A quantum approach to homomorphic encryption

Abstract

Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum homomorphic encryption scheme that enables a broad class of quantum computation on encrypted data. A particular instance of our encoding hides up to a constant fraction of the information encrypted. This fraction can be made arbitrarily close to unity with overhead scaling only polynomially in the message length. This highlights the potential of our protocol to hide a non-trivial amount of information, and is suggestive of a large class of encodings that might yield better security.

5 pages, 1 figure. Improved security bound over previous version. An erroneous proof of universality has been removed

References in corpus (9)

• Quantum computing on encrypted data
• Experimental verification of quantum computations
• Quantum homomorphic encryption for circuits of low $T$-gate complexity
• Quantum walks with encrypted data
• Efficient universal blind computation
• Optimal Blind Quantum Computation
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• Quantum Fully Homomorphic Encryption With Verification
• Experimental Demonstration of Quantum Fully Homomorphic Encryption with Application in a Two-Party Secure Protocol
• Practical quantum somewhat-homomorphic encryption with coherent states
• Computing on quantum shared secrets
• On the possibility of classical client blind quantum computing
• The Quantum Internet: A Hardware Review
• Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security
• Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption
• Error correctable efficient quantum homomorphic encryption using Calderbank-Shor-Steane codes
• Implementing Semiclassical Szegedy Walks in Classical-Quantum Circuits for Homomorphic Encryption
• Demonstrating Quantum Homomorphic Encryption Through Simulation
• Optical Quantum Computing