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ASTRA: High Throughput 3PC Over Rings with Application to Secure Prediction∗

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ASTRA: High Throughput 3PC Over Rings with Application to Secure Prediction∗ ASTRA: High Throughput 3PC over Rings with Application to Secure Prediction∗ Harsh Chaudhari Ashish Choudhury† Indian Institute of Science, Bangalore India International Institute of Information Technology [email protected] Bangalore, India [email protected] Arpita Patra‡ Ajith Suresh Indian Institute of Science, Bangalore India Indian Institute of Science, Bangalore India [email protected] [email protected] Abstract in a way that no coalition of t parties can learn more information The concrete efficiency of secure computation has been the focus than the output (privacy) or affect the true output of the compu- of many recent works. In this work, we present concretely-efficient tation (correctness). While MPC, in general, has been a subject protocols for secure 3-party computation (3PC) over a ring of inte- of extensive research, the area of MPC with a small number of gers modulo 2` tolerating one corruption, both with semi-honest parties in the honest majority setting [4, 18, 20, 35, 56] has drawn and malicious security. Owing to the fact that computation over ring popularity of late mainly due to its efficiency and simplicity. Fur- emulates computation over the real-world system architectures, thermore, most real-time applications involve a small number of secure computation over ring has gained momentum of late. parties. Applications such as statistical and financial data analy- Cast in the offline-online paradigm, our constructions present sis [16], email-filtering [49], distributed credential encryption [56], the most efficient online phase in concrete terms. In the semi-honest Danish sugar beet auction [17] involve 3 parties. Well-known MPC setting, our protocol requires communication of 2 ring elements per frameworks such as VIFF [37], Sharemind [15] have been explored multiplication gate during the online phase, attaining a per-party with 3 parties. Recent advances in secure machine learning (ML) cost of less than one element. This is achieved for the first time in based on MPC have shown applications with a small number of the regime of 3PC. In the malicious setting, our protocol requires parties [54, 55, 57, 64, 68]. MPC with a small number of parties helps communication of 4 elements per multiplication gate during the solve MPC over large population as well via server-aided computa- online phase, beating the state-of-the-art protocol by 5 elements. tion, where a small number of servers jointly hold the input data Realized with both the security notions of selective abort and fair- of the large population and run an MPC protocol evaluating the ness, the malicious protocol with fairness involves slightly more desired function. communication than its counterpart with abort security for the With motivations galore, the specific problem of three-party output gates alone. computation (3PC) tolerating one corruption has received phe- We apply our techniques from 3PC in the regime of secure server- nomenal attention of late [2, 4, 18, 21, 35, 41, 52, 56, 60, 60, 63]. aided machine-learning (ML) inference for a range of prediction Leveraging honest majority, this setting allows to attain stronger functions– linear regression, linear SVM regression, logistic re- security goals such as fairness (corrupt party receives the output gression, and linear SVM classification. Our setting considers a only if all honest parties receive output) which are otherwise im- model-owner with trained model parameters and a client with a possible with dishonest-majority [23]. In this work, we revisit the query, with the latter willing to learn the prediction of her query concrete efficiency of 3PC and to be specific, the efficiency ofthe based on the model parameters of the former. The inputs and com- input-dependent computation. putation are outsourced to a set of three non-colluding servers. Our The two typical lines of constructions that the regime of MPC constructions catering to both semi-honest and the malicious world, over small population offer are– high-throughput [2–4, 21, 35, 60], invariably perform better than the existing constructions. and low-latency [18, 20, 39, 41, 56, 63] protocols. Relying on secret sharing mechanism, the former category requires low communi- 1 INTRODUCTION cation overhead (bandwidth) and simple computations. Catering to low-latency networks, this category takes a number of com- Secure Multi-Party Computation (MPC) [12, 38, 69], the holy grail munication rounds proportional to the multiplicative depth of the of secure distributed computing, enables a set of n mutually distrust- circuit representing the function to be computed. On the other ing parties to perform joint computation on their private inputs, hand, the other category, relying on garbled circuits, requires a ∗This article is the full and extended version of an earlier article to appear in ACM constant number of communication rounds and serve better in CCSW 2019 high-latency networks such as the Internet. The focus of this work †This Publication is an outcome of the R&D work undertaken in the project under the Visvesvaraya PhD Scheme of Ministry of Electronics & Information Technology, is high-throughput 3PC. Government of India, being implemented by Digital India Corporation (formerly Media Almost all high-throughput protocols evaluate a circuit that Lab Asia) represents the function f to be computed in a secret-shared fash- ‡ Arpita Patra would like to acknowledge financial support by Tata Trust Travel Grant ion. Informally, the parties jointly maintain the invariant that for 2019 and SERB Women Excellence Award 2017 (DSTO 1706). each wire in the circuit, the exact value over that wire is avail- Secure 3PC. Our 3PC protocol with semi-honest security requires able in a secret-shared fashion among the parties, in a way that communication of two elements per multiplication during the on- the adversary learns no information about the exact value from line phase. The per-party online cost of our protocol is less than one the shares of the corrupt parties. Upon completion of the circuit element per multiplication, a property achieved for the first time in evaluation, the parties jointly reconstruct the secret-shared func- the 3PC setting. This improvement comes from the use of a form tion output. Intuitively, the security holds as no intermediate value of linear secret-sharing scheme inspired from the work of [39] that is revealed during the computation. The deployed secret-sharing allows offloading the task of one of the parties in the offline phase schemes are typically linear, ensuring non-interactive evaluation and requires only two parties to talk to each other in the online of the linear gates. The communication is required only for the phase. This essentially implies that the evaluation of multiplication non-linear (i.e.multiplication) gates in the circuit. The focus then gates in the online phase requires the presence of just two parties, turns on improving the communication overhead per multiplica- unlike the previous protocols [2, 4, 21, 35, 52] that insist all the tion gate. Recent literature has seen a range of customized linear three parties be awake throughout the computation. One exception secret-sharing schemes over a small number of parties, boosting is the case of Chameleon [64], where two parties perform the online the performance for multiplication gate spectacularly [2, 35, 39]. computation with the help of correlated randomness generated by In an interesting direction towards improving efficiency, MPC a semi-trusted party in the offline phase. Though the model looks protocols are suggested to be cast in two phases– an offline phase similar in the semi-honest setting, we achieve a stronger security that performs input-independent computation and an online phase guarantee by allowing the third party to be maliciously corrupted. that performs fast input-dependent computation utilizing the offline Moreover, our multiplication protocol in the semi-honest setting computation [6]. The offline phase, run in advance, generates ‘raw requires an online communication of 2 ring elements as opposed material’ in a relatively expensive way to yield a blazing-fast on- to 4 of [64]. We achieve this 2× improvement while maintaining line phase. This is very useful in a scenario where a set of parties the same offline cost (1 element) of [64]. agreed to perform a specific computation repetitively over a period For the malicious case, our protocol requires a total communica- of time. The parties can batch together the offline computations tion of four elements per multiplication during the online phase. and generate a large volume of offline data to support the execution The state-of-the-art protocol over rings requires nine ring elements of multiple online phases. Popularly referred as offline-online para- per multiplication in the online phase. Lastly, we boost the security digm [6], there are constructions abound that show effectiveness of our malicious protocol to fairness without affecting its cost per of this paradigm both in the theoretical [6–9, 13, 22] and practical multiplication. The inflation inflicted is purely for the output gates [5, 24, 28–30, 44–46, 64] regime. and to be specific for output reconstruction. The key contribution of In yet another direction to improve practical efficiency, secure the fair protocol lies in constructing a fair reconstruction protocol computation for arithmetic circuits over rings has gained momen- that ensures a corrupt party receives the output if and only if the tum of late, while traditionally fields have been the default choice. honest parties receive. The fair reconstruction does not resort to a Computation over rings models computation in the real-life com- broadcast channel and instead rely on a new concept of ‘proof of puter architectures such as computation over CPU words of size origin’ that tackles the confusion a sender can infuse in the absence 32 or 64 bits. In 3PC setting, the work of [15] supports arithmetic of broadcast channel by sending different messages to its fellow circuits over arbitrary rings with passive security, while [2] offers ac- parties over private channels.
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