基于旋转算子的非交互式量子同态加密方案

Non-interactive quantum homomorphic encryption scheme based on the rotation operator

量子同态加密是量子密码学的一个重要分支,它可以直接对密文量子态进行计算,同时保证计算的正确性和数据的安全性.对量子门T进行量子同态加密会产生额外的相位门S,如果不消除该错误则不能得到正确的输出.使用量子门隐形传态可以非交互地消除相位门错误,但是增加了解密复杂度.本文利用旋转算子实现了T/T?门的量子同态加密,提出了非交互式量子同态加密方案.该方案解密复杂度为O(1),加密复杂度为O(N),其中N是量子线路中量子门的数量.本文证明了该方案是信息论安全的以及能够实现对任意量子线路的量子同态加密,并且在IBM Quantum Experience上实现了对Toffoli门分解线路的量子同态加密.

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 Sgate.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 F-homomorphic,ie.,homomorphic for any quantum circuit,and implement QHE for a Toffoli-gate decomposition circuit on an IBM Quantum Experience platform.