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Mostly BIP39, an open standard for encoding a seed as a series of common words, but also collects other methodologies.
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Private key from 13/25 seed phrase
generate a 12-24 seed phrase: straightforward with ethers.js
import { entropyToMnemonic } from "@ethersproject/hdnode"
// 16 bytes / 128 bits => 12 words
// 32 bytes / 256 bits => 24 words
const mnemonic … = entropyToMnemonic(ethers.utils.randomBytes(32))
const wallet = ethers.Wallet.fromMnemonic(mnemonic) // wallet.privateKey
Now it's quite unclear how to derive wallets using 13th/25th word (12/24 words …