Multi-party Quantum Summation Research Articles

Secure Multi-Party Quantum Summation Based on Quantum Homomorphic Encryption

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.

Multi-party quantum summation without a third party based on d-dimensional Bell states

Multi-party quantum summation without a third party based on d-dimensional Bell states

Improvement of Quantum Protocols for Secure Multi-Party Summation

Secure multi-party quantum summation is an important branch of secure multi-party quantum computation. Recently, Ji et al. suggested a secure multi-party quantum summation scheme based on the entanglement swapping between the d-level Bell state and the d -level n+1-particle cat state (Quantum Inf Process (2019)18:168). In this paper, it is pointed out that Ji et al.’s secure multi-party quantum summation scheme has a security loophole, i.e., the third party (TP) can obtain the secret numbers of n communicants without being discovered. Then, in order to avoid this security loophole, an improvement is suggested by adopting the method of encrypting the secret integers of n communicants with a pre-shared private key sequence among them.

Hybrid Quantum Protocols for Secure Multiparty Summation and Multiplication

The summation and multiplication are two basic operations for secure multiparty quantum computation. The existing secure multiparty quantum summation and multiplication protocols have (n, n) threshold approach and their computation type is bit-by-bit, where n is total number of players. In this paper, we propose two hybrid (t, n) threshold quantum protocols for secure multiparty summation and multiplication based on the Shamir’s secret sharing, SUM gate, quantum fourier transform, and generalized Pauli operator, where t is a threshold number of players that can perform the summation and multiplication. Their computation type is secret-by-secret with modulo d, where d, n ≤ d ≤ 2n, is a prime. The proposed protocols can resist the intercept-resend, entangle-measure, collusion, collective, and coherent quantum attacks. They have better computation as well as communication costs and no player can get other player’s private input.

A Generalized Quantum Protocol for Secure Multiparty Summation

The secure multiparty quantum summation is an important primitive of quantum cryptography. The existing multiparty quantum summation protocols have $(n, n)$ threshold approach, where $n$ out of total $n$ players need compute the summation protocol. In this brief, we present a generalized secure multiparty quantum summation protocol. In our protocol, the linear secret sharing (LSS) and Quantum Fourier Transform (QFT) are used to take the advantages of both classical and quantum summation. We show that the outside and participant attacks are not possible in our protocol. We simulate it using the real quantum processor released by IBM corporation on “cloud”.

Multi-Party Quantum Summation within a d-Level Quantum System

At present, there are some quantum summation protocols calculating the addition in a bit-by-bit way so that they are inefficient and unpractical in certain circumstances. In this paper, a secure multi-party quantum summation protocol within a d-level quantum system is constructed by using the qudit shifting operation, where the encoded photons are transmitted in a circular way. The proposed protocol can calculate the addition of modulo d in an integer-by-integer way rather than a bit-by-bit way. The security analysis result shows that the proposed protocol is secure against both the outside attack and the participant attack.

Improvements on “Secure multi-party quantum summation based on quantum Fourier transform”

Recently, a quantum multi-party summation protocol based on the quantum Fourier transform has been proposed (Yang et al. in Quantum Inf Process 17:129, 2018). The protocol claims to be secure against both outside and participant attacks. However, a closer look reveals that the player in charge of generating the required multi-partite entangled states can launch two kinds of attacks to learn about other parties’ private integer strings without being caught. In this paper, we present these attacks and propose countermeasures to make the protocol secure again. The improved protocol not only can resist these attacks but also remove the need for the quantum Fourier transform and encoding quantum operations by participants.

Multi-Party Quantum Summation Based on Quantum Teleportation.

We present a secure multi-party quantum summation protocol based on quantum teleportation, in which a malicious, but non-collusive, third party (TP) helps compute the summation. In our protocol, TP is in charge of entanglement distribution and Bell states are shared between participants. Users encode the qubits in their hand according to their private bits and perform Bell-state measurements. After obtaining participants’ measurement results, TP can figure out the summation. The participants do not need to send their encoded states to others, and the protocol is therefore congenitally free from Trojan horse attacks. In addition, our protocol can be made secure against loss errors, because the entanglement distribution occurs only once at the beginning of our protocol. We show that our protocol is secure against attacks by the participants as well as the outsiders.

Improving the Security of ‘High-Capacity Quantum Summation with Single Photons in both Polarization and Spatial-Mode Degrees of Freedom’

In 2014, Zhang et al. (Int J Theor Phys:53:933–941, 2014) proposed a secure multi-party quantum summation protocol based on single photons in both polarization and spatial-mode degrees of freedom. They claimed that the proposed protocol can efficiently help the involved participants to sum their secrets, and at the same time, each participant’s secret can be kept from being known by others. However, this study shows that Zhang et al.’s protocol suffers from the intercept-resend attack. To solve this problem, a modification is proposed here.

Multi-party quantum summation with a single d-level quantum system

A multi-party quantum summation with a single [Formula: see text]-level quantum system is proposed, in which a semi-honest third party (TP) is employed. Only sequential communication of a single quantum [Formula: see text]-level system (for any prime [Formula: see text]) is required in the presented protocol, resulting in advantages in scalability. In addition, it can be realized with state-of-the-art technology. Due to the semi-honest TP, the protocol is not only secure against outside attacks, but also secure against participant attacks.

Secure multi-party quantum summation based on quantum Fourier transform

In this paper, we propose a novel secure multi-party quantum summation protocol based on quantum Fourier transform, where the traveling particles are transmitted in a tree-type mode. The party who prepares the initial quantum states is assumed to be semi-honest, which means that she may misbehave on her own but will not conspire with anyone. The proposed protocol can resist both the outside attacks and the participant attacks. Especially, one party cannot obtain other parties' private integer strings; and it is secure for the colluding attack performed by at most n-2 parties, where n is the number of parties. In addition, the proposed protocol calculates the addition of modulo d and implements the calculation of addition in a secret-by-secret way rather than a bit-by-bit way.

Multi-party quantum summation without a trusted third party based on single particles

We propose multi-party quantum summation protocols based on single particles, in which participants are allowed to compute the summation of their inputs without the help of a trusted third party and preserve the privacy of their inputs. Only one participant who generates the source particles needs to perform unitary operations and only single particles are needed in the beginning of the protocols.

An Efficient Protocol for the Secure Multi-party Quantum Summation

In this paper, a new and efficient quantum protocol which allows a group of mutually distrustful players to perform the summation computation is proposed. Different from previous protocols, we utilize the multi-particle entangled states as the information carriers. A third party, i.e. TP, is assumed semi-honest in the two-party quantum summation protocol. All various kinds of outside attacks and participant attacks are discussed in detail. In addition, we code all players’ Bell-basis measurement outcomes into one classical bit (cbit). Not only the cost of classical information in the public communication network is decreased, but also the security of the protocol is improved. The protocol is also generalized into multi-party quantum summation. It is secure for the collusive attack performed by at most n−2 players.