derandomize the common random string. Most of the technical difficulty lies in the first step. Here we prove a robustness property of the inner product randomness extractor to a certain type of linear splitting attacks. A caveat of our construction is that it relies on the so called low noise regime of LPN. This aligns with our current complexity-theoretic understanding of LPN, which only in the low noise regime is known to imply hardness in SZK

Non-Malleable Codes Against Bounded Polynomial Time Tampering

We construct efficient non-malleable codes (NMC) that are (computationally) secure against tampering by functions computable in any fixed polynomial time. Our construction is in the plain (no-CRS) model and requires the assumptions that (1) $\mathbf{E}$ is hard for $\mathbf{NP}$ circuits of some exponential $2^{\beta n}$ ($\beta>0$) size (widely used in the derandomization literature), (2) sub-exponential trapdoor permutations exist, and (3) $\mathbf{P}$ certificates with sub-exponential soundness exist. While it is impossible to construct NMC secure against arbitrary polynomial-time tampering (Dziembowski, Pietrzak, Wichs, ICS \u2710), the existence of NMC secure against $O(n^c)$-time tampering functions (for any fixed $c$), was shown (Cheraghchi and Guruswami, ITCS \u2714) via a probabilistic construction. An explicit construction was given (Faust, Mukherjee, Venturi, Wichs, Eurocrypt \u2714) assuming an untamperable CRS with length longer than the runtime of the tampering function. In this work, we show that under computational assumptions, we can bypass these limitations. Specifically, under the assumptions listed above, we obtain non-malleable codes in the plain model against $O(n^c)$-time tampering functions (for any fixed $c$), with codeword length independent of the tampering time bound. Our new construction of NMC draws a connection with non-interactive non-malleable commitments. In fact, we show that in the NMC setting, it suffices to have a much weaker notion called quasi non-malleable commitments---these are non-interactive, non-malleable commitments in the plain model, in which the adversary runs in $O(n^c)$-time, whereas the honest parties may run in longer (polynomial) time. We then construct a 4-tag quasi non-malleable commitment from any sub-exponential OWF and the assumption that $\mathbf{E}$ is hard for some exponential size $\mathbf{NP}$-circuits, and use tag amplification techniques to support an exponential number of tags

A New Approach to Efficient Non-Malleable Zero-Knowledge

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 (IB-NMC). We show how to construct practical IB-NMC 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 IB-NMC, 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

Four-Round Black-Box Non-Malleable Commitments from One-Way Permutations

We construct the first four-round non-malleable commitment scheme based solely on the black-box use of one-to-one one-way functions. Prior to our work, all non-malleable commitment schemes based on black-box use of polynomial-time cryptographic primitives require more than $16$ rounds of interaction. A key tool for our construction is a proof system that satisfies a new definition of security that we call non-malleable zero-knowledge with respect to commitments. In a nutshell, such a proof system can be safely run in parallel with a (potentially interactive) commitment scheme. We provide an instantiation of this tool using the MPC-in-the-Head approach in combination with BMR

A New Approach to Post-Quantum Non-Malleability

We provide the first $\mathit{constant}$-$\mathit{round}$ construction of post-quantum non-malleable commitments under the minimal assumption that $\mathit{post}$-$\mathit{quantum}$ $\mathit{one}$-$\mathit{way}$ $\mathit{functions}$ exist. We achieve the standard notion of non-malleability with respect to commitments. Prior constructions required $\Omega(\log^*\lambda)$ rounds under the same assumption. We achieve our results through a new technique for constant-round non-malleable commitments which is easier to use in the post-quantum setting. The technique also yields an almost elementary proof of security for constant-round non-malleable commitments in the classical setting, which may be of independent interest. When combined with existing work, our results yield the first constant-round quantum-secure multiparty computation for both classical and quantum functionalities $\mathit{in}$ $\mathit{the}$ $\mathit{plain}$ $\mathit{model}$, under the $\mathit{polynomial}$ hardness of quantum fully-homomorphic encryption and quantum learning with errors

One-Message Zero Knowledge and Non-Malleable Commitments

We introduce a new notion of one-message zero-knowledge (1ZK) arguments that satisfy a weak soundness guarantee — the number of false statements that a polynomial-time non-uniform adversary can convince the verifier to accept is not much larger than the size of its non-uniform advice. The zero-knowledge guarantee is given by a simulator that runs in (mildly) super-polynomial time. We construct such 1ZK arguments based on the notion of multi-collision-resistant keyless hash functions, recently introduced by Bitansky, Kalai, and Paneth (STOC 2018). Relying on the constructed 1ZK arguments, subexponentially-secure time-lock puzzles, and other standard assumptions, we construct one-message fully-concurrent non-malleable commitments. This is the first construction that is based on assumptions that do not already incorporate non-malleability, as well as the first based on (subexponentially) falsifiable assumptions

Round-Optimal Secure Multi-Party Computation

Secure multi-party computation (MPC) is a central cryptographic task that allows a set of mutually distrustful parties to jointly compute some function of their private inputs where security should hold in the presence of a malicious adversary that can corrupt any number of parties. Despite extensive research, the precise round complexity of this standard-bearer\u27\u27 cryptographic primitive is unknown. Recently, Garg, Mukherjee, Pandey and Polychroniadou, in EUROCRYPT 2016 demonstrated that the round complexity of any MPC protocol relying on black-box proofs of security in the plain model must be at least four. Following this work, independently Ananth, Choudhuri and Jain, CRYPTO 2017 and Brakerski, Halevi, and Polychroniadou, TCC 2017 made progress towards solving this question and constructed four-round protocols based on non-polynomial time assumptions. More recently, Ciampi, Ostrovsky, Siniscalchi and Visconti in TCC 2017 closed the gap for two-party protocols by constructing a four-round protocol from polynomial-time assumptions. In another work, Ciampi, Ostrovsky, Siniscalchi and Visconti TCC 2017 showed how to design a four-round multi-party protocol for the specific case of multi-party coin-tossing. In this work, we resolve this question by designing a four-round actively secure multi-party (two or more parties) protocol for general functionalities under standard polynomial-time hardness assumptions with a black-box proof of security

Post-Quantum Multi-Party Computation

We initiate the study of multi-party computation for classical functionalities (in the plain model) with security against malicious polynomial-time quantum adversaries. We observe that existing techniques readily give a polynomial-round protocol, but our main result is a construction of constant-round post-quantum multi-party computation. We assume mildly super-polynomial quantum hardness of learning with errors (LWE), and polynomial quantum hardness of an LWE-based circular security assumption. Along the way, we develop the following cryptographic primitives that may be of independent interest: - A spooky encryption scheme for relations computable by quantum circuits, from the quantum hardness of an LWE-based circular security assumption. This yields the first quantum multi-key fully-homomorphic encryption scheme with classical keys. - Constant-round zero-knowledge secure against multiple parallel quantum verifiers from spooky encryption for relations computable by quantum circuits. To enable this, we develop a new straight-line non-black-box simulation technique against parallel verifiers that does not clone the adversary\u27s state. This forms the heart of our technical contribution and may also be relevant to the classical setting. - A constant-round post-quantum non-malleable commitment scheme, from the mildly super-polynomial quantum hardness of LWE