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Distributed (Correlation) Samplers:A Study on the Round Complexity of Cryptographic Sampling Protocols

Damiano Abram

Published Jun 25, 2024• 0 citations
OpenAlex

Abstract

This thesis presents a theoretical analysis of round complexity in cryptographic sampling protocols. We study the following problem: how can n participants agree on a random sample from the distribution D without anybody knowing any secret information hidden in the chosen sample? How many rounds of interactions are needed in any such protocol? Which assumptions are required? These questions are particularly interesting in the context of multiparty computation (MPC) due to the extensive reliance (often unavoidable) on trusted setups such as common reference strings (CRSs). These are samples from known distributions made public before the beginning of the protocol. Security proofs often require CRSs to hide trapdoors. However, if these trapdoors get leaked, security is often fatally compromised. Since trusted setups are inherently single points of failure, it is desirable to generate CRSs in a distributed fashion using MPC protocols: as long as at least one of the participants remains honest, any trapdoor hidden in the CRS is guaranteed to remain secret. Previous research (Garg et al. TCC ’14) had shown that, in the setting of semi-honest security with dishonest majority, any functionality can be implemented in two rounds. In this thesis, we show that, using strong primitives such as indistinguishability obfuscation (iO), it is possible to build one-round sampling protocols. We call these constructions distributed samplers. We show that these protocols can be used to securely generate large amounts of correlated randomness with sublinear communication in a single round. We study different ways to upgrade our semi-honest construction to active security. First, we try to circumvent Cleve’s impossibility (STOC ’86) by allowing the adversary limited influence on the output of the protocol: we consider the functionality F_D^{Active} that proposes a polynomial number of different outputs to the adversary, letting it choose its favourite one (F_D^{Active} can still be used to generate CRSs). We show how to implement F_D^{Active} in one round by relying on a programmable random oracle. In subsequent work, we show that random oracles are necessary: any actively secure distributed samplers implementing F_D^{Active} needs to rely on a CRS that is non-reusable, as large as a sample from D and structured (unless D is an obliviously samplable distribution). This suggests that, without random oracles, simulation-based, actively secure distributed samplers provide no advantage over trusted dealers. We get around this impossibility by proposing new game-based definitions for actively secure distributed samplers. Hardness-preserving distributed samplers allow the removal of CRSs from MPC protocols preserving at the same time the hardness of search problems. Indistinguishability-preserving distributed samplers, on the other hand, substitute the trusted setup while preserving the functionality, however, the protocol needs to satisfy particular conditions. We show how to build distributed samplers with the defined properties by relying on extremely lossy functions, the subexponential security of iO and other primitives. Next, in the context of active security with dishonest majority, we study the feasibility of protocols producing unbiased samples with guaranteed output: to circumvent Cleve's impossibility, we assume the existence of an auxiliary functionality that, upon invocation, publishes a random , short k-bit string. We first study the question when D is the uniform distribution over {0, 1}^m where m>k. This problem is called coin tossing extension (CTE) (Bellare et al. PODC '96). We show the existence of O(1)-round CTE constructions producing an arbitrarily large quantity of unbiased randomness based on various assumptions (OWFs, DDH, QR and DCR, class groups). Our most important result is an LWE-based, one-round, UC-secure, n-party CTE protocol withstanding adaptive corruption. The protocol can be viewed as an explainable randomness extractor. By relying on distributed samplers and the auxiliary functionality, we build one-round unbiased sampling protocols for any distribution. Finally, we present a lower bound for statistically secure CTE with black-box simulation: an R-round protocol can generate at most k+R·O(log λ) bits of randomness.

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On the Impossibility of Actively Secure Distributed Samplers

Damiano Abram, Serge Fehr, Maciej Obremski +1 more

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.

Lecture notes in computer science•Dec 4, 2025•2 citations

Towards Optimality in Secure Computation

Saikrishna Badrinarayanan

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 N$^{th}$-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 N$^{th}$-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 N$^{th}$-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.

•Jan 1, 2019•0 citations

Two Round MPC from LWE via Multi-Key FHE.

Pratyay Mukherjee, Daniel Wichs

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.

