blocksight 2021-04-26 16:18:46 阅读数:332

本文一共[544]字，预计阅读时长:1分钟~

mathematics
blockchain
zero
knowledge
proof

** 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 ！**

** 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 .**

** 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 ****** Outsource 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 .**

** 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 .**

**integrity : Just state (statement) That's right. ,prover You can make verifier Conviction ;****reliability : If you state (statement) It's wrong. , So cheating prover There's no way to verifier Believe in****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 )**** :

** Non-interactive ( Non interactivity )**** :

** Arguments ( Controversial )**** :

** of Knowledge**** :

** 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 ！.**

** Welcome to your attention & Looking at , If you have any questions, please leave a message ！**

** Mathematics in blockchain （ Seventy two ）**** RSA Accumulator Non member proof and blockchain applications **

** Mathematics in blockchain （ seventy-one )**** Accumulator and RSA Accumulator**

** Mathematics in blockchain （ Sixty-nine )**** Kate Promise volume Certification **

** Mathematics in blockchain （ sixty-seven ）**** Knowledge and commitment **

** Mathematics in blockchain （ sixty-six ）**** Pedersen Key sharing **

** Mathematics in blockchain （ Sixty five ）**** Cryptography promises --Pedersen promise **

** Mathematics in blockchain （ sixty-three ）**** Oblivious transport protocol **

** Mathematics in blockchain （ Twelve ）**** RSA Encryption and decryption algorithm **

** Mathematics in blockchain （ sixty one ）**** BLS m of n Threshold signature **

** Mathematics in blockchain （ fifty-nine ）**** BLS Key aggregation **

**Schnorr Signature and elliptic curve **** Schnorr Signature and elliptic curve **

** Mathematics in blockchain （ Thirty-seven ）**** Uniwap Core algorithm analysis （ in ）**

版权声明：本文为[blocksight]所创，转载请带上原文链接，感谢。 https://netfreeman.com/2021/04/20210426102605589C.html

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