We provide new two-round multiparty secure computation (MPC) protocols in the dishonest majority setting assuming the minimal assumption that two-round oblivious transfer (OT) exists. If the assumed two-round OT protocol is secure against semi-honest adversaries (in the plain model) then so is our two-round MPC protocol. Similarly, if the assumed two-round OT protocol is secure against malicious adversaries (in the common random/reference string model) then so is our two-round MPC protocol. Previously, two-round MPC protocols were only known under relatively stronger computational assumptions.
We provide new two-round multiparty secure computation (MPC) protocols in the dishonest majority setting assuming the minimal assumption that two-round oblivious transfer (OT) exists. If the assumed two-round OT protocol is secure against semi-honest adversaries (in the plain model) then so is our two-round MPC protocol. Similarly, if the assumed two-round OT protocol is secure against malicious adversaries (in the common random/reference string model) then so is our two-round MPC protocol. Previously, two-round MPC protocols were only known under relatively stronger computational assumptions.
Secure Multiparty Computation (MPC) allows a set of parties, each having its own private data, to compute a function of their joint data such that the parties only learn the output of this function and everything else about their data is hidden. MPC is a fundamental cryptographic abstraction that captures many other natural cryptographic primitives as special cases. It also has a wide range of practical applications such as conducting secure electronic auctions, delegating sensitive computation to untrusted cloud service providers, secure computation on genomic data and training machine learning models on private data.A long-standing open problem in this area is to construct MPC protocols that have {\\it optimal} (two-round) round complexity under the {\\it weakest} possible cryptographic hardness assumptions.We {\\it completely resolve} this problem by showing lower bounds and matching upper bounds on the hardness assumptions required for constructing round-optimal MPC. Specifically, we obtain the following results.\\begin{itemize}\\item \\textbf{Black-Box Separation.} We show that there exists no construction of two-round semi-honest MPC protocol for general functions that makes black-box use of a two-round oblivious transfer. As a corollary, a similar separation holds when starting with any 2-party functionality other than oblivious transfer. \\item \\textbf{Non-Black-Box Construction.} We show that the above negative result can be bypassed by making non-black-box use of a two-round oblivious transfer. Specifically, starting from a semi-honest (resp. malicious) secure two-round oblivious transfer protocol, we construct a two-round MPC protocol against semi-honest (resp. malicious) adversaries. \\end{itemize}Since any two-round MPC protocol for general functionalities implies a two-round oblivious transfer as a special case, the above two results show that non-black-box use of oblivious transfer is {\\it necessary and sufficient} to construct round-optimal MPC protocols.
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.
We present a round-efficient black-box construction of a general multi-party computation (MPC) protocol that satisfies composability in the plain model. The security of our protocol is proven in the angel-based UC framework [Prabhakaran and Sahai, STOC’04] under the minimal assumption of the existence of semi-honest oblivious transfer protocols. The round complexity of our protocol is max(O(log2n),O(ROT))
when the round complexity of the underlying oblivious transfer protocol is ROT
. Since constant-round semi-honest oblivious transfer protocols can be constructed under standard assumptions (such as the existence of enhanced trapdoor permutations), our result gives a O(log2n)
-round protocol under these assumptions. Previously, only an O(max(nϵ,ROT))
-round protocol was shown, where ϵ>0
is an arbitrary constant. We obtain our MPC protocol by constructing a O(log2n)
-round CCA-secure commitment scheme in a black-box way under the assumption of the existence of one-way functions.
Secure Multi-Party Computation (MPC) protocols allow a group of mutually distrusting users to compute a function jointly on their inputs without revealing any information beyond the output. For many years, implementations of MPC protocols have targeted security against semi-honest adversaries, i.e., attackers are assumed to execute the protocol honestly but try to learn private information after the fact. Protocols secure against stronger and more realistic malicious adversaries, who could behave arbitrarily during the protocol execution, were known to exist but were much less efficient. This thesis introduces a new paradigm to construct extremely efficient MPC protocols with malicious security. In particular, this thesis consists of three major contributions. 1. We introduce the authenticated garbling framework, and present an efficient concrete instantiation of the protocol. The resulting protocol partially closes the gap between semi-honest and malicious MPC protocols asymptotically; the implementation of the protocol represents the state-of-the-art system for malicious two-party computation. 2. We discuss how to apply authenticated garbling to the multi-party setting, where all-but-one parties can be corrupted by the adversary. The resulting protocol improves upon the best previous constant-round protocol by orders of magnitude. We also present a system that, for the first time, enables MPC executions among hundreds of parties, distributed globally. 3. We present a series of optimizations to two-party authenticated garbling by interpreting authenticated garbling in a new way. The improved malicious protocol has essentially the same concrete efficiency as the best semi-honest protocol in the preprocessing model. 4. We develop these protocols in EMP-toolkit, a practical and efficient MPC tool that can be used to build new protocols and to develop applications using our existing protocols.
