Fast secure matrix multiplications over ring-based homomorphic encryption

Mishra, Pradeep Kumar; Rathee, Deevashwer; Duong, Dung Hoang; Yasuda, Masaya

doi:10.1080/19393555.2020.1836288

Cited by 14 publications

(4 citation statements)

References 35 publications

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“…Only several MPC implementations are available [8]. Some of them are for two parties only and most of the others are generic and transform programs into circuits or use oblivious transfer [13,14].…”

Section: Related Workmentioning

confidence: 99%

Lightweight Privacy-Preserving (t, m, n) Multi-Party Computation Based on Secret Sharing in Untrusted Cloud Environments

Harn

Hsu

Xia

2023

Preprint

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The next generation of Internet of Things (IoT) networks and mobile communications (5G IoT networks) has the particularity of being heterogeneous, therefore, it has very strong ability to compute, store, etc. Group-oriented applications demonstrate its potential ability in Untrusted Cloud Environments (UCE). One of the main challenges for secure group-oriented applications (SGA) in UCE is how to secure communication and computation between these heterogeneous devices. Conventional protocols are not suitable for SGA in UCE since multiparty secure computation in this environment requires lightweight communication and computation overhead. Multi-Party Computation (MPC) takes multiple inputs and outputs their sum/product without revealing each individual input. MPC has found ways in electronic voting, electronic auctions, electronic cash schemes, contract signing, etc. Motivated by the first arithmetic MPC protocol (also known as BGW protocol) proposed by Ben-Or et al. based on the secret sharing scheme, in this paper, we give a novel definition, called (t, m, n) MPC, where m is the number of data inputs, t is a threshold and n is the number of shares, which is similar to the definition of a (t, n) secret sharing scheme; but with some additional security requirements. BGW is a (t, m, n) MPC but has following limitations, (1) BGW cannot be used to implement a (m, m, m) MPC; and (2) in computing multiplicative product, BGW needs degree-reduction process which is a communication intensive process. In this paper, we propose a simple and lightweight (m, m, m) MPC which involves only additions/multiplications. Then, we extend our simple (m, m, m) MPC to design a general (t, m, n) MPC. Our proposed MPC is more efficient than BGW since our MPC does not need degree-reduction process. It is really attractive for lightweight privacy-preserving multi-party computation in UCE.

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Section: Related Workmentioning

confidence: 99%

Lightweight Privacy-Preserving (t, m, n) Multi-Party Computation Based on Secret Sharing in Untrusted Cloud Environments

Harn

Hsu

Xia

2023

Preprint

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“…Matrix Multiplication. The typical methods for matrix multiplication in fully homomorphic encryption (FHE) [48], [89] do not preserve the structure of the matrix in the plaintext slots, i.e., the shape of the computation output is different than that of the inputs, or one of the…”

Section: A Packing and Optimized Matrix Operationsmentioning

confidence: 99%

Privacy-Preserving Federated Recurrent Neural Networks

Sav¹,

Abdulrahman²,

Pyrgelis³

et al. 2022

Preprint

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We present RHODE, a novel system that enables privacy-preserving training of and prediction on Recurrent Neural Networks (RNNs) in a federated learning setting by relying on multiparty homomorphic encryption (MHE). RHODE preserves the confidentiality of the training data, the model, and the prediction data; and it mitigates the federated learning attacks that target the gradients under a passive-adversary threat model. We propose a novel packing scheme, multi-dimensional packing, for a better utilization of Single Instruction, Multiple Data (SIMD) operations under encryption. With multi-dimensional packing, RHODE enables the efficient processing, in parallel, of a batch of samples. To avoid the exploding gradients problem, we also provide several clip-by-value approximations for enabling gradient clipping under encryption. We experimentally show that the model performance with RHODE remains similar to non-secure solutions both for homogeneous and heterogeneous data distribution among the data holders. Our experimental evaluation shows that RHODE scales linearly with the number of data holders and the number of timesteps, sub-linearly and sub-quadratically with the number of features and the number of hidden units of RNNs, respectively. To the best of our knowledge, RHODE is the first system that provides the building blocks for the training of RNNs and its variants, under encryption in a federated learning setting.

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“…The computation of matrix products is a fundamental operation in all computation applications of linear algebra. MM is a binary operation in which we produce the result from two matrices in a new matrix (Mishra et al, 2020), whereas, CMM is a sequence of matrices in which we find the most efficient way to multiply a sequence of matrices, to decide which order to accomplish the multiplications. We only defined the number of operations to multiply the matrices.…”

Section: Introductionmentioning

confidence: 99%

Optimal sequence for chain matrix multiplication using evolutionary algorithm

Iqbal

Shoukat

Elahi

et al. 2021

PeerJ Computer Science

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The Chain Matrix Multiplication Problem (CMMP) is an optimization problem that helps to find the optimal way of parenthesization for Chain Matrix Multiplication (CMM). This problem arises in various scientific applications such as in electronics, robotics, mathematical programing, and cryptography. For CMMP the researchers have proposed various techniques such as dynamic approach, arithmetic approach, and sequential multiplication. However, these techniques are deficient for providing optimal results for CMMP in terms of computational time and significant amount of scalar multiplication. In this article, we proposed a new model to minimize the Chain Matrix Multiplication (CMM) operations based on group counseling optimizer (GCO). Our experimental results and their analysis show that the proposed GCO model has achieved significant reduction of time with efficient speed when compared with sequential chain matrix multiplication approach. The proposed model provides good performance and reduces the multiplication operations varying from 45% to 96% when compared with sequential multiplication. Moreover, we evaluate our results with the best known dynamic programing and arithmetic multiplication approaches, which clearly demonstrate that proposed model outperforms in terms of computational time and space complexity.

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Fast secure matrix multiplications over ring-based homomorphic encryption

Cited by 14 publications

References 35 publications

Lightweight Privacy-Preserving (t, m, n) Multi-Party Computation Based on Secret Sharing in Untrusted Cloud Environments

Lightweight Privacy-Preserving (t, m, n) Multi-Party Computation Based on Secret Sharing in Untrusted Cloud Environments

Privacy-Preserving Federated Recurrent Neural Networks

Optimal sequence for chain matrix multiplication using evolutionary algorithm

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