基于混淆 S 盒的高维量子同态加密机制

Abstract

在量子同态加密机制中, 对密文量子态执行同态评估计算并解密得到的结果与对明文量子态直接评估计算所得的结果相同. 现有的量子同态加密机制不仅评估算子的逻辑门种类有限, 而且使用单点或多点混淆导致计算开销较大. 鉴于此, 本文使用量子随机游走构建了一个混淆 S 盒并将其应用到高维量子同态加密机制的设计之中. 客户端使用高维的 Pauli 算子对明文量子态加密之后, 将密文量子态发送至服务器; 服务器从评估算子集合中选取客户端需要的评估算子, 配合评估参数对密文量子态执行评估操作, 并将评估结果发送至解密方执行解密运算. 为了避免服务器在执行评估操作时泄露解密密钥, 客户端通过设计的混淆 S 盒来完成对解密密钥的混淆并将结果传输给解密方. 解密方执行逆混淆 S 盒还原出解密密钥, 并使用该密钥执行解密操作得到委托计算结果. 对比同类型的相似机制, 该机制增加了评估算子的种类, 降低了量子混淆 S 盒的开销; 通过仿真实验结果证明了提出机制的正确性, 并从信息理论层面证明了该机制的安全性.

Alternate abstract:

In the homomorphic encryption mechanism, the result of homomorphic evaluation calculation and decryption of the ciphertext quantum state is the same as that of direct evaluation calculation of the plaintext quantum state. The existing quantum homomorphic encryption mechanisms not only are limited to the types of logic gates for evaluating operators, but also use single or multi-point confusions, which lead to high computational overhead. In view of this, a confusion S-box based on quantum random walks is constructed, which is applied to the design of a high-dimensional quantum homomorphic encryption mechanism (HQHEM). In HQHEM, the client encrypts the plaintext states by using high-dimensional Pauli operators, and then sends ciphertext states to the server. The server selects the evaluation operator required by the client from the set of evaluation operators, and then performs the homomorphic operations on the ciphertext state with evaluation parameters. Finally, the server sends the evaluation result to the decryptor. In order to avoid the key being leaked by the server during the evaluation, the client obfuscates the decryption key and transmits the result to the decryptor through the designed S-box. The decryptor performs the reverse obfuscation S-box to obtain the decryption key and uses it to decrypt the evaluation results. Compared to the similar schemes, the proposed HQHEM expands the types of evaluation operators and reduces the cost of the quantum obfuscation S-box. The correctness of HQHEM is demonstrated by simulation results, and the security of it is analyzed by information theory.