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No geth, or other command line tools, or clients like MetaMask and Mist. What I need is the exact algorithm to recover an account from mnemonics and the other way around.Appreciate implementations of any programming language, or just pseudo-code. What I've already known is the algorithm to get an entropy and a seed from the mnemonics, and the algorithm to get the mnemonics from an entropy. How can I recover an account from the entropy or the seed? When an account is provided, how can I get the entropy to generate the mnemonics?

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For ethereum most wallets use bip39 with 44'/60'/0'/0/0 as derivation path. You can use this tool https://github.com/iancoleman/bip39 to found the private key and seed from the mnemonics.

The other way around should be almost impossible. To go from the seed to obtain the mnemonic you need to reverse the HMAC-SHA512.

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