Fast Plaintext-Ciphertext Matrix Multiplication from Additively Homomorphic Encryption

2025-04-08

IACR Communications in Cryptology

AI Summary

To address the low efficiency of plaintext-ciphertext matrix multiplication (PC-MM) under unpacked additive homomorphic encryption (AHE), this work pioneers the adaptation of the Cussen compression-reconstruction algorithm to the unpacked AHE setting, overcoming the performance bottlenecks of conventional schoolbook and Strassen methods. Leveraging an elliptic-curve ElGamal cryptosystem, we integrate SIMD-style data layout optimization with a tree-based reconstruction strategy to enable lightweight deployment on edge devices—specifically, the Raspberry Pi 5. Experiments demonstrate up to a 10× throughput improvement in PC-MM for large matrices and low bit-width operands over state-of-the-art approaches, significantly enhancing the feasibility of privacy-preserving machine learning and encrypted signal processing under resource constraints. Our core contribution is the first compression-reconstruction PC-MM paradigm tailored for unpacked AHE, jointly optimizing security, numerical precision, and edge-device efficiency.

Technology Category

• Machine Learning: Hardware-aware ML
• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Data Compression

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Plaintext-ciphertext matrix multiplication (PC-MM) is an indispensable tool in privacy-preserving computations such as secure machine learning and encrypted signal processing. While there are many established algorithms for plaintext-plaintext matrix multiplication, efficiently computing plaintext-ciphertext (and ciphertext-ciphertext) matrix multiplication is an active area of research which has received a lot of attention. Recent literature have explored various techniques for privacy-preserving matrix multiplication using fully homomorphic encryption (FHE) schemes with ciphertext packing and Single Instruction Multiple Data (SIMD) processing. On the other hand, there hasn't been any attempt to speed up PC-MM using unpacked additively homomorphic encryption (AHE) schemes beyond the schoolbook method and Strassen's algorithm for matrix multiplication. In this work, we propose an efficient PC-MM from unpacked AHE, which applies Cussen's compression-reconstruction algorithm for plaintext-plaintext matrix multiplication in the encrypted setting. We experimentally validate our proposed technique using a concrete instantiation with the additively homomorphic elliptic curve ElGamal encryption scheme and its software implementation on a Raspberry Pi 5 edge computing platform. Our proposed approach achieves up to an order of magnitude speedup compared to state-of-the-art for large matrices with relatively small element bit-widths. Extensive measurement results demonstrate that our fast PC-MM is an excellent candidate for efficient privacy-preserving computation even in resource-constrained environments.

Problem

• Efficient plaintext-ciphertext matrix multiplication for privacy-preserving computations
• Speeding up matrix multiplication using unpacked additively homomorphic encryption
• Validating performance in resource-constrained edge computing environments

Innovation

• Uses unpacked additively homomorphic encryption
• Applies Cussen's compression-reconstruction algorithm
• Validated with elliptic curve ElGamal encryption