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Under the premise of fully protecting privacy, how to know who is richer?

2020-12-08 12:28:58 Ontology

secure multi-party computation (Secure Multi-party Computing,(s)MPC), It is an important area of data privacy protection, which was introduced by Mr. Yao Qizhi, a Turing prize winner, through the millionaire problem . Yao's million question can be expressed as :Alice and Bob It's two millionaires , They want to know who is richer , But they don't want to reveal any information about their wealth to each other . In this case , Both sides don't want to reveal their true information , Compare the wealth of two people , And give credible proof .

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To put it simply , Multi party computing is a process in which multiple participants cooperate to calculate a function . And the word "security" means that these participants get results at the same time , You can't get any other information . In a slightly formalized way , In secure multiparty Computing , Suppose each participant has a secret , And calculate it together

In this calculation , The only information that any one of the participants gets is some information about the result , And you don't know anything about secret input and results from other users . In general , There are two forms of expression :

That is, all users know the calculation results ;

That is, all users share the calculation results .

The correctness and security of multi-party output not only needs to be guaranteed , The privacy of the input data of the participants , Fairness should also be reflected . That is to say to all participants , Or we can get the output value together , Or we can't get results . The other thing to emphasize is , Multi party computing only ensures that the whole calculation process does not leak additional information , The information leakage of the calculation function itself is not guaranteed .

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If there is a trusted center , This problem is easy to solve . Each user sends the secret value to the trusted center , The computation of the function is performed by a trusted center , And return the results to the user . In fact , It's hard to build a trusted center that all participants trust , Therefore, multi party computing is to consider in the absence of such a trusted center , How to achieve the efficiency and security in the presence of such a trusted center .

In this paper , We use Damgar Et al SPDZ For example, the plan , Briefly explain the calculation process of secure multi-party computing protocol . In the scheme , The calculation result is expressed in the second way , That is to say, after many calculations , Each participant has , Satisfy . It should be noted that , The scheme has been optimized and improved in the later stage , Here we only describe the original scheme , To illustrate the general principle of this kind of scheme .

1.1 Security model

In most of the early secure multiparty computing schemes , Only the attacker is semi honest ( An attacker who can infer secret input from other participants based on the information they have ) Or only a few malicious attackers ( An attacker who, in his or her own interest, would breach the operation of the agreement ) In order to meet some security features . A more practical adversary model is “dishonest majority”, That is, the hostile adversary model , Most of the participants were dishonest . And the security that the scheme wants to achieve , It should be equivalent to the situation in which a trust center is involved .

1.2 Circuit selection

Generally speaking , There are Boolean circuits and arithmetic circuits .

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In Boolean circuits , All operations can be performed with XOR gates ; And in arithmetic circuits , All operations can be performed using addition and multiplication . There are many multiparty computing protocols constructed on Boolean circuits , For example, Mr. Yao Qizhi's millionaire problem . And arithmetic circuit can express integer and other operations more simply and efficiently , Therefore, it has important application value . In this article , We are talking about multiparty computation based on arithmetic circuit model .

In the next issue, we will focus on the calculation process , How to ensure correct calculation .


To be continued ......

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This article is from WeChat official account. - Ontology Research Institute (ontologyresearch) , author :0x6d78

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Original publication time : 2020-11-20

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