•Jan 1, 2015•12 citations

Round-Optimal Secure Multiparty Computation from Minimal Assumptions

Akshayaram Srinivasan

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.

•Jan 1, 2020•0 citations

Two-round Multiparty Secure Computation from Minimal Assumptions

Sanjam Garg, Akshayaram Srinivasan

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.

Journal of the ACM•Oct 7, 2022•12 citations

New Models for Multi-party Computation - eScholarship

Wutichai Chongchitmate

Secure multi-party computation (MPC) is one of the most important primitives in cryptography. Several directions to construct and improve MPC protocols have been studied over the past decades. The majority of existing MPC protocols rely on assumptions such as every party communicates with every other party or every party needs to know every other party and the computation algorithm well in advance. Such assumptions can be difficult to achieve in modern large scale networks. This thesis explores two distinct lines of work leading to new practical models in response to these scenarios.First, we examine communication locality, the total number of other parties that each party communicates with in the protocol, as a new measure for an MPC protocol. Although progress has been made, the question of achieving low communication locality and round complexity at the same time for adaptive adversaries corrupting t l n/2 parties remains open. We show that by assuming a public-key infrastructure (PKI) and a symmetric-key infrastructure (SKI) the above question can be answered affirmatively, under standard assumptions. In particular, we describe a protocol with polylogarithmic communication locality and round complexity which tolerates up to t l n/2 adaptive corruptions. Our results are based on a new model of hidden random graphs obtained from the SKI, and using them to emulate a complete network in polylogarithmic rounds and polylogarithmic locality.We then examine multi-key fully homomorphic encryption (MFHE) schemes, which allow computation on data encrypted under different public keys chosen independently of each other. One of the main problems left in MFHE has been on how to deal with malicious users without trusted setup assumptions. We show how this can be done through circuit privacy, which guarantees that even if both ciphertexts and public keys are not well-formed, no information is revealed regarding the computation, other than what follows from the output on some well-formed inputs. Generalizing the result for circuit-private FHE, we provide a framework for adding circuit privacy to existing MFHE schemes.Finally, we incorporate the circuit privacy in a variant of server-assisted MPC, called on-the-fly MPC, where a server or a “cloud” performs an arbitrary dynamically chosen computation on a subset of data uploaded by multiple clients and encrypted under different keys on-the-fly. Circuit privacy allows the server to keep the algorithm used in the computation private even from a malicious adversary corrupting any number of clients. In particular, we construct a three-round on-the-fly MPC protocol with circuit privacy against malicious clients without the trusted setup.

