Machine learning algorithms crucially depend on non-linear mathematical functions such as division (for normalization), exponentiation (for softmax and sigmoid), tanh (as an activation function), logarithm (for crossentropy loss), and square root (for back-propagation of normalization layers). However, when machine learning is performed over secure computation, these protocols incur a large communication overhead and high round complexity. In this work, we propose new multi-party computation (MPC) protocols for such functions. Our protocols achieve constant round complexity (3 for semi-honest, 4 for malicious), an order of magnitude lower communication (54 − 121× lower than prior art), and high concrete efficiency (2−1163× faster runtime). We rely on recent advances in function secret sharing (FSS) to construct these protocols. Our contributions can be summarized as follows: (1) A constant round protocol to securely evaluate nonlinear functions such as division, exponentiation, logarithm, and tanh (in comparison to prior art which uses round complexity proportional to the rounds of iterative methods/required precision) with high accuracy. This construction largely follows prior work in look-up style secure computation. (2) Our main contribution is the extension of the above protocol to be secure in the presence of malicious adversaries in the honest majority setting. We provide a malicious sketching protocol for FSS schemes that works over rings and in order to prove its security, we extend (and prove) a corresponding form of SchwartzZippel lemma over rings. This is the first such extension of the lemma and it can be of independent interest in other domains of secure computation. (3) We implement our protocol and showcase order of magnitude improvements in runtime and communication. Given the low round complexity and substantially lower communication, our protocols achieve even better performance over network constrained environments such as WAN. Finally, we showcase how such functions can lead to scalability in machine learning. Note that techniques presented are applicable beyond the application of machine learning as the protocols effectively present an efficient 1-out-of-N oblivious transfer or an efficient private information retrieval protocol.
Machine learning algorithms crucially depend on non-linear mathematical functions such as division (for normalization), exponentiation (for softmax and sigmoid), tanh (as an activation function), logarithm (for crossentropy loss), and square root (for back-propagation of normalization layers). However, when machine learning is performed over secure computation, these protocols incur a large communication overhead and high round complexity. In this work, we propose new multi-party computation (MPC) protocols for such functions. Our protocols achieve constant round complexity (3 for semi-honest, 4 for malicious), an order of magnitude lower communication (54 − 121× lower than prior art), and high concrete efficiency (2−1163× faster runtime). We rely on recent advances in function secret sharing (FSS) to construct these protocols. Our contributions can be summarized as follows: (1) A constant round protocol to securely evaluate nonlinear functions such as division, exponentiation, logarithm, and tanh (in comparison to prior art which uses round complexity proportional to the rounds of iterative methods/required precision) with high accuracy. This construction largely follows prior work in look-up style secure computation. (2) Our main contribution is the extension of the above protocol to be secure in the presence of malicious adversaries in the honest majority setting. We provide a malicious sketching protocol for FSS schemes that works over rings and in order to prove its security, we extend (and prove) a corresponding form of SchwartzZippel lemma over rings. This is the first such extension of the lemma and it can be of independent interest in other domains of secure computation. (3) We implement our protocol and showcase order of magnitude improvements in runtime and communication. Given the low round complexity and substantially lower communication, our protocols achieve even better performance over network constrained environments such as WAN. Finally, we showcase how such functions can lead to scalability in machine learning. Note that techniques presented are applicable beyond the application of machine learning as the protocols effectively present an efficient 1-out-of-N oblivious transfer or an efficient private information retrieval protocol.
