On perfectly secure 2PC in the OT-hybrid model

A well known result by Kilian (ACM 1988) asserts that general secure two computation (2PC) with statistical security, can be based on OT. Specifically, in the client-server model, where only one party -- the client -- receives an output, Kilian’s result shows that given the ability to call an ideal oracle that computes OT, two parties can securely compute an arbitrary function of their inputs with unconditional security. Ishai et al. (EUROCRYPT 2011) further showed that this can be done efficiently for every two-party functionality in $\mathrm{NC}^1$ in a single round. However, their results only achieve statistical security, namely, it is allowed to have some error in security. This leaves open the natural question as to which client-server functionalities can be computed with perfect security in the OT-hybrid model, and what is the round complexity of such computation. So far, only a handful of functionalities were known to have such protocols. In addition to the obvious theoretical appeal of the question towards better understanding secure computation, perfect, as opposed to statistical reductions, may be useful for designing secure multiparty protocols with high concrete efficiency, achieved by eliminating the dependence on a security parameter. In this work, we identify a large class of client-server functionalities $f:\mathcal{X}\times \mathcal{Y}\mapsto \{0,1\}$, where the server\u27s domain $\mathcal{X}$ is larger than the client\u27s domain $\mathcal{Y}$, that have a perfect reduction to OT. Furthermore, our reduction is 1-round using an oracle to secure evaluation of many parallel invocations of $\binom21$-bit-OT, as done by Ishai et al. (EUROCRYPT 2011). Interestingly, the set of functions that we are able to compute was previously identified by Asharov (TCC 2014) in the context of fairness in two-party computation, naming these functions full-dimensional. Our result also extends to randomized non-Boolean functions $f:\mathcal{X}\times \mathcal{Y}\mapsto\{0,\ldots,k-1\}$ satisfying $|\mathcal{X}|>(k-1)\cdot|\mathcal{Y}|$

Round-Optimal Secure Two-Party Computation from Trapdoor Permutations

In this work we continue the study on the round complexity of secure two-party computation with black-box simulation. Katz and Ostrovsky in CRYPTO 2004 showed a 5 (optimal) round construction assuming trapdoor permutations for the general case where both players receive the output. They also proved that their result is round optimal. This lower bound has been recently revisited by Garg et al. in Eurocrypt 2016 where a 4 (optimal) round protocol is showed assuming a simultaneous message exchange channel. Unfortunately there is no instantiation of the protocol of Garg et al. under standard polynomial-time hardness assumptions. In this work we close the above gap by showing a 4 (optimal) round construction for secure two-party computation in the simultaneous message channel model with black-box simulation, assuming trapdoor permutations against polynomial-time adversaries. Our construction for secure two-party computation relies on a special 4-round protocol for oblivious transfer that nicely composes with other protocols in parallel. We define and construct such special oblivious transfer protocol from trapdoor permutations. This building block is clearly interesting on its own. Our construction also makes use of a recent advance on non-malleability: a delayed-input 4-round non-malleable zero knowledge argument

Separating Two-Round Secure Computation From Oblivious Transfer

We consider the question of minimizing the round complexity of protocols for secure multiparty computation (MPC) with security against an arbitrary number of semi-honest parties. Very recently, Garg and Srinivasan (Eurocrypt 2018) and Benhamouda and Lin (Eurocrypt 2018) constructed such 2-round MPC protocols from minimal assumptions. This was done by showing a round preserving reduction to the task of secure 2-party computation of the oblivious transfer functionality (OT). These constructions made a novel non-black-box use of the underlying OT protocol. The question remained whether this can be done by only making black-box use of 2-round OT. This is of theoretical and potentially also practical value as black-box use of primitives tends to lead to more efficient constructions. Our main result proves that such a black-box construction is impossible, namely that non-black-box use of OT is necessary. As a corollary, a similar separation holds when starting with any 2-party functionality other than OT. As a secondary contribution, we prove several additional results that further clarify the landscape of black-box MPC with minimal interaction. In particular, we complement the separation from 2-party functionalities by presenting a complete 4-party functionality, give evidence for the difficulty of ruling out a complete 3-party functionality and for the difficulty of ruling out black-box constructions of 3-round MPC from 2-round OT, and separate a relaxed "non-compact" variant of 2-party homomorphic secret sharing from 2-round OT

