Is there any solution if the key is lost in Ethereum or Bitcoin? Can I use the some algorithm, which can bind key and biometrics, to solve this problem? Why don't Ethereum/Bitcoin use it?

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Your private key is just a string. It's required for you to send transactions to the Ethereum blockchain.

That being said, nothing prevents you from using whatever means you want, to keep your private key safe and recoverable. You can tie it to biometrics, in some fashion, if you wish.

From the blockchain's perspective, it only cares that the private key is right. It doesn't care what methods you use to store the private key, and therefore the blockchain standards don't talk about private key storage much. The community around the blockchain may endorse whatever means, and I'd say it's also important to talk about the different means.

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