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I think in a normal database,the username and password gets stored in the database and when a user enters his/her credentials,it checks with the content in the database to know his/her Authenticity. But in Ethereum,The Address and Private key doesn't get stored,so how will it validate users?

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Digital Signature

Just like in traditional web2.0 system username and password are the signature of a user, in web3.0 digital signature generated by the private key of the user does the same. Therefore, private key security is so much of importance.

When you perform a transaction on Ethereum, the transaction object will have the transaction digital signature that only you can generate and no one else. The miner will only need to check this digital signature to validate.

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