The need for Cryptography arises out of the following fundamental question: can we perform useful computation while ensuring that an adversary does not learn anything about our private sensitive data? The notion of secure multiparty computation (MPC) \\cite{Yao82,GMW87} is a unifying framework for general secure protocols. MPC allows mutually distrusting parties to jointly evaluate any efficiently computable function on their private inputs in such a manner that each party does not learn anything beyond the output of the function. In this thesis, we study the question of building MPC protocols in various security models from standard cryptographic assumptions while minimizing the number of rounds of interaction amongst parties. In the first part of this thesis, (in a joint work with Vipul Goyal, Abhishek Jain, Yael Kalai, Dakshita Khurana and Amit Sahai, CRYPTO 2018) we construct the first round-optimal (i.e., four round) MPC protocol for general functions based on polynomially hard DDH (or QR or Nth-Residuosity) in the plain model where parties have access to no trusted setup. We further show how to overcome the four-round barrier for MPC by constructing a three-round protocol for ``list coin-tossing'' -- a slight relaxation of coin-tossing that suffices for most conceivable applications -- based on polynomially hard DDH (or QR or Nth-Residuosity). This result generalizes to randomized input-less functionalities. Previously, four round MPC protocols required sub-exponential-time hardness assumptions and no multi-party three-round protocols were known for any relaxed security notions with polynomial-time simulation against malicious adversaries. In order to build these protocols, we devise a new {\\em partitioned simulation} technique for MPC where the simulator uses different strategies for simulating the view of aborting adversaries and non-aborting adversaries. The protagonist of this technique is a new notion of {\\em promise zero knowledge} (ZK) where the ZK property only holds against non-aborting verifiers. We show how to realize promise ZK in three rounds in the simultaneous-message model assuming polynomially hard DDH (or QR or Nth-Residuosity). We also rely upon a new {\\em leveled rewinding security} technique that can be viewed as a polynomial-time alternative to leveled complexity leveraging for achieving ``non-malleability'' across different primitives. Then, we also we study the round complexity of concurrently secure multi-party computation (MPC) with super-polynomial simulation (SPS) in the plain model (in a joint work with Vipul Goyal, Abhishek Jain, Dakshita Khurana and Amit Sahai, TCC 2017). In the plain model, there are known explicit attacks that show that concurrently secure MPC with polynomial simulation is impossible to achieve; SPS security is the most widely studied model for concurrently secure MPC in the plain model. We construct a three-round concurrent MPC with SPS security against Byzantine adversaries, assuming sub-exponentially secure DDH and LWE. Prior to our work, the best known round complexity for SPS concurrent MPC was around twenty, although to the best of our knowledge, no previous work even gave an approximation of the constant round complexity that is sufficient for concurrent MPC.In the second part of the thesis, (in a joint work with Abhishek Jain, Rafail Ostrovsky and Ivan Visconti, ASIACRYPT 2018), we study the problem of non-interactive secure computation in the stateless hardware token model where parties have access to physical hardware as part of a trusted setup phase. The notion of non-interactive secure computation (NISC) first introduced in the work of Ishai et al. [EUROCRYPT 2011] studies the following problem: Suppose a receiver R wishes to publish an encryption of her secret input y so that any sender S with input x can then send a message m that reveals f(x,y) to R (for some function f). Here, m can be viewed as an encryption of f(x,y) that can be decrypted by R. NISC requires security against both malicious senders and receivers, and also requires the receiver's message to be reusable across multiple computations (w.r.t. a fixed input of the receiver). All previous solutions to this problem necessarily rely upon OT (or specific number-theoretic assumptions) even in the common reference string model or the random oracle model or to achieve weaker notions of security such as super-polynomial-time simulation. In this work, we construct a NISC protocol based on the minimal assumption of one way functions, in the stateless hardware token model. Our construction achieves UC security and requires a single token sent by the receiver to the sender.
Protocols for secure multiparty computation enable a set of parties to compute a function of their inputs without revealing anything but the output. The security properties of the protocol must be preserved in the presence of adversarial behavior. The two classic adversary models considered are semi-honest (where the adversary follows the protocol specification but tries to learn more than allowed by examining the protocol transcript) and malicious (where the adversary may follow any arbitrary attack strategy). Protocols for semi-honest adversaries are often far more efficient, but in many cases the security guarantees are not strong enough.