One fundamental complexity measure of an MPC protocol is its round complexity. Asharov et al. recently constructed the first three-round protocol for general MPC in the CRS model. Here, we show how to achieve this result with only two rounds. We obtain UC security with abort against static malicious adversaries, and fairness if there is an honest majority. Additionally the communication in our protocol is only proportional to the input and output size of the function being evaluated and independent of its circuit size. Our main tool is indistinguishability obfuscation, for which a candidate construction was recently proposed by Garg et al. The technical tools that we develop in this work also imply virtual black box obfuscation of a new primitive that we call a dynamic point function. This primitive may be of independent interest. The second and third authors were supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center (DoI/NBC) contract number D11PC20202. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DoI/NBC, or the U.S. Government.
One fundamental complexity measure of an MPC protocol is its round complexity. Asharov et al. recently constructed the first three-round protocol for general MPC in the CRS model. Here, we show how to achieve this result with only two rounds. We obtain UC security with abort against static malicious adversaries, and fairness if there is an honest majority. Additionally the communication in our protocol is only proportional to the input and output size of the function being evaluated and independent of its circuit size. Our main tool is indistinguishability obfuscation, for which a candidate construction was recently proposed by Garg et al. The technical tools that we develop in this work also imply virtual black box obfuscation of a new primitive that we call a dynamic point function. This primitive may be of independent interest. The second and third authors were supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center (DoI/NBC) contract number D11PC20202. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DoI/NBC, or the U.S. Government.
We construct a general multiparty computation (MPC) protocol in the common random string (CRS) model with only two rounds of interaction, which is known to be optimal. In the honest-but-curious setting we only rely on the learning with errors (LWE) assumption, and in the fully malicious setting we additionally assume the existence of non-interactive zero knowledge arguments (NIZKs). Previously, Asharov et al. (EUROCRYPT ’12) showed how to achieve three rounds based on LWE and NIZKs, while Garg et al. (TCC ’14) showed how to achieve the optimal two rounds based on indistinguishability obfuscation, but it was unknown if two rounds were possible under simpler assumptions without obfuscation. Our approach relies on multi-key fully homomorphic encryption (MFHE), introduced by Lopez-Alt et al. (STOC ’12), which enables homomorphic computation over data encrypted under different keys. We simplify a recent construction of MFHE based on LWE by Clear and McGoldrick (ePrint ’14), and give a stand-alone exposition of that scheme. We then extend this construction to allow for a one-round distributed decryption of a multi-key ciphertext. Our entire MPC protocol consists of the following two rounds: 1. Each party individually encrypts its input under its own key and broadcasts the ciphertext. All parties can then homomorphically compute a multi-key encryption of the output. 2. Each party broadcasts a partial decryption of the output using its secret key. The partial decryptions can be combined to recover the output in plaintext. ∗Aarhus University. E-mail: pratyay85@gmail.com †Northeastern University. E-mail: danwichs@gmail.com.
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.
Secure multi-party computation (MPC) protocols that are resilient to a dishonest majority allow the adversary to get the output of the computation while, at the same time, forcing the honest parties to abort. Aumann and Lindell introduced the enhanced notion of security with identifiable abort , which still allows the adversary to trigger an abort but, at the same time, it enables the honest parties to agree on the identity of the party that led to the abort. More recently, in Eurocrypt 2016, Garg et al. showed that, assuming access to a simultaneous message exchange channel for all the parties, at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. Following Garg et al., a sequence of works has matched this lower bound, but none of them achieved security with identifiable abort. In this work, we close this gap and show that four rounds of communication are also sufficient to securely realize any functionality with identifiable abort using standard and generic polynomial-time assumptions. To achieve this result we introduce the new notion of bounded-rewind secure MPC that guarantees security even against an adversary that performs a mild form of reset attacks. We show how to instantiate this primitive starting from any MPC protocol and by assuming trapdoor-permutations. The notion of bounded-rewind secure MPC allows for easier parallel composition of MPC protocols with other (interactive) cryptographic primitives. Therefore, we believe that this primitive can be useful in other contexts in which it is crucial to combine multiple primitives with MPC protocols while keeping the round complexity of the final protocol low.