CoVault: A Secure Analytics Platform

In a secure analytics platform, data sources consent to the exclusive use oftheir data for a pre-defined set of analytics queries performed by a specificgroup of analysts, and for a limited period. If the platform is secure under asufficiently strong threat model, it can provide the missing link to enablingpowerful analytics of sensitive personal data, by alleviating data subjects'concerns about leakage and misuse of data. For instance, many types of powerfulanalytics that benefit public health, mobility, infrastructure, finance, orsustainable energy can be made differentially private, thus alleviatingconcerns about privacy. However, no platform currently exists that issufficiently secure to alleviate concerns about data leakage and misuse; as aresult, many types of analytics that would be in the interest of data subjectsand the public are not done. CoVault uses a new multi-party implementation offunctional encryption (FE) for secure analytics, which relies on a uniquecombination of secret sharing, multi-party secure computation (MPC), anddifferent trusted execution environments (TEEs). CoVault is secure under a verystrong threat model that tolerates compromise and side-channel attacks on anyone of a small set of parties and their TEEs. Despite the cost of MPC, we showthat CoVault scales to very large data sizes using map-reduce based queryparallelization. For example, we show that CoVault can perform queries relevantto epidemic analytics at scale.<br

On the Power of Secure Two-Party Computation

Ishai, Kushilevitz, Ostrovsky and Sahai (STOC 2007, SIAM JoC 2009) introduced the powerful ``MPC-in-the-head\u27\u27 technique that provided a general transformation of information-theoretic MPC protocols secure against passive adversaries to a ZK proof in a ``black-box\u27\u27 way. In this work, we extend this technique and provide a generic transformation of any semi-honest secure two-party computation (2PC) protocol (with mild adaptive security guarantees) in the so called oblivious-transfer hybrid model to an adaptive ZK proof for any NP language, in a ``black-box\u27\u27 way assuming only one-way functions. Our basic construction based on Goldreich-Micali-Wigderson\u27s 2PC protocol yields an adaptive ZK proof with communication complexity proportional to quadratic in the size of the circuit implementing the NP relation. Previously such proofs relied on an expensive Karp reduction of the NP language to Graph Hamiltonicity (Lindell and Zarosim (TCC 2009, Journal of Cryptology 2011)). As an application of our techniques, we show how to obtain a ZK proof with an ``input-delayed\u27\u27 property for any NP language without relying on expensive Karp reductions that is black-box in the underlying one-way function. Namely, the input delayed property allows the honest prover\u27s algorithm to receive the actual statement to be proved only in the final round. We further generalize this to obtain a ``commit and prove\u27\u27 protocol with the same property where the prover commits to a witness w in the second message and proves a statement x regarding the witness w in zero-knowledge where the statement is determined only in the last round. This improves a previous construction of Lapidot and Shamir (Crypto 1990) that was designed specifically for the Graph Hamiltonicity problem and relied on the underlying primitives in a non-black-box way. Additionally, we provide a general transformation to construct a randomized encoding of a function f from any 2PC protocol that securely computes a related functionality (in a black-box way) from one-way functions. We show that if the 2PC protocol has mild adaptive security guarantees (which are satisfied by both the Yao\u27s and GMW\u27s protocol) then the resulting randomized encoding (RE) can be decomposed to an offline/online encoding

Post-Quantum Simulatable Extraction with Minimal Assumptions: Black-Box and Constant-Round

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\u2721) 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 post-extraction state of the adversary

Two-Round Concurrent 2PC from Sub-Exponential LWE

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)

Blazing Fast 2PC in the Offline/Online Setting with Security for Malicious Adversaries

Recently, several new techniques were presented to dramatically improve key parts of secure two-party computation (2PC) protocols that use the cut-and-choose paradigm on garbled circuits for 2PC with security against malicious adversaries. These include techniques for reducing the number of garbled circuits (Lindell 13, Huang et al.~13, Lindell and Riva 14, Huang et al.~14) and techniques for reducing the overheads besides garbled circuits (Mohassel and Riva 13, Shen and Shelat~13). We design a highly optimized protocol in the offline/online setting that makes use of all state-of-the-art techniques, along with several new techniques that we introduce. A crucial part of our protocol is a new technique for enforcing consistency of the inputs used by the party who garbles the circuits. This technique has both theoretical and practical advantages over \mbox{previous methods.} We present a prototype implementation of our new protocol, which is also the first implementation of the amortized cut-and-choose technique of Lindell and Riva (Crypto 2014). Our prototype achieves a speed of just \emph{$7$ ms in the online stage} and just $74$ ms in the offline stage per 2PC invoked, for securely computing AES in the presence of malicious adversaries (using 9 threads on two 2.9GHz machines located in the same Amazon region). We note that no prior work has gone below one second overall on average for the secure computation of AES for malicious adversaries (nor below 20ms in the online stage). Our implementation securely evaluates SHA-256 (which is a \emph{much bigger circuit}) with $33$ ms online time and $206$ ms offline time, per 2PC invoked