•Jan 1, 2016•0 citations
This thesis presents a theoretical analysis of round complexity in cryptographic sampling protocols. We study the following problem: how can n participants agree on a random sample from the distribution D without anybody knowing any secret information hidden in the chosen sample? How many rounds of interactions are needed in any such protocol? Which assumptions are required? These questions are particularly interesting in the context of multiparty computation (MPC) due to the extensive reliance (often unavoidable) on trusted setups such as common reference strings (CRSs). These are samples from known distributions made public before the beginning of the protocol. Security proofs often require CRSs to hide trapdoors. However, if these trapdoors get leaked, security is often fatally compromised. Since trusted setups are inherently single points of failure, it is desirable to generate CRSs in a distributed fashion using MPC protocols: as long as at least one of the participants remains honest, any trapdoor hidden in the CRS is guaranteed to remain secret. Previous research (Garg et al. TCC ’14) had shown that, in the setting of semi-honest security with dishonest majority, any functionality can be implemented in two rounds. In this thesis, we show that, using strong primitives such as indistinguishability obfuscation (iO), it is possible to build one-round sampling protocols. We call these constructions distributed samplers. We show that these protocols can be used to securely generate large amounts of correlated randomness with sublinear communication in a single round. We study different ways to upgrade our semi-honest construction to active security. First, we try to circumvent Cleve’s impossibility (STOC ’86) by allowing the adversary limited influence on the output of the protocol: we consider the functionality F_D^{Active} that proposes a polynomial number of different outputs to the adversary, letting it choose its favourite one (F_D^{Active} can still be used to generate CRSs). We show how to implement F_D^{Active} in one round by relying on a programmable random oracle. In subsequent work, we show that random oracles are necessary: any actively secure distributed samplers implementing F_D^{Active} needs to rely on a CRS that is non-reusable, as large as a sample from D and structured (unless D is an obliviously samplable distribution). This suggests that, without random oracles, simulation-based, actively secure distributed samplers provide no advantage over trusted dealers. We get around this impossibility by proposing new game-based definitions for actively secure distributed samplers. Hardness-preserving distributed samplers allow the removal of CRSs from MPC protocols preserving at the same time the hardness of search problems. Indistinguishability-preserving distributed samplers, on the other hand, substitute the trusted setup while preserving the functionality, however, the protocol needs to satisfy particular conditions. We show how to build distributed samplers with the defined properties by relying on extremely lossy functions, the subexponential security of iO and other primitives. Next, in the context of active security with dishonest majority, we study the feasibility of protocols producing unbiased samples with guaranteed output: to circumvent Cleve's impossibility, we assume the existence of an auxiliary functionality that, upon invocation, publishes a random , short k-bit string. We first study the question when D is the uniform distribution over {0, 1}^m where m>k. This problem is called coin tossing extension (CTE) (Bellare et al. PODC '96). We show the existence of O(1)-round CTE constructions producing an arbitrarily large quantity of unbiased randomness based on various assumptions (OWFs, DDH, QR and DCR, class groups). Our most important result is an LWE-based, one-round, UC-secure, n-party CTE protocol withstanding adaptive corruption. The protocol can be viewed as an explainable randomness extractor. By relying on distributed samplers and the auxiliary functionality, we build one-round unbiased sampling protocols for any distribution. Finally, we present a lower bound for statistically secure CTE with black-box simulation: an R-round protocol can generate at most k+R·O(log λ) bits of randomness.
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.
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^{th}th-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^{th}th-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^{th}th-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 RRR wishes to publish an encryption of her secret input yyy so that any sender SSS with input xxx can then send a message mmm that reveals f(x,y)f(x,y)f(x,y) to RRR (for some function fff). Here, mmm can be viewed as an encryption of f(x,y)f(x,y)f(x,y) that can be decrypted by RRR. 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.
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.
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 multi-party computation (MPC) is one of the most important primitives in cryptography. Several directions to construct and improve MPC protocols have been studied over the past decades. The majority of existing MPC protocols rely on assumptions such as every party communicates with every other party or every party needs to know every other party and the computation algorithm well in advance. Such assumptions can be difficult to achieve in modern large scale networks. This thesis explores two distinct lines of work leading to new practical models in response to these scenarios.First, we examine communication locality, the total number of other parties that each party communicates with in the protocol, as a new measure for an MPC protocol. Although progress has been made, the question of achieving low communication locality and round complexity at the same time for adaptive adversaries corrupting t l n/2 parties remains open. We show that by assuming a public-key infrastructure (PKI) and a symmetric-key infrastructure (SKI) the above question can be answered affirmatively, under standard assumptions. In particular, we describe a protocol with polylogarithmic communication locality and round complexity which tolerates up to t l n/2 adaptive corruptions. Our results are based on a new model of hidden random graphs obtained from the SKI, and using them to emulate a complete network in polylogarithmic rounds and polylogarithmic locality.We then examine multi-key fully homomorphic encryption (MFHE) schemes, which allow computation on data encrypted under different public keys chosen independently of each other. One of the main problems left in MFHE has been on how to deal with malicious users without trusted setup assumptions. We show how this can be done through circuit privacy, which guarantees that even if both ciphertexts and public keys are not well-formed, no information is revealed regarding the computation, other than what follows from the output on some well-formed inputs. Generalizing the result for circuit-private FHE, we provide a framework for adding circuit privacy to existing MFHE schemes.Finally, we incorporate the circuit privacy in a variant of server-assisted MPC, called on-the-fly MPC, where a server or a “cloud” performs an arbitrary dynamically chosen computation on a subset of data uploaded by multiple clients and encrypted under different keys on-the-fly. Circuit privacy allows the server to keep the algorithm used in the computation private even from a malicious adversary corrupting any number of clients. In particular, we construct a three-round on-the-fly MPC protocol with circuit privacy against malicious clients without the trusted setup.