Research On Private Collection And Private Geometric Computing Based On Quantum Algorithm

Secure Multiparty Computation(SMC)based on Quantum unconditional security and parallel computing capability is an important research topic,which is called Quantum Multiparty Computation(QSMC).Private set computing and privacy-preserving geometric computing are two important SMC problems,which are widely used in the era of big data.However,current research on this problem is relatively lacking in QSMC.The protocols constructed generally have high complexity,and can rarely be extended to any multi-party occasions.Some quantum algorithms have exponential acceleration capability,which can further improve the efficiency of existing quantum private sets and privacy-preserving geometric computation.Based on this,this paper deeply explores the quantum private set computation and privacy-preserving geometric computation,and the main work contents are as follows.(1)Private Set Union(PSU)allows multiple participants to obtain the union without disclosing their private sets.The existing private set union protocols usually have polynomial complexity for the full set size,and it is difficult to compute the set union of any many parties at once.In this paper,we propose a quantum multi-party private set union protocol based on Least Common Multiple(LCM)and Shor’s algorithm.This protocol makes the union of multiple sets can be obtained through one-time computation.In order to improve the one-time success probability of the protocol,we first improve the Shor’s period-finding algorithm(QPA).Then the private set of each party is encoded into an integer obtained bymultiplying several prime numbers,thus transforming the private set union problem into the least common multiple problem.We implement the Oracle of modulo function in detail,and on this basis,we use the improved Shor’s period-finding algorithm to calculate the least common multiple of these integers,and factor to get the union.We demonstrate the correctness of the proposed protocol and its unconditional security against semi-honest attacks.In the complexity analysis,we show that our protocol has logarithmic complexity for the full set size.(2)In geometric computation,privacy-preserving area intersection decision,especially privacy-preserving circle intersection decision has important research and application value.The existing quantum privacy-preserving region intersection decision protocol needs a lot of computational complexity.In quantum field,the phase-encoded query protocol can achieve very low communication complexity,so it is often used for QSMC.However,on the one hand,the implementation of its query requires the application of high-dimensional Oracle operator,and its required computational complexity is often ignored by people.On the other hand,there is also a lack of research on the realization of privacy-preserving circle intersection by using phase-encoded query.In this paper,we use the principle of phaseencoded query to realize the quantum privacy-preserving circle intersection decision.We studied the implementation of Oracle operator in detail,and realized the computational complexity of polynomial level by decomposing it into quantum arithmetic operation,so as to realize the efficiency of quantum geometry computation.