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What is the purpose for and distinction between each of the following keys commonly used in cryptocurrencies?

  1. Address

  2. Tracking key

  3. Passphrase

  4. Private key

For context:
I got a bytecoin paper wallet which has a QR code for each of the 4 things above and just wanted to know what they are for / mainly want to know how to check the paper wallet balance to ensure what was sent to the qr code and is actually there.

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As I've rewritten your question:

What is the purpose for and distinction between each of the following keys commonly used in cryptocurrencies?

Public keys

  1. Address

You may think of your address like a mailbox that receives money. Anyone can put money into the mailbox, but they cannot take it out.

  1. Tracking key

A variant of the address that derives many addresses for a single identity. This enables you to check the balance for all of your addresses without using your secret keys, which enable you to spend the money. This is useful to isolate your secret keys, or to use a less trusted device like your phone to check your balance, without enabling it to spend.

Secret keys

  1. Passphrase

If this is a 12-word phrase you didn't choose, it is the seed. This seed is a convenient way to derive the next key.

  1. Private key

The secret variant of the tracking key. Deriving the secret keys for all addresses under the same identity. You may prefer to keep this key cold (offline), or on a dedicated hardware device.

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