Research Of Secure Multiparty Computation Protocols Based On ElGamal Homomorphic Encryption

As modern technology continues to make breakthroughs and data explodes,the importance of data as a resource is coming to the fore.To maximize the value of data,federated computing of data has become a necessary and common phenomenon.From the perspective of information security,data federated computing is not only subject to traditional threats such as data eavesdropping,tampering and forgery,but also encounters new information security issues such as increasing data misuse,personal privacy leakage and data silos.Secure Multiparty Computation can well balance the availability and security of data,and it has the characteristics of decentralization,rich protocol types,and wide application prospects,which are of great value for studying data privacy and confidentiality issues.One of the most fundamental problems in Secure Multiparty Computation is to perform multiple data-optimal confidentiality calculations,which can be applied to various practical scenarios and have great practical significance in security practice and mathematics.The maximum(minimum)secrecy calculation scheme for multiple data can also be widely used in practical scenarios such as secrecy set computing,secrecy data mining and query,and secrecy e-auction,etc.Meanwhile,these algorithms and protocols can also be used as basic modules for designing various more secure and efficient secrecy bidding,secrecy selection recommendation,secrecy optimization,secrecy determination of point and interval relationships with multiple participants,and other Secure Multiparty Computation protocols.Generally to calculate the maximum and minimum requires a two-by-two comparison of multiple data or converting the problem into a ranking problem,but this approach can greatly increase the computational complexity or even reveal private information other than the maximum and minimum.Therefore,it is necessary to conduct research on confidential computation schemes for maximum(minimum).In addition,with the increasingly complex problems of privacy leakage and resource waste in the second-hand trading industry,the information security in the joint computing of various second-hand trading platforms has also received wide attention.Secure multiparty computation is gradually applied in the field of second-hand e-commerce transactions by virtue of its safe and reliable as well as decentralized features.Considering the demand for data privacy protection in the idle item trading scenario and the problem of information opacity in the valuation process of idle items,it is of great practical significance to design a second-hand e-commerce platform transaction model based on MPC that can avoid privacy data leakage,to protect platform and user data privacy and property security,and to promote the healthy development of second-hand transaction industry in China.In this thesis,based on the ElGamal homomorphic encryption algorithm,the confidentiality calculation of the maximum(minimum)and the confidential determination of point and interval relations are studied from the perspective of Secure Multiparty Computation privacy protection,respectively,as follows.(1)Aiming at the problems of traditional Secure Multiparty Computation schemes that cannot compute maximum and minimum confidentially at one time,inefficiency,and the need for trusted third parties,a secure confidentiality scheme that can solve maximum(minimum)simultaneously is proposed with the ElGamal homomorphic encryption algorithm as the cornerstone.A privacy data encoding method is designed in the scheme to effectively overcome the problem of not being able to calculate the maximum(minimum)confidentially at one time in the traditional scheme.In addition,a threshold decryption method is used to effectively ensure the fairness of computation for all participants and achieve the purpose of decentralization.Finally,the desirability of the proposed scheme is illustrated by analyzing and comparing its performance and efficiency with similar schemes.(2)To address the problem that the existing Secure Multiparty Computation protocol under the semi-honest model can only resist passive attacks but not active attacks by malicious attackers,we propose a maximum(minimum)secrecy computation protocol based on ElGamal homomorphic encryption and threshold decryption under the malicious model by combining the above proposed maximum(minimum)secrecy computation scheme that can be solved simultaneously under the semi-honest model,and improve the model security.Zero-knowledge proof techniques are utilized to resist active attacks,and are able to detect malicious behavior and terminate the protocol in time.Then,the proposed scheme is proved to be secure under the malicious model based on an ideal-reality simulation paradigm approach,and finally,the performance is compared with existing similar schemes to illustrate the superiority of the proposed scheme.(3)Most of the existing point and interval secrecy determination schemes are for two participants,one of whom holds the data and the other holds the interval,and the two parties cooperate in the secrecy determination of the point and interval relationship.In real life,it may be necessary to consider the case of secrecy determination of point and interval relationship involving multiple participants,that is to determine whether the nth participant’s secret data falls within the maximum and minimum interval of the secret data held by the previous n-1 participants.To solve the above problem,the existing method can only find out the maximum-minimum interval of the secret data of multiple participants by first invoking the maximum(minimum)confidentiality calculation protocol,and then invoke the point and interval confidentiality determination protocol involving two parties.Although this method can achieve the expansion of participants from two to many parties,it will lead to high complexity of protocol communication and calculation due to multiple interactions.In this thesis,based on the protocol designed in(1)above,we give a secure protocol that can confidentially determine the relationship between data points and intervals held by n participants at once.Then,the correctness and security of the proposed scheme are proved under the semi-honest model based on the ideal-realistic simulation example,and the performance and efficiency analysis are compared with similar schemes to show the good performance of the proposed scheme.Finally,the point and interval secrecy determination protocol is applied to the second-hand e-commerce transaction scenario to give a scheme for secrecy determination of valuation between users and the second-hand e-commerce platform,which can solve the problem of user data privacy leakage in the joint calculation of the second-hand e-commerce platform and improve the satisfaction of consumers trading idle items.