Do I need to backup my private key?

Per my understanding, the recover phrase is NOT the private key and cannot generate the private key. Normally a passphrase is used to encrypt/decrypt the private key file so that in case the private key file itself falls in the wrong hands it cannot be used without first decrypting it using the passphrase. Can someone confirm?

If this is the case then losing the private key itself means losing access to the ADA even if I have the passphrase since the passphrase does not generate the private key. The only was a recovery key can be used to recover the wallet in this case is if the private key is backed up somewhere. So how does Daedalus recover the wallet using the passphrase? Do they have my private key backed up somewhere?

Additionally, if this is correct then it is critical to backup one’s private key and not only the passphrase as each independently is useless, both the private key and passphrase are required to spend from the wallet. I could not find where exactly is the private key in my Daedalus wallet and the documentation is not clear on this.

Please clarify or let me know if my understanding is incorrect.

The only thing you need is to backup your seedphrase.

With that you will be able to restore your wallet at any time.

“Regardless, a seed phrase is simply a representation of a random number. It’s an ordered sequence of 12 or 24 words , chosen from a list of 2048 words. Using cryptography, your wallet can derive your private key using your seed phrase . And with that private key, your wallet can spend your bitcoin.”

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How is this possible when the wallet has many pairs of public and private keys, each used for different transactions? How can a single 12-24 word phrase generate all of them if they are lost?

Yes, with that one 12-24 word phrase a modern cryptocurrency wallet can create new public/private key pairs. All old and future (not yet generated keys) can be restored with that phrase. See Cryptocurrency wallet - Wikipedia for extra info.

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It is more clear now. I was not aware there is such thing as a deterministic wallet.

But isn’t this less secure than a non-deterministic wallet? If one can eventually generate the addresses from the mnemonic phrase, and all addresses used are public on the blockchain, what stops someone from generating random phrases and their addresses and looking for them on the blockchain? If one is found then the attacker would confirm the seed phrase and all associated private keys, public keys and addresses.

I am not saying this is easy or not time consuming but feels less secure than using private keys that are randomly generated and cannot all be regenerated from a single phrase.

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A mnemonic sentence is considered secure. The BIP-39 standard creates a 512-bit seed from any given mnemonic. The set of possible wallets is 2^512. It is the defacto standard. Hardware wallets like Trezor and Ledger also use these standards. They are considered the most secure.

In adittion here are some tips on how to split the seed phrase for a robuust backup: Seed phrase wallet backup template - Google Docs