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) allows a set of parties to compute a function jointly while keeping their inputs private. Compared with the MPC based on garbled circuits, some recent research results show that MPC based on secret sharing (SS) works at a very high speed. Moreover, SS-based MPC can be easily vectorized and achieve higher throughput. In SS-based MPC, however, we need many communication rounds for computing concrete protocols like equality check, less-than comparison, etc. This property is not suited for large-latency environments like the Internet (or WAN). In this paper, we construct semi-honest secure communication-efficient two-party protocols. The core technique is Beaver triple extension, which is a new tool for treating multi-fan-in gates, and we also show how to use it efficiently. We mainly focus on reducing the number of communication rounds, and our protocols also succeed in reducing the number of communication bits (in most cases). As an example, we propose a less-than comparison protocol (under practical parameters) with three communication rounds. This is less than a half compared with the previous work. Moreover, the number of communication bits is also 38.4% fewer. As a result, total online execution time is 56.1% shorter than the previous work adopting the same settings. Although the computation costs of our protocols are more expensive than those of previous work, we confirm via experiments that such a disadvantage has small effects on the whole online performance in the typical WAN environments.
Secure Multi-party Computation (MPC) allows a set of mutually distrusting parties to jointly evaluate a function on their private inputs while maintaining input privacy. In this work, we improve semi-honest secure two-party computation (2PC) over rings, with a focus on the efficiency of the online phase. We propose an efficient mixed-protocol framework, outperforming the state-of-the-art 2PC framework of ABY. Moreover, we extend our techniques to multi-input multiplication gates without inflating the online communication, i.e., it remains independent of the fan-in. Along the way, we construct efficient protocols for several primitives such as scalar product, matrix multiplication, comparison, maxpool, and equality testing. The online communication of our scalar product is two ring elements irrespective of the vector dimension, which is a feature achieved for the first time in the 2PC literature. The practicality of our new set of protocols is showcased with four applications: i) AES S-box, ii) Circuit-based Private Set Intersection, iii) Biometric Matching, and iv) Privacy-preserving Machine Learning (PPML). Most notably, for PPML, we implement and benchmark training and inference of Logistic Regression and Neural Networks over LAN and WAN networks. For training, we improve online runtime (both for LAN and WAN) over SecureML (Mohassel et al., IEEE S&P '17) in the range 1.5x–6.1x, while for inference, the improvements are in the range of 2.5x–754.3x.
In this paper, we propose memory- and round-efficient protocols for securely evaluating arithmetic primitives. We focus on secure two-party computation over the ring ℤ2k that achieves security against semi-honest adversaries and works in the pre-processing model. Our protocols rely on the unit vectorization technique introduced by Boyle et al. (TCC 2019). The unit vectorization technique provides online-optimal protocols for several fundamental operations in the pre-processing model. However, a relatively large memory cost for correlated randomness is required, which might become an obstacle in a large-scale application. In order to achieve both memory and communication efficiency, we propose a size reduction method that uses unit vectorization only for short-length inputs, and based on this, construct two-round protocols for equality test, detecting the most significant non-zero bit, detecting wrap-around, and less-than comparison. In addition, as applications of these results, we provide practically efficient protocols for integer division, integer square root, integer logarithm, and modular exponentiation.
Secure multi-party computation (MPC) is a cryptographic tool that enables a set of parties to compute a function jointly while keeping each input secret. Since MPC based on secret sharing (SS) achieves high throughput and works fast, many applications have been developed. However, SS-based MPC requires many communication rounds in general, and this becomes a performance bottleneck in real-world applications under high-latency networks. In this paper, we propose SS-based secure three-party computation with almost no preprocessing based on our new (small-)constant-round fundamental gates, by revisiting a framework in a few previous works where a number of parties are assisted by another party who may partially learn secret information. Instead of ordinary logical gates, our fundamental gate is an efficient Equality, for which the result leaks to the third party, and we develop novel two-round constructions of secure building-block protocols (LessThan Comparison, RightShift, Table LookUp, etc.) from the insecure Equality. To show the practicality of our protocols, we implement a secure exact edit distance protocol for two genome strings. Our experiments show that in some network setting our protocol is about 2 times faster (14 times faster taking preprocessing into consideration) than the state-of-the-art SS-based protocol (Ohata and Nuida, FC 2020).
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