Research On Two Basic Problems In Secure Multi-party Computation

Secure multi-party computation(SMC)was first proposed by Yao in 1982,and so far,it has become a major research hot spot in cryptography.It has significant theoretical research significance and practical application value.This paper makes an in-depth study of the problem of privacy-preserving determination of spatial location relation and the maximum,the least common multiple and the greatest common divisor of secure multi-party computation.The specific work is as follows,Aiming at the problem of determining the positional relationship,the three points collinear,and the location relation among of point line and plane in space of computational geometry,this paper analyzes the current research state of the problem,summarizes their advantages and disadvantages,points out their drawbacks,and converts the original problem into a parallelogram problem.Combining the scalar protocol,this paper design six protocols for privacy-preserving determination of the three points collinear,and the location relation of point line and plane in space,the correctness,security,and complexity of the new protocol are analyzed at the theoretical,.Compared with existing solutions,our protocols not only applies to a wider scope,but also has higher security and is superior to existing solutions.Aiming at the problem of multi-party privacy-preserving computation of the maximum,the least common multiple and the greatest common divisor of in scientific computing,this paper analyzes the current research state of the problem,summarizes their advantages and disadvantages,points out their drawbacks.Aiming at the existing solutions cannot resist the quantum attack and cannot also be applied to cloud computing,a 1-0 encoding and 0-1 encoding method are proposed,and combining the NTRU multi-key homomorphic encryption algorithm,this paper design three new protocols for the maximum,the least common multiple,and the greatest common divisor for anti-quantum attacks under cloud environment.Examples of their applications in education,sports,and finance are given.The theoretical analysis of the correctness,complexity,and security of the new design protocol.The analysis and comparison demonstrate that the three protocols designed in this paper are more efficient than the previously known.In addition,it is the fist time that our solution not only can resist the anti-quantum attack,but also is applicable in the cloud computing environment.