MPC is a primitive which allows for mutually distrusting parties to jointly compute the output of a function over their private inputs. This technology has many practical applications and, as such, has seen extensive research, which has generated several different methods for achieving MPC. In this thesis, we discuss and expand on three of the best known methods for achieving MPC. The first is based on Shamir's secret sharing scheme. We present a novel secret sharing based scheme which achieves MPC under the following constraints. We allow for a malicious adversary that can arbitrarily delay any parties for a number of rounds. While these parties are delayed they can neither send nor receive messages. Furthermore, we assume that all messages between the parties are sent via a set of central parties called Relays. We provide a UC functionality and protocol for the relays, and for the MPC protocol. The second is based on Yao's garbled circuits protocol. Here we expand on the row reduction technology already present in maliciously secure two party garbled circuits and show how to achieve similar results in the multiparty setting. This reduces the number of ciphertexts that must be sent per AND gate in the multiparty Garbled Circuits setting from four to three. The third is based on Fully Homomorphic Encryption. The particular protocol we introduce expands the FINAL FHE scheme and expands it to accept multiple keys, which can then be used by different parties to collectively outsource a computation to an untrusted server. We cover the various different obstacles that needed to be overcome in this expansion, and we show that our protocol has an asymptotic improvement in the efficiency of the bootstrapping over other multi-key FHE schemes. This now requires a number of polynomial multiplications which is linear in the number parties, rather than quadratic.
MPC is a primitive which allows for mutually distrusting parties to jointly compute the output of a function over their private inputs. This technology has many practical applications and, as such, has seen extensive research, which has generated several different methods for achieving MPC. In this thesis, we discuss and expand on three of the best known methods for achieving MPC. The first is based on Shamir's secret sharing scheme. We present a novel secret sharing based scheme which achieves MPC under the following constraints. We allow for a malicious adversary that can arbitrarily delay any parties for a number of rounds. While these parties are delayed they can neither send nor receive messages. Furthermore, we assume that all messages between the parties are sent via a set of central parties called Relays. We provide a UC functionality and protocol for the relays, and for the MPC protocol. The second is based on Yao's garbled circuits protocol. Here we expand on the row reduction technology already present in maliciously secure two party garbled circuits and show how to achieve similar results in the multiparty setting. This reduces the number of ciphertexts that must be sent per AND gate in the multiparty Garbled Circuits setting from four to three. The third is based on Fully Homomorphic Encryption. The particular protocol we introduce expands the FINAL FHE scheme and expands it to accept multiple keys, which can then be used by different parties to collectively outsource a computation to an untrusted server. We cover the various different obstacles that needed to be overcome in this expansion, and we show that our protocol has an asymptotic improvement in the efficiency of the bootstrapping over other multi-key FHE schemes. This now requires a number of polynomial multiplications which is linear in the number parties, rather than quadratic.
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.
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.
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 < 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 < 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.
Many services that people use daily require computation that depends on the private data of multiple parties. While the utility of the final result of such interactions outweighs the privacy concerns related to output release, the inputs for such computations are much more sensitive and need to be protected. Secure multiparty computation (MPC) considers the question of constructing computation protocols that reveal nothing more about their inputs than what is inherently leaked by the output. There have been strong theoretical results that demonstrate that every functionality can be computed securely. However, these protocols remain unused in practical solutions since they introduce efficiency overhead prohibitive for most applications. Generic multiparty computation techniques address homogeneous setups with respect to the resources available to the participants and the adversarial model. On the other hand, realistic scenarios present a wide diversity of heterogeneous environments where different participants have different available resources and different incentives to misbehave and collude. In this thesis we introduce techniques for multiparty computation that focus on heterogeneous settings. We present solutions tailored to address different types of asymmetric constraints and improve the efficiency of existing approaches in these scenarios. We tackle the question from three main directions: New Computational Models for MPC - We explore different computational models that enable us to overcome inherent inefficiencies of generic MPC solutions using circuit representation for the evaluated functionality. First, we show how we can use random access machines to construct MPC protocols that add only polylogarithmic overhead to the running time of the insecure version of the underlying functionality. This allows to achieve MPC constructions with computational complexity sublinear in the size for their inputs, which is very important for computations that use large databases. We also consider multivariate polynomials which yield more succinct representations for the functionalities they implement than circuits, and at the same time a large collection of problems are naturally and efficiently expressed as multivariate polynomials. We construct an MPC protocol for multivariate polynomials, which improves the communication complexity of corresponding circuit solutions, and provides currently the most efficient solution for multiparty set intersection in the fully malicious case. Outsourcing Computation - The goal in this setting is to utilize the resources of a single powerful service provider for the work that computationally