Efficient Information-Theoretic Secure Multiparty Computation over $$\mathbb {Z}/p^k\mathbb {Z}$$ via Galois Rings

Abspoel, Mark; Cramer, Ronald; Damgård, Ivan; Escudero, Daniel; Yuan, Chen

doi:10.1007/978-3-030-36030-6_19

Cited by 32 publications

(10 citation statements)

References 14 publications

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“…However, this solution does not work naively over rings since not every element in the ring has an inverse, as opposed to fields. Concretely, the check can still pass with a probability of at most 1/2 [39], [40]. To reduce the cheating probability, the check is repeated κ times, thereby bounding the cheating probability by 1/2 κ .…”

Section: Achieving Robustnessmentioning

confidence: 99%

Tetrad: Actively Secure 4PC for Secure Training and Inference

Koti¹,

Patra²,

Rachuri³

et al. 2022

Proceedings 2022 Network and Distributed System Security Symposium

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Mixing arithmetic and boolean circuits to perform privacy-preserving machine learning has become increasingly popular. Towards this, we propose a framework for the case of four parties with at most one active corruption called Tetrad.Tetrad works over rings and supports two levels of security, fairness and robustness. The fair multiplication protocol costs 5 ring elements, improving over the state-of-the-art Trident (Chaudhari et al. NDSS'20). A key feature of Tetrad is that robustness comes for free over fair protocols. Other highlights across the two variants include (a) probabilistic truncation without overhead, (b) multi-input multiplication protocols, and (c) conversion protocols to switch between the computational domains, along with a tailor-made garbled circuit approach.Benchmarking of Tetrad for both training and inference is conducted over deep neural networks such as LeNet and VGG16. We found that Tetrad is up to 4 times faster in ML training and up to 5 times faster in ML inference. Tetrad is also lightweight in terms of deployment cost, costing up to 6 times less than Trident.

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Section: Achieving Robustnessmentioning

confidence: 99%

Tetrad: Actively Secure 4PC for Secure Training and Inference

Koti¹,

Patra²,

Rachuri³

et al. 2022

Proceedings 2022 Network and Distributed System Security Symposium

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“…In the presence of semi-honest adversaries, the GMW-like protocols and the MPC protocols based on replicated secret sharing can be straightforwardly extended to work over a ring such as Z 2 k for k = 32 or k = 64. Furthermore, the BGW-like protocols based on Shamir secret sharing can also work over a general ring (see, e.g., [127]). While integer computations modulo Z 2 k are more natural for modern computers, and may be useful for simplifying implementations and applications such as machine learning (ML), we focus on the case of finite fields for the sake of simplicity.…”

Section: Semi-honest Protocolsmentioning

confidence: 99%

Concretely efficient secure multi-party computation protocols: survey and more

Feng

Yang

2022

Security and Safety

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Secure multi-party computation (MPC) allows a set of parties to jointly compute a function on their private inputs, and reveals nothing but the output of the function. In the last decade, MPC has rapidly moved from a purely theoretical study to an object of practical interest, with a growing interest in practical applications such as privacy-preserving machine learning (PPML). In this paper, we comprehensively survey existing work on concretely efficient MPC protocols with both semi-honest and malicious security, in both dishonest-majority and honest-majority settings. We focus on considering the notion of security with abort, meaning that corrupted parties could prevent honest parties from receiving output after they receive output. We present high-level ideas of the basic and key approaches for designing different styles of MPC protocols and the crucial building blocks of MPC. For MPC applications, we compare the known PPML protocols built on MPC, and describe the efficiency of private inference and training for the state-of-the-art PPML protocols. Furthermore, we summarize several challenges and open problems to break though the efficiency of MPC protocols as well as some interesting future work that is worth being addressed. This survey aims to provide the recent development and key approaches of MPC to researchers, who are interested in knowing, improving, and applying concretely efficient MPC protocols.

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“…Fortunately, we can address the issue of soundness and non-invertibility by sampling challenges from an exceptional set, which consists of elements whose non-zero pairwise differences are invertible. This approach has been used in quite a few works in the context of secure multiparty computation [1], but also recently in zero-knowledge proofs [31].…”

Section: Overview Of the Techniques Inmentioning

confidence: 99%

“…. , P d ), i.e., a protocol for proving knowledge of d witnesses for relation X 1 . This compares positively to the alternatives: instantiating d different Σ-protocols defined directly over Z m would result in a larger knowledge error; while applying standard amortization techniques to prove knowledge of d witnesses with the same communication costs as proving knowledge of only 1 witness (see e.g.…”

Section: Remark 4 (Proving Openings Of D Z M -Commitments)mentioning

confidence: 99%

“…Typically, zero knowledge techniques operate by somehow translating general statements to arithmetic statements, ultimately dealing with additions and multiplications over some algebraic structure. Traditionally, this arithmetic happens over what is known as a finite field, such as Z p , the set of integers modulo p, for prime p. The tendency to use this type of structures is also present in other areas such as secure multiparty computation [24,1,26,18] and, in essence, this is due to the fact that these structures possess very nice properties that make them "easy" to work with.…”

Section: Introductionmentioning

confidence: 99%

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Vector Commitments over Rings and Compressed $$\varSigma $$-Protocols

Attema

Cascudo

Cramer

et al. 2022

Theory of Cryptography

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Compressed Σ-Protocol Theory (CRYPTO 2020) presents an "alternative" to Bulletproofs that achieves the same communication complexity while adhering more elegantly to existing Σ-protocol theory, which enables their techniques to be directly applicable to other widely used settings in the context of "plug & play" algorithmics. Unfortunately, their techniques are restricted to arithmetic circuits over prime fields, which rules out the possibility of using more machine-friendly moduli such as powers of 2, which have proven to improve efficiency in applications. In this work we show that such techniques can be generalized to the case of arithmetic circuits modulo any number. This enables the use of powers of 2, which can prove to be beneficial for efficiency, but it also facilitates the use of other moduli that might prove useful in different applications.In order to achieve this, we first present an instantiation of the main building block of the theory of compressed Σ-protocols, namely compact vector commitments. Our construction, which may be of independent interest, is homomorphic modulo any positive integer m, a result that was not known in the literature before. Second, we generalize Compressed Σ-Protocol Theory from finite fields to Zm. The main challenge here is ensuring that there are large enough challenge sets as to fulfill the necessary soundness requirements, which is achieved by considering certain ring extensions. Our techniques have direct application for example to verifiable computation on homomorphically encrypted data.

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Efficient Information-Theoretic Secure Multiparty Computation over $$\mathbb {Z}/p^k\mathbb {Z}$$ via Galois Rings

Cited by 32 publications

References 14 publications

Tetrad: Actively Secure 4PC for Secure Training and Inference

Tetrad: Actively Secure 4PC for Secure Training and Inference

Concretely efficient secure multi-party computation protocols: survey and more

Vector Commitments over Rings and Compressed $$\varSigma $$-Protocols

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