A quantum approach to homomorphic encryption

Shreya Girish Savadatti, Aswani Kumar Cherukuri, Annapurna Jonnalagadda +1 more

Homomorphic encryption is a recent and fundamental breakthrough in modern cryptography, which allows the performance of operations on encrypted data without unveiling the data. Leveraging quantum mechanics principles, quantum computers can potentially solve certain computational problems exponentially faster than classical computers. This immense computational power offers new possibilities for various fields, including cryptography. The rapid evolution of both these fields has led to the development of quantum fully homomorphic encryption (QFHE), which makes the capabilities of classical HE extend into the quantum domain. However, many existing QFHE schemes require significant memory due to complex calculations and fault-tolerance needs. This paper contributes in two ways. First, we provide a comprehensive survey of two specific QFHE schemes, discussing their underlying principles, mathematical frameworks, security aspects, and practical applications. We also explore the challenges posed by quantum computing and how QFHE addresses these to achieve both security and computational efficiency. Second, we propose a new hierarchical memory management system for QFHE, which includes a “quantum cache” (a specialized memory storage for quantum data) and a “reinforcement learning agent” (an intelligent system that learns from experience to optimize decisions). This system dynamically manages data movement between the cache and classical memory, improving memory efficiency and potentially boosting computational performance.

Si-Hui Tan, Joshua A. Kettlewell, Yingkai Ouyang +2 more

Surojit Mondal, Bikash Debnath, Jadav Chandra Das +1 more

Homomorphic encryption (HE) is a groundbreaking cryptographic method that allows calculations on encrypted data without the need for decryption, thus safeguarding privacy and security. This article investigates how to implement homomorphic encryption with QISKIT, a free-to-use quantum computing framework. The research investigates the theoretical underpinnings of HE, its use in quantum computing, and its importance for privacy-preserving calculations. Moreover, the study covers adder circuits based on quantum logic gates, their realization with QISKIT, and the prospects for improving computational security in cloud environments. The results stress the practical viability of HE in quantum environments, underscoring its possible uses in secure data processing and privacy-enhancing technologies.

Tao Shang

Liangxin Qian, Yang Li, Jun Zhao

Ensuring secure and efficient data processing in mobile edge computing (MEC) systems is a critical challenge. While quantum key distribution (QKD) offers unconditionally secure key exchange and homomorphic encryption (HE) enables privacy-preserving data processing, existing research fails to address the comprehensive trade-offs among QKD utility, HE security, and system costs. This paper proposes a novel framework integrating QKD, transciphering, and HE for secure and efficient MEC. QKD distributes symmetric keys, transciphering bridges symmetric encryption, and HE processes encrypted data at the server. We formulate an optimization problem balancing QKD utility, HE security, processing and wireless transmission costs. However, the formulated optimization is non-convex and NPhard. To solve it efficiently, we propose the Quantum-enhanced Homomorphic Encryption resource allocation (QuHE) algorithm. Theoretical analysis proves the proposed QuHE algorithm’s convergence and optimality, and simulations demonstrate its effectiveness across multiple performance metrics.

Yajun Liu