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.