One-round secure computation is generally believed impossible due to the residual function attack : any honest-but-curious participant can replay the protocol in their head changing their input, and learn, in this way, a new output. Inputless functionalities are among the few that are immune to this problem. This paper studies one-round, multi-party computation protocols (MPC) that implement the most natural inputless functionality: one that generates a random sample from a fixed distribution. These are called distributed samplers . At Eurocrypt 2022, Abram, Scholl and Yakoubov showed how to build this primitive in the semi-honest model with dishonest majority. In this work, we give a lower bound for constructing distributed samplers with a malicious adversary in the standard model. More in detail, we show that for any construction in the stand-alone model with black-box simulation, even with a CRS and honest majority, the output of the sampling protocol must have low entropy. This essentially implies that this type of construction is useless in applications. Our proof is based on an entropic argument, drawing a new connection between computationally secure MPC, information theory and learning theory.
Abstract. We present the first general MPC protocol that satisfies the following: (1) the con-struction is black-box, (2) the protocol is universally composable in the plain model, and (3) the number of rounds is constant. The security of our protocol is proven in angel-based UC security under the assumption of the existence of one-way functions that are secure against sub-exponential-time adversaries and constant-round semi-honest oblivious transfer protocols that are secure against quasi-polynomial-time adversaries. We obtain the MPC protocol by constructing a constant-round CCA-secure commitment scheme in a black-box way under the assumption of the existence of one-way functions that are secure against sub-exponential-time adversaries. To justify the use of such a sub-exponential hardness assumption in obtaining our constant-round CCA-secure commitment scheme, we show that if black-box reductions are used, there does not exist any constant-round CCA-secure commitment scheme under any falsifiable polynomial-time hardness assumptions. 1
Secure multi-party computation (MPC) enables distrustful parties to jointly perform computations while guaranteeing both the privacy of their inputs and the correctness of the computation.
This thesis explores two aspects of secure multi-party computation: adaptive security and round efficiency. Adaptive security is concerned with an adversary that adaptively determines who and when to corrupt during the course of the computation. Even though this is a very natural and realistic assumption about the adversary, most of the MPC literature addresses security only against a static adversary — an adversary that chooses (and fixes) which parties to corrupt before the protocol starts executing. A protocol is called round-efficient if it runs in a small number of rounds. Constructing such protocols is important since efficiency of a protocol is greatly influenced by its round complexity.
The security in this thesis is formulated in the universal composability (UC) framework introduced by Canetti [Can01]. Protocols secure in the UC framework remain secure even when executed concurrently with other arbitrary protocols running in some larger network, and can be used as subroutines of larger protocols in a modular fashion. This property is important considering that nowadays many protocols are executed concurrently with others in the Internet.
With the focus on adaptive security and round efficiency, we obtain the following results:
(1) We show that with access to an ideal commitment functionality, there exists a protocol that UC realizes any well-formed multi-party functionality against a malicious, adaptive adversary that may corrupt any number of parties, with black-box access to any protocol that UC realizes oblivious transfer against a semi-honest, adaptive adversary.
(2) We show that there exists a protocol that UC realizes oblivious transfer against a semi-honest, adaptive adversary, with black-box access to a cryptographic primitive called a trapdoor simulatable cryptosystem, which is a natural relaxation of a simulatable cryptosystem introduced by Damgard and Nielsen [3N00].
We also show that the primitive can be constructed based on hardness of factoring.
(3) We present a single-message protocol that UC realizes two-party computing with encrypted data (a variant of secure two-party computation), based on the DDH assumption and non- interactive zero-knowledge arguments. The protocol achieves security against a malicious, static adversary.
(4) We present two round-efficient protocols that UC realize multi-party computing with encrypted data (a variant of secure multi-party computation), based on the DDH assumption and non-interactive zero-knowledge arguments. The first (resp. second) protocol requires one round (resp. two rounds) with appropriate preprocessing, which is independent of the exact circuit and actual inputs of the specific instance problem to solve — only the bound on the circuit size is known. Although the first protocol is more round-efficient, the preprocessing of the second is sometimes better under some efficiency considerations. Both protocols achieve security against a malicious, static adversary that may corrupt up to all but one parties.