Secure Multiparty Quantum Computation Research Articles

Erratum: Secure multiparty quantum computation with few qubits [Phys. Rev. A 102 , 022405 (2020)

Erratum: Secure multiparty quantum computation with few qubits [Phys. Rev. A <b>102</b> , 022405 (2020)

A privacy preserving quantum aggregating technique with simulation

Quantum aggregation is a basic operation of secure multiparty quantum computation. All the existing techniques are based on the (n,n) threshold, where n is the total number of players. If any of them is corrupted then these techniques cannot execute correctly. However, the proposed technique is based on the (t,n) threshold. If the players are honest then this technique can perform the aggregation. This technique is based on the monotone span program, access structure, linear secret sharing, control-NOT gate, quantum Fourier transform, blind matrix, and Pauli operator. The proposed technique can aggregate the secrets securely and efficiently. We also simulate the proposed technique using IBM quantum computer to verify the correctness and feasibility.

Secure multiparty quantum aggregating protocol

Secure multiparty quantum computation is an important and essential paradigm of quantum computing. All the existing aggregating protocols are $(n, n)$ threshold approaches, where $n$ represents the total number of players. If one player is dishonest, the aggregation protocols cannot aggregate efficiently. In this paper, we propose a $(t, n)$ threshold-based aggregating protocol, where $t$ represents the threshold number of players. This protocol uses Shamir's secret sharing, quantum state, SUM gate, quantum Fourier transform, blind matrix, and Pauli operator. This protocol can perform the aggregation securely and efficiently. In this protocol, we simulate this aggregating protocol using the IBM quantum processor to verify the correctness and feasibility.

(t,n) Threshold d-level QSS based on QFT

Quantum secret sharing (QSS) is an important branch of secure multiparty quantum computation. Several schemes for (n, n) threshold QSS based on quantum Fourier transformation (QFT) have been proposed. Inspired by the flexibility of (t, n) threshold schemes, Song {\it et al.} (Scientific Reports, 2017) have proposed a (t, n) threshold QSS utilizing QFT. Later, Kao and Hwang (arXiv:1803.00216) have identified a {loophole} in the scheme but have not suggested any remedy. In this present study, we have proposed a (t, n)threshold QSS scheme to share a d dimensional classical secret. This scheme can be implemented using local operations (such as QFT, generalized Pauli operators and local measurement) and classical communication. Security of the proposed scheme is described against outsider and participants' eavesdropping.

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.

Secure multiparty quantum computation with few qubits

We consider the task of secure multi-party distributed quantum computation on a quantum network. We propose a protocol based on quantum error correction which reduces the number of necessary qubits. That is, each of the $n$ nodes in our protocol requires an operational workspace of $n^2+\Theta(s) n$ qubits, as opposed to previously shown $\Omega\big((n^3+n^2s^2)\log n\big)$ qubits, where $s$ is a security parameter. To achieve universal computation, we develop a distributed procedure for verifying magic states based on magic state distillation and statistical testing of randomly selected states. This allows us to apply distributed $T$ gate and which may be of independent interest. We showcase our protocol on a small example for a 7-node network.

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.

Continuous variable controlled quantum dialogue and secure multiparty quantum computation

A continuous variable (CV) controlled quantum dialogue (QD) scheme is proposed. The scheme is further modified to obtain two other protocols of (CV) secure multiparty computation. The first one of these protocols provides a solution of two-party socialist millionaire problem, while the second protocol provides a solution for a special type of multi-party socialist millionaire problem which can be viewed as a protocol for multiparty quantum private comparison. It is shown that the proposed scheme of (CV) controlled (QD) can be performed using bipartite entanglement and can be reduced to obtain several other two- and three-party cryptographic schemes in the limiting cases. The security of the proposed scheme and its advantage over corresponding discrete variable (DV) counterpart are also discussed. Specifically, the ignorance of an eavesdropper, i.e., information encoded by Alice/Bob, in the proposed scheme is shown to be more than that in the corresponding (DV) scheme, and thus the present scheme is less prone to information leakage inherent with the (DV) (QD) based schemes. It is further established that the proposed scheme can be viewed as a (CV) counterpart of quantum cryptographic switch which allows a supervisor to control the information transferred between the two legitimate parties to a continuously varying degree.

Secure multiparty quantum computation based on Lagrange unitary operator

As an important subtopic of classical cryptography, secure multiparty quantum computation allows multiple parties to jointly compute their private inputs without revealing them. Most existing secure multiparty computation protocols have the shortcomings of low computational efficiency and high resource consumption. To remedy these shortcomings, we propose a secure multiparty quantum computation protocol by using the Lagrange unitary operator and the Shamir (t, n) threshold secret sharing, in which the server generates all secret shares and distributes each secret share to the corresponding participant, in addition, he prepares a particle and sends it to the first participant. The first participant performs the Lagrange unitary operation on the received particle, and then sends the transformed particle to the next participant. Until the last participant’s computation task is completed, the transformed particle is sent back to the server. The server performs Lagrange unitary operation on the received particle by using a secret message, and then measures the transformed particle to obtain the sum of the calculations of multiple participants. Security analysis shows that the proposed protocol can resist intercept-measurement attack, intercept-resend attack, entanglement-swapping attack, entanglement-measurement attack and collusion attack. Performance comparison shows that it has higher computation efficiency and lower resource consumption than other similar protocols.

A Novel and Efficient Quantum Private Comparison Scheme

A quantum private comparison is a primitive protocol of secure multiparty quantum computation that enables two parties to privately decide whether x = y or not, given two integers x and y, that are held as private inputs by the two parties, respectively. However, many existing quantum private comparison schemes may not be efficient enough, especially applied in big-data and large-scale network environments, because of low efficiency bit-by-bit comparisons. In this paper, we present a novel and efficient quantum private comparison scheme. The proposed scheme provides higher communication efficiency because a secret-by-secret comparison instead of a bit-by-bit comparison is used.

Quantum secret sharing affected by vacuum fluctuation

Quantum secret sharing (QSS) as an important protocol of secure multiparty quantum computation plays a vital role in quantum cryptography. In the real world, any quantum communication protocols are inevitably affected by external noisy environment. In this paper, we investigate the influence of vacuum fluctuation of a massless scalar field on QSS. We firstly construct the noisy model of QSS via two uniformly accelerated atoms coupled with a fluctuating massless scalar field with a perfectly reflecting plane boundary and then derive the master equation that governs the QSS evolution. It is shown that fluctuation of scalar field would lower the performance of QSS. Furthermore, we analyze the impacts of acceleration, two-atom separation and distance from the boundary on the QSS. It is found that increasing acceleration weakens the QSS performance, but in the presence of the reflecting boundary, QSS performance can be improved effectively.

Secure Multiparty Quantum Computation for Summation and Multiplication.

As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantum mechanics.