At CIEP 2024, a session on fully homomorphic encryption showcased how SIMD techniques enhance secure matrix computations on remote servers, enabling efficient and private data processing.
During CIEP 2024 at NUAA, Professor Çetin Kaya Koç and colleagues presented cutting-edge advancements in secure matrix computations using SIMD-based fully homomorphic encryption (FHE). The session emphasized how the Chinese Remainder Theorem supports efficient FHE schemes like BGV, BFV, and CKKS, allowing secure operations on matrix data stored on external servers. This initiative marks NUAA’s efforts to create an SIMD FHE library capable of handling large matrix dimensions in a single encrypted ciphertext, making data processing both scalable and privacy-preserving.
CIEP 2024 Conference: Exploring Innovations in Secure Matrix Computations through SIMD and Fully Homomorphic Encryption
Shanghai, China—The annual Conference on International Exchange of Professionals (CIEP 2024) held a landmark session at Nanjing University of Aeronautics & Astronautics (NUAA), bringing together experts from around the world to discuss the latest advances in matrix computations using secure encryption methods. This year’s focus was a groundbreaking session titled “Matrix Computations Using SIMD Fully Homomorphic Encryption (FHE)”, led by notable cryptography and secure computation expert, Professor Çetin Kaya Koç.
During the session, Professor Koç and other conference attendees addressed the application of the Chinese Remainder Theorem (CRT) to enhance fully homomorphic encryption schemes, such as BGV, BFV, and CKKS. This methodology enables the transformation of cryptographic operands into integer vectors, significantly optimizing secure computations by facilitating Single Instruction, Multiple Data (SIMD) operations on matrix row and column vectors. In particular, the CRT application in FHE allows for efficient addition and multiplication on encrypted data, paving the way for new possibilities in secure outsourced computations.
Revolutionizing Matrix Computation Security
Fully homomorphic encryption has been a cornerstone in data privacy, particularly for securely outsourcing computations to third-party servers without compromising sensitive information. Traditional matrix operations, however, encounter limitations due to the high computational costs involved in secure encryption. Over the past decade, researchers have developed algorithms capable of performing homomorphic operations, including addition and multiplication, directly on encrypted matrices. Yet, Professor Koç emphasized that the recent advances discussed at CIEP go beyond previous methods by embedding a complete matrix within a single FHE ciphertext or plaintext, achieving secure computations with increased efficiency.
“This approach allows us to represent larger matrix dimensions, a breakthrough in FHE technology. At NUAA, we are pushing the boundaries by embedding an entire matrix of dimensions k×k into one FHE unit, achieving scalability with security,” said Professor Koç.
The NUAA Research Program: Developing an SIMD FHE Library
In collaboration with NUAA, a new research initiative aims to develop an SIMD FHE library specifically tailored for matrix computations. This program addresses a critical gap in homomorphic encryption applications, offering a secure and efficient framework for storing and processing encrypted matrices on external servers. By embedding matrices of up to 256 x 256 dimensions within a single FHE block, the research opens up potential for securely handling large-scale data without compromising encryption standards.
Professor Koç noted the innovative approach taken in this research, which employs a matrix size kxk constrained by a plaintext or ciphertext n ensuring k2≤ n. For security reasons, n is set as high as 64k, allowing the NUAA library to manage substantial matrices in a secure, encrypted environment.
Real-World Applications and Future Directions
The NUAA project marks a significant step forward in the field of encrypted computations, potentially impacting industries ranging from finance and healthcare to government and defense. By enabling SIMD matrix operations, this research addresses a critical need for secure, efficient data processing on sensitive information in a range of applications.
At the conference, attendees were introduced to the first algorithms produced by the NUAA team, which include functions for homomorphic matrix addition and multiplication. These algorithms will be foundational in the development of a more comprehensive library and may serve as a reference for future secure computation frameworks.
