Secure Multi-Party Computation (MPC) is a cryptographic framework that enables multiple parties to jointly compute a function over their inputs while keeping those inputs private. MPC has found applications in privacy-preserving data analytics, secure voting, private machine learning, and secure financial transactions. This article provides a comprehensive survey of recent advances in MPC protocols, including fully homomorphic encryption, garbled circuits, and oblivious transfer. It also explores the challenges in efficiency, scalability, and real-world deployment of MPC and discusses future research directions to enhance its practicality and security.
Secure Multi-Party Computation (MPC) is a cryptographic framework that enables multiple parties to jointly compute a function over their inputs while keeping those inputs private. MPC has found applications in privacy-preserving data analytics, secure voting, private machine learning, and secure financial transactions. This article provides a comprehensive survey of recent advances in MPC protocols, including fully homomorphic encryption, garbled circuits, and oblivious transfer. It also explores the challenges in efficiency, scalability, and real-world deployment of MPC and discusses future research directions to enhance its practicality and security.
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.
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.
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 1982, Yao presented a protocol that allowed two parties to compute over their private inputs while revealing nothing but the final output. This first theoretical construction originated a fruitful line of research exploring the possibilities of the cryptographic technique known as multi-party computation, or MPC. Today, we have MPC schemes with practical efficiency that can be used for a wide range of applications and use cases, from securing cryptographic keys to training Machine Learning models on private data. Despite the advancements from the past few decades, we have only started to bridge the gap between theory and practice, and several obstacles stand in the way of the widespread adoption of MPC. First, the performance overhead depends heavily on the computation we want to perform. Not all computations are well-suited to be distributed with MPC, and algorithms must usually be refactored before they can be executed securely. Furthermore, the practical efficiency of most modern protocols quickly deteriorates as the number of parties increases and comes at the expense of the security guarantees provided. On the other hand, almost all academic works assume a static set of MPC parties, all pairwise connected by dedicated channels in a network without delays or failures. Yet, these assumptions are hardly achievable in current real-world networks. In this thesis, we study three practical aspects of multi-party computation: (i) we discuss how to improve performance by designing algorithms tailor-made for execution with MPC. To this end, we present and evaluate secure auction mechanisms for the financial setting and for the peer-to-peer electricity market. (ii) We analyse the information leakage from the MPC computation outputs. In particular, we focus on the case of individual and private correlated outputs, for which we propose a new privacy notion. Lastly, (iii) we consider the problem of building efficient large-scale MPC. We explore the possibilities and limitations associated with standard (fully connected) networks and present a new protocol with a star-like network topology and resilience against delayed parties.
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) has evolved from a theoretical curiosity in the 1980s to a tool for building real systems today. Over the past decade, MPC has been one of the most active research areas in both theoretical and applied cryptography. This article introduces several important MPC protocols, and surveys methods for improving the efficiency of privacy-preserving applications built using MPC. Besides giving a broad overview of the field and the insights of the main constructions, we overview the most currently active areas of MPC research and aim to give readers insights into what problems are practically solvable using MPC today and how different threat models and assumptions impact the practicality of different approaches.