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I wonder how crypto wallet like BitPay works?

They claim to be an offline wallet that you can back up with simply a 12 words phrase. Yet, they allow you to create an infinite number of wallets across multiple coins like BTC, BCH, ETH, XRP ...

How does such wallet keep track of the created addresses without relying on an external 3rd party server and how it uses to the 12-word phrase to access the private key of each and all of these created wallets?

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    There's a specification that defines a common algorithm to derive private keys (BIP 32). It's used with (BIP 44 which specifies the "derivation path" for different accounts.) – MCCCS Jun 10 at 17:57
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Per BIP39 the original entropy in form of mnemonic can be translated to master seed per BIP32.

This document describes hierarchical deterministic wallets (or "HD Wallets"): wallets which can be shared partially or entirely with different systems, each with or without the ability to spend coins.

The specification is intended to set a standard for deterministic wallets that can be interchanged between different clients. Although the wallets described here have many features, not all are required by supporting clients.

Using BIP44 one can use different coin_type codes for different currencies and standard derivation is m / 44' / 0' / 0'

BIP44:

m / purpose' / coin_type' / account' / change / address_index

As far as I know BitPay/Copay use this derivation type.

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