On Statistically-Secure Quantum Homomorphic Encryption
This addresses the security and efficiency limitations in quantum cryptography for researchers in quantum computing and encryption.
The paper tackles the problem of constructing quantum homomorphic encryption with information-theoretic security, showing that such fully homomorphic encryption necessarily incurs exponential overhead, and proposes a scheme for instantaneous quantum polynomial-time circuits based on the one-time pad.
Homomorphic encryption is an encryption scheme that allows computations to be evaluated on encrypted inputs without knowledge of their raw messages. Recently Ouyang et al. constructed a quantum homomorphic encryption (QHE) scheme for Clifford circuits with statistical security (or information-theoretic security (IT-security)). It is desired to see whether an information-theoretically-secure (ITS) quantum FHE exists. If not, what other nontrivial class of quantum circuits can be homomorphically evaluated with IT-security? We provide a limitation for the first question that an ITS quantum FHE necessarily incurs exponential overhead. As for the second one, we propose a QHE scheme for the instantaneous quantum polynomial-time (IQP) circuits. Our QHE scheme for IQP circuits follows from the one-time pad.