On statistically-secure quantum homomorphic encryption (pp0785-0794)
          Ching-Yi Lai and Kai-Min Chung
          doi:https://doi.org/10.26421/QIC18.9-10-4
Abstracts: 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.
Key words: quantum homomorphic encryption, information-theoretical security, quantum private information retrieval, instantaneous quantum polynomial-time