A quantum homomorphic encryption scheme for polynomial-sized circuits
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Quantum homomorphic encryption (QHE) is an encryption method that allows quantum computation to be performed on one party's private data with the program provided by another party, without revealing much information about the data nor about the program to the opposite party. It usually allows only two rounds of communication. It is known that information-theoretically-secure QHE for arbitrary circuits would require exponential resources, and efficient computationally-secure QHE schemes for polynomial-sized quantum circuits have been constructed. In this paper we propose an information-theoretically-secure QHE scheme suitable for quantum circuits of size polynomial in the number of data qubits. The scheme keeps the data perfectly secure, and the circuit quite secure with the help of a polynomial amount of entanglement and classical communication.
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