SPD$$\mathbb {Z}_{2^k}$$: Efficient MPC mod $$2^k$$ for Dishonest Majority

Cramer, Ronald; Damgård, Ivan; Escudero, Daniel; Schöll, Peter; Xing, Chaoping

doi:10.1007/978-3-319-96881-0_26

Cited by 94 publications

(122 citation statements)

References 19 publications

(24 reference statements)

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“…This overhead comes from the fact that we need to work over a larger structure (a Galois ring) in order to obtain algebraic properties that resemble those on fields, and that can be used for multiparty computation. A similar approach is taken in the SPDZ 2 k protocol [8] for computation over Z/2 k Z by using the larger ring Z/2 k+s Z. In that work it is conjectured that this is an inherent price to pay for working over an algebraic structure with less nice properties than a field, and our current approach to information-theoretic MPC over Z/p k Z seems to support this claim, at least in the setting of a single circuit execution.…”

Section: Discussionmentioning

confidence: 99%

“…The overall protocol for secure computation follows the offline/online phase paradigm, which is typical from other secret-sharing based protocols, like these from [3][4][5]8,12,14]. Essentially, the parties preprocess some material in the offline phase which is used in the online phase to perform the computation, after sharing the inputs.…”

Section: Sub-protocols For Secure Computation Over Galois Ringsmentioning

confidence: 99%

“…This question was solved recently in the setting of dishonest majority (i.e. t ≤ n − 1), where cryptography is required to provide security, with the introduction of the SPDZ 2 k protocol [8]. This protocol computes with computational security circuits defined over the ring Z/2 k Z (in fact, 2 can be replaced by any prime).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Abspoel

Cramer

Damgård

et al. 2019

Lecture Notes in Computer Science

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At CRYPTO 2018, Cramer et al. introduced a secret-sharing based protocol called SPDZ 2 k that allows for secure multiparty computation (MPC) in the dishonest majority setting over the ring of integers modulo 2 k , thus solving a long-standing open question in MPC about secure computation over rings in this setting. In this paper we study this problem in the information-theoretic scenario. More specifically, we ask the following question: Can we obtain information-theoretic MPC protocols that work over rings with comparable efficiency to corresponding protocols over fields? We answer this question in the affirmative by presenting an efficient protocol for robust Secure Multiparty Computation over Z/p k Z (for any prime p and positive integer k) that is perfectly secure against active adversaries corrupting a fraction of at most 1/3 players, and a robust protocol that is statistically secure against an active adversary corrupting a fraction of at most 1/2 players.

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Section: Discussionmentioning

confidence: 99%

Section: Sub-protocols For Secure Computation Over Galois Ringsmentioning

confidence: 99%

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

Abspoel

Cramer

Damgård

et al. 2019

Lecture Notes in Computer Science

Self Cite

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“…For the actively secure case, in contrast to our work over fields i.e. modulo prime, another direction can be an implementation over rings of the form 2 k using SPDZ-2k protocol [23]. Such an setting can leverage the efficiency of native operations in a 32-bit/64-bit standard CPU to show efficient results.…”

Section: A Future Workmentioning

confidence: 99%

Secure and Efficient Federated Transfer Learning

Sharma

Xing

Liu³

et al. 2019

2019 IEEE International Conference on Big Data (Big Data)

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Machine Learning models require a vast amount of data for accurate training. In reality, most data is scattered across different organizations and cannot be easily integrated under many legal and practical constraints. Federated Transfer Learning (FTL) was introduced in [1] to improve statistical models under a data federation that allow knowledge to be shared without compromising user privacy, and enable complementary knowledge to be transferred in the network. As a result, a target-domain party can build more flexible and powerful models by leveraging rich labels from a source-domain party. However, the excessive computational overhead of the security protocol involved in this model rendered it impractical. In this work, we aim towards enhancing the efficiency and security of existing models for practical collaborative training under a data federation by incorporating Secret Sharing (SS). In literature, only the semihonest model for Federated Transfer Learning has been considered. In this paper, we improve upon the previous solution, and also allow malicious players who can arbitrarily deviate from the protocol in our FTL model. This is much stronger than the semi-honest model where we assume that parties follow the protocol precisely. We do so using the one of the practical MPC protocol called SPDZ, thus our model can be efficiently extended to any number of parties even in the case of a dishonest majority. In addition, the models evaluated in our setting significantly outperform the previous work, in terms of both runtime and communication cost. A single iteration in our model executes in 0.8 seconds for the semihonest case and 1.4 seconds for the malicious case for 500 samples, as compared to 35 seconds taken by the previous implementation.

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“…These protocols were designed to generate triples over a finite field which can only be used to support finite field arithmetic in the online phase. In 2018, Cramer et al [7] proposed an OT-based protocol that generates triples over rings of the form Z 2 . Designing protocols over rings is useful in a lot of applications since it greatly simplifies implementation of comparisons and bitwise operations, which are inefficient to realize with finite field arithmetic.…”

Section: Introductionmentioning

confidence: 99%

Improved Multiplication Triple Generation over Rings via RLWE-Based AHE

Rathee

Schneider

Shukla

2019

Lecture Notes in Computer Science

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An important characteristic of recent MPC protocols is an input-independent setup phase in which most computations are offloaded, which greatly reduces the execution overhead of the online phase where parties provide their inputs. For a very efficient evaluation of arithmetic circuits in an information-theoretic online phase, the MPC protocols consume Beaver multiplication triples generated in the setup phase. Triple generation is generally the most expensive part of the protocol, and improving its efficiency is the aim of our work. We specifically focus on computation over rings of the form Z 2 in the semi-honest model and the two-party setting, for which an Oblivious Transfer (OT)-based protocol is currently the best solution. To improve upon this method, we propose a protocol based on RLWE-based Additively Homomorphic Encryption. Our experiments show that our protocol is more scalable, and it outperforms the OT-based protocol in most cases. For example, we improve communication by up to 6.9x and runtime by up to 3.6x for 64-bit triple generation.

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SPD$$\mathbb {Z}_{2^k}$$: Efficient MPC mod $$2^k$$ for Dishonest Majority

Cited by 94 publications

References 19 publications

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

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

Secure and Efficient Federated Transfer Learning

Improved Multiplication Triple Generation over Rings via RLWE-Based AHE

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