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For ETH and BTH you can generate a private/public keys (secp256k1 Elliptical curve) and SHA-3 (Keccak) hashed public wallet address via code (Python, Java or what ever language) via an pure math algorithm externally then use that address in wallets for payment to cold storage.

Is it possible to generate keys/addresses for Cardano ADA this way in code externally without any interaction from any 3rd party wallet application (Daedalus, Yoroi), then import it later into a wallet when needed to be used for payment or redeeming from cold address storage?

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There are a variety of projects within the IOHK Github repository that may give the correct level of interaction you desire. After some digging I think the cardano-addresses project would fulfill your needs.

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The answer is: definitely yes.

You can generate those keys offline and off-sync using cardano-wallet utility. Please read my medium stories to find out how to do that: Wallet Command Line Interface.

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As others stated above, yes you can. You will need the cardano-wallet or CLI from iohk but I wouldn't consider that 3rd party. There is actually an easy way to do it following Coin Cashew's How to Build a Cardano Stake Pool Guide

Go to Section 10. Setup Payment and Stake Keys. Then skip down and choose the Mnemonic Method. This will walk you through doing this.

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