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I've been reading the book, Mastering Bitcoin by Andreas M. Antonopoulos, in chapter 4, the cryptography used in bitcoin is classified as: keys, bitcoin addresses and digital signatures. I understand the keys come in pairs of private and public.

The part I didn't understand is where it's written: "the recipient's public key is represented by its digital fingerprint, called bitcoin address"

What exactly does a digital fingerprint mean in this context? How is it different from a digital signature and how does it represent a bitcoin address?

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A "digital fingerprint" is a unique identifier that references some particular piece of data. Typically, the fingerprint is fixed in size and the information it references is much larger in size. In this case, a bitcoin address is a 160-bit digital fingerprint of a 256-bit public key created by hashing the public key twice.

The difference between a digital signature and a digital fingerprint is that anyone can produce a digital fingerprint while a secret key is needed to produce a digital signature. Digital signatures are used to prove that a particular piece of data was provided or approved by a particular party. Digital fingerprints are used to ensure that the data provided is the correct data.

When a typical bitcoin transaction is performed, the transaction includes a digital signature. It is not enough to ensure the digital signature is valid though, the signature must be made with the correct key. To determine that, the digital fingerprint of the public key used to sign the transaction is checked against the address. If they match, then the public key is correct, meaning the transaction was signed by someone possessing the appropriate secret key.

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