Secure Multi-Party Quantum Summation Based on Quantum Homomorphic Encryption

Abstract

Secure multi-party computation has been playing a fundamental role in terms of classical cryptography. Quantum homomorphic encryption (QHE) could compute the encrypted data without decryption. At present, most protocols use a semi-honest third party (TP) to protect participants' secrets. We use a quantum homomorphic encryption scheme instead of TP to protect the privacy of parties. Based on quantum homomorphic encryption, a secure multi-party quantum summation scheme is proposed in which N participants can delegate a server with strong quantum computing power to assist computation. By delegating the computation and key update processes to a server and a semi-honest key center, participants encrypt their private information data using Pauli operators to get the sum. Besides, the server can design and optimize the summation lines itself, and the correct results can be obtained even if the secret information is negative. The correctness analysis showed that the participants could correctly obtain the results of the calculation. The security analysis proves the scheme is resistant to both outside attack and participant's attack, and is secure against collusive attack by up to N-2 participants. From the theoretical point of view, our protocol can extend to other secure multi-party computing problems.

Semi‐Quantum Secure Multiparty Summation and its Applications to Anonymous Auction and Ranking

“…3) d-level entangled state: According to the refs. [17,26], the dlevel n-particle entangled state has the form It has many interesting properties, here we focus on the following two properties.…”

“…$$B_C$$ and $$B_F$$ are mutual unbiased basis, they can transform each other through QFT. 3) d ‐level entangled state: According to the refs. [17, 26], the $$d$$‐level $$n$$‐particle entangled state has the form $$$$\begin{equation} \begin{aligned} &|\Phi \rangle =\frac{1}{\sqrt d}\sum ^{d-1}_{j=0}{|j\rangle} _1{|j\rangle} _2 \dots{|j\rangle} _n \end{aligned} \end{equation}$$$$…”

“…QSMC has garnered considerable interest among researchers for its ability to provide quantum-level security. Presently, there exist various branches of research within the field, encompassing topics such as quantum private set intersection cardinality, [9][10][11] quantum private comparison, [12][13][14] quantum secure multiparty summation, [15][16][17][18][19] and more.…”

Arbitrated quantum (t,n) threshold group signature scheme based on multi-coin quantum walk

“…随着量子网络技术的发展, 点对点的量子网络通 信正在向分布式量子网络通信发展, 如何安全地在 分布式量子网络中进行通信和计算具有广泛的研究 意义 [8] , 量子安全多方计算 [9] 、 量子同态加密 [10] 以 及量子(t, n)门限群签名技术 [11][12][13][14] 应运而生. 其中, 量 子(t, n)门限群签名技术在量子网络通信中保障量子 信息传输的完整性、 发送者的身份认证以及签名消 息的不可抵赖性.…”