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Lecture notes in computer science

Computational Irrelevancy: Bridging the Gap Between Pseudo- and Real Randomness in MPC Protocols

Nariyasu Heseri, Koji Nuida

Published Jan 1, 2022• 1 citation
Publisher
DOI
10.1007/978-3-031-15255-9_11

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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.

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Dishonest Majority Passive-to-Active Compiler Over Rings for MPC With Constant Online Communication

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Secure multiparty computation (MPC) over Z2kis more efficient than computations over fields, and studying MPC protocols under malicious security has practical application value. Malicious security with a dishonest majority over rings remains challenging. The most popular approach is SPDZ2k, however, this is a specific protocol that does not support the transformation of any existing semi-honest MPC protocols into malicious security protocols. The zero knowledge proof (ZKP)-based compiler satisfies this requirement. Existing state-of-the-art protocols have logarithmic online communication overhead in terms of the circuit size |C|, and their direct application to rings is nontrivial as they were originally designed for finite fields. In this work, we investigate the communication overhead to develop malicious security protocols. We bridge the gap between malicious security with abort and semi-honest security, by constructing a “GMW-style” verification protocol to achieve malicious security in a dishonest majority setting. This approach incurs a constant online communication overhead by enhancing the machinery of zero-knowledge fully linear interactive oracle proof (zk-FLIOP). Additionally, we extend the zk-FLIOP to work over any ring by invoking reverse multiplication friendly embeddings (RMFEs). Our results show that the online communication complexity of the verification process depends on only the security parameter, the number of parties, and the ring size. Furthermore, for small-scale circuits over Z2, we designed a distributed lookup table argument where both the total communication complexity and the computational cost are independent of the circuit size but of the input wires.

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Secure Multi-Party Computation with Identifiable Abort

Yuval Ishai, Rafail Ostrovsky, Vassilis Zikas

Protocols for secure multi-party computation (MPC) that resist a dishonest majority are susceptible to “denial of service ” attacks, allowing even a single malicious party to force the protocol to abort. In this work, we initiate a systematic study of the more robust notion of security with identifiable abort, which leverages the effect of an abort by forcing, upon abort, at least one malicious party to reveal its identity. We present the first information-theoretic MPC protocol which is secure with identifiable abort (in short ID-MPC) using a correlated randomness setup. This complements a negative result of Ishai et al. (TCC 2012) which rules out information-theoretic ID-MPC in the OT-hybrid model, thereby showing that pairwise correlated randomness is insufficient for information-theoretic ID-MPC. In the standard model (i.e., without a correlated randomness setup), we present the first computationally secure ID-MPC protocol making black-box use of a standard cryptographic primitive, namely an (adaptively secure) oblivious transfer (OT) protocol. This provides a more efficient alternative to existing ID-MPC protocols, such as the GMW protocol, that make

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On the Bottleneck Complexity of MPC with Correlated Randomness

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Lecture notes in computer science•Jan 1, 2022•2 citations
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) over Z2kis more efficient than computations over fields, and studying MPC protocols under malicious security has practical application value. Malicious security with a dishonest majority over rings remains challenging. The most popular approach is SPDZ2k, however, this is a specific protocol that does not support the transformation of any existing semi-honest MPC protocols into malicious security protocols. The zero knowledge proof (ZKP)-based compiler satisfies this requirement. Existing state-of-the-art protocols have logarithmic online communication overhead in terms of the circuit size |C|, and their direct application to rings is nontrivial as they were originally designed for finite fields. In this work, we investigate the communication overhead to develop malicious security protocols. We bridge the gap between malicious security with abort and semi-honest security, by constructing a “GMW-style” verification protocol to achieve malicious security in a dishonest majority setting. This approach incurs a constant online communication overhead by enhancing the machinery of zero-knowledge fully linear interactive oracle proof (zk-FLIOP). Additionally, we extend the zk-FLIOP to work over any ring by invoking reverse multiplication friendly embeddings (RMFEs). Our results show that the online communication complexity of the verification process depends on only the security parameter, the number of parties, and the ring size. Furthermore, for small-scale circuits over Z2, we designed a distributed lookup table argument where both the total communication complexity and the computational cost are independent of the circuit size but of the input wires.
Protocols for secure multi-party computation (MPC) that resist a dishonest majority are susceptible to “denial of service ” attacks, allowing even a single malicious party to force the protocol to abort. In this work, we initiate a systematic study of the more robust notion of security with identifiable abort, which leverages the effect of an abort by forcing, upon abort, at least one malicious party to reveal its identity. We present the first information-theoretic MPC protocol which is secure with identifiable abort (in short ID-MPC) using a correlated randomness setup. This complements a negative result of Ishai et al. (TCC 2012) which rules out information-theoretic ID-MPC in the OT-hybrid model, thereby showing that pairwise correlated randomness is insufficient for information-theoretic ID-MPC. In the standard model (i.e., without a correlated randomness setup), we present the first computationally secure ID-MPC protocol making black-box use of a standard cryptographic primitive, namely an (adaptively secure) oblivious transfer (OT) protocol. This provides a more efficient alternative to existing ID-MPC protocols, such as the GMW protocol, that make