More Efficient Secure Matrix Multiplication for Unbalanced Recommender Systems

Abstract

With recent advances in homomorphic encryption (HE), it becomes feasible to run non-interactive machine learning (ML) algorithms on encrypted data without decryption. In this work, we propose novel encoding methods to pack matrix in a compact way and more efficient methods to perform matrix multiplication on homomorphically encrypted data, leading to a speed boost of 1.5 × −20× for slim rectangular matrix multiplication compared with state-of-the-art. Moreover, we integrate our optimized secure matrix arithmetic with the MPI distributed computing framework, achieving scalable parallel secure matrix computation. Equipped with the optimized matrix multiplication, we propose uSCORE, a privacy-preserving cross-domain recommendation system for the unbalanced scenario, where a big data owner provides recommendation as a service to a client who has less data and computation power. Our design delegates most of the computation to the service provider, and has a low communication cost, which previous works failed to achieve. For a client who has 16 million user-item pairs to update, it only needs about 3 minutes (in the LAN setting) to prepare the encrypted data. The server can finish the update process on the encrypted data in less than half an hour, effectively reducing the client's test error from 0.72 to 0.62.

Secure and Efficient General Matrix Multiplication On Cloud Using Homomorphic Encryption

“…Source matrices can be enlarged to suit shape requirements for MM with variable shapes, although this may increase processing time and resource utilization. Huang et al [28] advocated using blocking to better handle rectangular MM with source matrices as block matrices with square matrices. This method is appealing for big matrices that cannot fit in one ciphertext.…”

“…When l = min{m, l, n}, we make no change of A and B (lines 11 -15). After initializing several relevant variables (lines 16 -18), Algorithm 2 goes through a loop to compute and accumulate the partial products (lines [19][20][21][22][23][24][25][26][27][28]. To be more specific, we first conduct ϵ and ω transformations based on the expanded matrix (A or B) (lines 20 -21), which are combined together into C temp using the element-wise HE multiplication (line 22).…”

Discovering Millennials’ Migration Clusters in Seoul, South Korea: A Local Spatial Network Autocorrelation Approach

“…The main goal of our algorithm is to reduce the number of rotations and multiplications used, which occupy most of the algorithm runtime (see Section 5.1 for the costs of each operation in HE). Note that including a transpose in multiplication is more efficient than computing matrix multiplication of the form AB directly as in (Jiang et al, 2018;Huang et al, 2021), since we need to perform transpose for each iteration of training, which is a costly operation and requires additional multiplicative depth.…”

“…We experimentally showed that the execution times of our algorithms are significantly smaller than that of (Crockett, 2020). Some encrypted matrix multiplication algorithms (Jiang et al, 2018;Huang et al, 2021) are of the form AB, that is, they do not include transpose. As mentioned previously, these are unsuitable for our purpose because they add transpose operations for each training iteration.…”

Privacy-preserving keyword query quantum scheme for outsourced data in cloud environments

“…On one hand, encryption increases the management cost for cloud service providers in handling user data. On the other hand, encrypted data significantly limits its operability, making it difficult to implement common data services such as keyword search [5,6,7] and online editing [8,9].…”