### Mathematics in blockchain - what is zero knowledge proof?

blocksight 2021-04-26 20:07:21 阅读数:562

mathematics blockchain zero knowledge proof

## Write it at the front

In the last introduction RSA Accumulator Non member proof and application in blockchain , Some of the details didn't unfold , For example, why use prime factors ？ Because their product will uniquely represent the set . otherwise , There will be confusion 【 The same product , There will be different combinations of factors , Such as 18 = 2 9 = 3 6】 wait .

Up to now , There's a signature , Cryptography promises , Homomorphic computation , Elliptic curve and so on , Next, we can see the specific content of zero knowledge proof . This article belongs to popular science , Compared with the previous , Happy reading does not burn the brain ！

## What is zero knowledge proof

Generally speaking, zero knowledge proof makes the verifier believe by some means （ confirm ） The witness's statement is correct （ For example, knowing some key information ）, Without exposing the information itself . There are many examples on the Internet to help understand , Here's a scene ： If V Found a lost bank card ,P Come and say that the bank card is his , And said he knew the bank card number and password , Because the bank card is V In the hands of ,V It's easy to judge P Is the card number correct , however V I still don't believe it P It's the owner of the card , therefore P He also said that he knew the withdrawal code of the bank card , But I can't tell you directly V Otherwise, it will be leaked . So they agreed , Come to the nearby ATM By the machine ,V leave ATM Keep a certain distance from the plane , To make visible P Perform the withdrawal operation , But not so close as to see P The withdrawal code you entered .P It's just ATM Wait by the side V Operation instructions of .

When they're in place ,V Let's take it out 100 element ,P Insert the card , Enter the password and take it out 100 element （ Suppose that Cary is rich ）,V Let's take it out again 300 element ,P Do it and take it out again 300 element , After a few repetitions ,V Make sure the bank card is P Of .

P I got my bank card in this way , Didn't let V Know the withdrawal code , This simulation scenario is the application scenario of zero knowledge proof .

### purpose

Zero knowledge proof is often used in the following scenarios ：(1） Proof of privacy data ： A person's bank account is more than X; last year , A bank is not associated with an entity Y Make a deal ; A person's credit score is higher than Z; Without exposing the whole DNA Matching on the premise of data DNA

(2） Anonymous Authentication ： Without revealing identity （ Like the login password ）, Prove that the requester R Have access to restricted areas of the site ; Prove that a person comes from a group of allowed countries / A country in the region list / region , But it doesn't reveal which one ; Prove that a person is a member of an organization but not who .（3） Anonymous payment / Tokens, ： In the blockchain （ Untraceable ） Privacy coin ; Payment is completely separated from any kind of display identity ; Paying taxes without disclosing income ;

（4） Outsourcing computing outsources expensive computing tasks , And verify whether the calculation results are correct without re execution ; It opens up a category of zero Trust Computing ; Improve the blockchain model , Do the same calculation from all nodes , To only need one side to calculate and then other nodes to verify and so on ,zk rollup layer2 Plan, etc .

## ZK-SNARK

since 1985 year , The concept of zero knowledge proof is in “ Knowledge complexity of interactive proof system ” In this paper, we introduce , Later included non interactive research , In recent years, the research and application of blockchain has developed rapidly . The zero knowledge proof system should satisfy the following properties .

1. integrity : Just state (statement) That's right. ,prover You can make verifier Conviction ;
2. reliability : If you state (statement) It's wrong. , So cheating prover There's no way to verifier Believe in
3. Zero knowledge : The interaction of protocols only exposes statements (statement) Whether it is correct without disclosing any other information

At present, the mature application is zk-SNARK Technical solution . This term means ：

ZK-SNARK Full name :zero-knowledge succinct non-interactive arguments of knowledge

Succint ( Conciseness ) : Compared with the actual calculated length , The generated zero knowledge evidence message is very small .

Non-interactive ( Non interactivity ) : about zk-SNARK Algorithm , There is usually a build phase , After the build phase is complete , Certifier (prover) Just report to the verifier (verifier) Just send a message . and ,SNARK There's usually another one called " Public verifier " Characteristics of , It means that anyone can verify zero knowledge evidence without any interaction , This is crucial to blockchain .

Arguments ( Controversial ) : The verifier can only resist the attack of the verifier with limited computing power . The prover with enough computing power can create forged zero knowledge evidence to deceive the verifier . This is also often called " Computational completeness (computational soundness)", instead of " Perfect integrity (perfect soundness) ".

of Knowledge : For a certifier , Without knowing the specific proof (witness) Under the premise of , It is impossible to construct an effective zero knowledge evidence .

## Summary

In any zero knowledge proof system , There is one. prover Let... Without divulging any additional information verifier Be sure of certain statements （Statement） That's right. .

ZK-SNARK At present, it is widely used , There are many mature Libraries , Such as libsnark,bellman etc. . Some don't need to setup Of zk-stark The plan , Let's talk about it later .

Okay , Next, we'll go on to zero knowledge proof ！.

Link to the original text ：https://mp.weixin.qq.com/s/LHuRAA1RPzbccKHZ1wdU6g Welcome to the official account ：blocksight

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