Design Of Several Primitive Protocols For Secure Multi-Party Numerical Calculation

Secure Multi-Party Computation(hereinafter called SMC)is a protocol.In this protocol,several participants cooperate to use a special calculation method to calculate a convention function.Any party has an obligation to execute the protocol without revealing its own private information;and finally every participant can know the output result of the function.Aiming at specific problems of Secure Multi-Party Computation,it is a hot issue now to explore a safe and high-efficiency SMC protocol.Secure Multi-Party Computation has four demands:the first one is the input confidentiality of each participant;the second one is the output correctness of each participant;the third one is the input independence of each party;the fourth one is the fairness of the output;in other words,if and only if honest participants get their output,corrupt participants cannot get any correct output.Nowadays,there are many researches on the problems of Secure Multi-Party Computation such as geometric calculation,value calculation,electronic voting,multi-party sorting and secret sharing.However,as primitive protocols among SMC problems,they have extremely important research value.The research in this paper mainly aims at the application problems of Secure Multi-Party Computation in value calculation field.The working point of this paper is tantamount to study the following three aspects.The first one is the integral solution problem of two-party polynomial with private information protection.Alice owns the function f(x);Bob owns the integrating range[a,b];Bob wants to know the integral value of f(x)in the integrating range[a,b]but does not know any private information of Alice.Furthermore,Alice does not know any private information of Bob.We utilize the scalar product protocol and secure two-party multiplication protocol and convert private information of the participant to a vector.Under the premise that private information is not revealed,scalar product protocol and secure two-party multiplication protocol are used to calculate.Two integral solution protocols for the polynomial with private information protection can be designed in detail.The second one is the linear equation solving problem of private information protection.Two problems are proposed.In the first problem,Alice has the equation f(x);Bob owns the range[a,b];the roots of the equation f(x)= 0 can be obtained through interacting computations.In addition,besides a root of the equation,Bob does not know any private information of the equation f(x)of Alice.Alice does not know any private information of the private range[a,b]of Bob yet.In the situation that both parties do not reveal their private information,the scalar product protocol and two-party polynomial evaluation protocol are utilized to design an equation solving protocol of private information protection.The second is to design the secure protocol for solving the linear equations Ax = b.It is an important problem in scientific calculation to solve linear system of the equation of private information protection.It is widely applied in the fields of finance and communication.In the latest years,a series of research achievements have been gained in this field.The eigenvalue and eigenvector solution of linear system of equations and the solution problem of two-party linear equation and multi-party linear system of equations have different multi-party solution protocols.As for the security solution protocol for the linear equations Ax = b,there is little research.In order to solve this problem,data hiding and oblivious transfer protocol are utilized to design two solution protocols for linear system of equations of private information protection.The last one is the Lagrange's interpolation polynomial problem of private information protection.This problem is defined as follows:Suppos n parties have n points(xi,yi).In the condition that private information of each party is not revealed,an interpolation formula f(x)is calculated to make all points(xi,yi)meet the equation yi =f(xi).In the situation that private information of each party is protected,secret sharing,secure two-party summation protocol and secure multi-party multiplication protocol are utilized to design a Lagrange's interpolation polynomial protocol of private information protection.