Sign In

Efficient and Secure General Matrix Multiplication on the Cloud Using Homomorphic Encryption

Core Concepts
A novel element-wise algorithm and two efficient HE-based General Matrix Multiplication (HEGMM) algorithms are developed to significantly reduce the computational cost of HE-based matrix multiplication.
The paper presents a novel approach for efficient and secure general matrix multiplication on the cloud using homomorphic encryption (HE). The key contributions are: A novel element-wise algorithm for general matrix multiplication that can handle source matrices of arbitrary shapes. This method can be applied to improve the performance of matrix multiplication. Two HE-based General Matrix Multiplication (HEGMM) algorithms that leverage the SIMD operations supported by HE schemes. The algorithms pack matrix elements judiciously in encrypted message "slots" and perform pertinent operations to reduce the number of expensive HE operations, such as HE multiplications, rotations, and additions. Rigorous analysis of the logical correctness and computational complexities of the proposed algorithms. The enhanced HEGMM algorithm can significantly outperform the state-of-the-art approaches by reducing the number of HE operations, especially the costly HE-Mult operations. Implementation and extensive experimental evaluation using a Python HE library, Pyfhel, demonstrating the effectiveness of the proposed algorithms.
Encryption latency: 5.50 ms Decryption latency: 2.57 ms Message size: 0.5 MB HE Addition latency: 0.550 ms HE Multiplication latency (ciphertext-ciphertext): 20.874 ms HE Multiplication latency (ciphertext-plaintext): 4.138 ms HE Rotation latency: 5.350 ms
"One major obstacle to employing HE-based computation, however, is its excessive computational cost, which can be orders of magnitude higher than its counterpart based on the plaintext." "Unless HE computation cost can be effectively reduced, it would be infeasible to apply HE schemes in practical cloud applications."

Deeper Inquiries

How can the proposed HEGMM algorithms be extended to handle other linear algebra operations beyond matrix multiplication

The proposed HEGMM algorithms can be extended to handle other linear algebra operations beyond matrix multiplication by leveraging the same principles of homomorphic encryption (HE) and SIMD operations. For example, operations like matrix addition, matrix subtraction, and matrix transposition can be implemented using similar strategies as in the HEGMM algorithms. By defining appropriate transformation matrices and applying element-wise operations, it is possible to perform various linear algebra operations on encrypted data efficiently. Additionally, by optimizing the algorithms for specific operations and data structures, the computational cost can be further reduced, making HE-based computations more practical for a wider range of linear algebra operations.

What are the potential security and privacy implications of using HE-based computations in real-world cloud applications

The use of HE-based computations in real-world cloud applications introduces both security and privacy implications that need to be carefully considered. While HE provides a way to perform computations on encrypted data without revealing the underlying information, there are still potential risks and challenges. One major security concern is the vulnerability of the encryption scheme itself. If the encryption scheme is compromised, it could lead to the exposure of sensitive data and compromise the privacy of the users. Additionally, the computational overhead of HE-based computations can impact the performance of cloud applications, potentially leading to slower processing times and increased costs. It is crucial to implement robust security measures, such as key management protocols and secure communication channels, to mitigate these risks and ensure the confidentiality and integrity of the data.

How can the performance of HE-based computations be further improved by leveraging emerging hardware accelerators or specialized HE libraries

The performance of HE-based computations can be further improved by leveraging emerging hardware accelerators or specialized HE libraries that are optimized for specific operations. Hardware accelerators, such as GPUs or FPGAs, can be used to offload the computational workload of HE operations, speeding up the processing and reducing the overall latency. These accelerators are designed to handle parallel processing efficiently, which is well-suited for the SIMD operations required in HE computations. Additionally, specialized HE libraries, such as SEAL or HElib, offer optimized implementations of HE schemes and operations, allowing for faster and more efficient computations. By integrating these hardware accelerators and libraries into cloud infrastructure, the performance of HE-based computations can be significantly enhanced, making them more practical for real-world applications.