weak clients need to perform on their data. We present a new paradigm for constructing verifiable computation (VC) schemes, which enables a computationally limited client to verify efficiently the result of a large computation. Our construction is based on attribute-based encryption and avoids expensive primitives such as fully homomorphic encryption andprobabilistically checkable proofs underlying existing VC schemes. Additionally our solution enjoys two new useful properties: public delegation and verification. We further introduce the model of server-aided computation where we utilize the computational power of an outsourcing party to assist the execution and improve the efficiency of MPC protocols. For this purpose we define a new adversarial model of non-collusion, which provides room for more efficient constructions that rely almost completely only on symmetric key operations, and at the same time captures realistic settings for adversarial behavior. In this model we propose protocols for generic secure computation that offload the work of most of the parties to the computation server. We also construct a specialized server-aided two party set intersection protocol that achieves better efficiencies for the two participants than existing solutions. Outsourcing in many cases concerns only data storage and while outsourcing the data of a single party is useful, providing a way for data sharing among different clients of the service is the more interesting and useful setup. However, this scenario brings new challenges for access control since the access control rules and data accesses become private data for the clients with respect to the service provide. We propose an approach that offers trade-offs between the privacy provided for the clients and the communication overhead incurred for each data access. Efficient Private Search in Practice - We consider the question of private search from a different perspective compared to traditional settings for MPC. We start with strict efficiency requirements motivated by speeds of available hardware and what is considered acceptable overhead from practical point of view. Then we adopt relaxed definitions of privacy, which still provide meaningful security guarantees while allowing us to meet the efficiency requirements. In this setting we design a security architecture and implement a system for data sharing based on encrypted search, which achieves only 30% overhead compared to non-secure solutions on realistic workloads.
ulti-Party Computation (MPC) protocols allow a set of mutually distrustful parties to securely compute on their joint private inputs, maintaining the privacy of those.Since its early conception in the eighties, a plethora of research as well as some real world deployments have taken place, demonstrating the relevance of such an interesting mathematical problem.Nevertheless, most of the research and all deployments have focused on scenarios where both the number of parties and network latency are very low.This thesis lays out the first steps towards practical deployments of large-scale MPC, where many parties may be involved and they might only be connected through a high-latency network such as the Internet.Both theoretical and empirical evidence shows that non-constant-round protocols cannot perform well on slow networks for many functions.In order to overcome this issue, all the works in this thesis include concretely efficient constant-round protocols based on multi-party garbled circuits.Chapter 3 and Chapter 4 deal with the very strong setting where an active adversary corrupts all but one parties.The former achieves such goal by using homomorphic encryption for low-depth circuits.The latter, based on subsequent work, improves the theoretical understanding of the problem and utilises oblivious transfer to improve efficiency.In Chapter 5 we provide both constant and non-constant round protocols that can handle large numbers of parties more efficiently.We leverage our performance improvements by relaxing the setting where all but one parties are corrupted to one where a small minority of honest participants can be assumed.Concretely, such change allows to distribute secret key material so that each party only holds a 'short' part of the key.Security is then based on the concatenation of all honest parties' keys rather than on each party's individual key, improving both the communication and computation complexities.iii researcher.They would have not been the same without the support of family, friends and colleagues.I would like to start by thanking Nigel Smart for giving me this opportunity, being my advisor and introducing me to others in the community.Martijn Stam
In this thesis we design and implement three approaches to provide efficient Secure Two- Party Computation (2PC) protocols that are secure in presence of malicious adversaries. The field of secure two-party computation enables two mutually distrusting parties, each with their own private input, to run a computation of an arbitrary program. At the end of the computation, nothing about their private input is leaked except for what can be learned from the output of the computation. The seminal work of Yao in 1986 provided the first proof that such a computation is feasible using the so called garbled circuits and given an Oblivious Transfer protocol. In this thesis, we follow Yao’s garbled circuit approach and focus on efficient protocols that are secure against malicious adversaries. We examine three different categories of optimization. In each category, we present a 2PC protocol, prove its security, and implement it as a proof of concept to demonstrate its running time in practice. Non-interactive Secure Computation: In this category, we offer the first implementation of a malicious 2PC protocol that reduces the required rounds of interaction between the two parties to only two rounds (i.e., each party sends only one message to the other party). Mixed Secure Two-Party Computation: In the second category we target big and complex programs and break them into subprograms. Then, we compute each subprogram using the most efficient 2PC protocol that is suitable for it. Finally, we securely connect these subprograms together. The goal is to reduce the overhead of the garbled circuits significantly, which results in a more efficient overall 2PC protocol for programs with specific properties. Secure Computation for Random Access Machine Programs: In the third category, we target programs that require random access to the memory (as opposed to a sequential access). We present the first efficient maliciously-secure protocol for computing such programs.