Non-interactive quantum homomorphic encryption scheme based on the rotation operator
WANG ShuoLin, SHANG Tao, LIU JianWei · Zhongguo kexue. Wulixue Lixue Tianwenxue · 2022
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.