Non-interactive quantum homomorphic encryption scheme based on the rotation operator
Abstract
Quantum homomorphic encryption (QHE) is an important branch of quantum cryptography. It can directly calculate the quantum ciphertext while ensuring calculation correctness and data security. QHE for a T-gate generates an additional S-gate. If this error is not eliminated, the desired output cannot be obtained. Using quantum gate teleportation can eliminate the S-error non-interactively, but increases the decryption complexity. This paper uses the rotation operator to realize QHE for the T / T^† -gate, and proposes a non-interactive QHE scheme. The decryption complexity of this scheme is O(1), and the encryption complexity is O(N) , where N is the number of quantum gates in the evaluated circuit. We prove that the scheme is information-theoretic secure and mathcalF-homomorphic, i.e., homomorphic for any quantum circuit, and implement QHE for a Toffoli-gate decomposition circuit on an IBM Quantum Experience platform.
