The mathematics underneath.
WHAT A HASH FUNCTION DOES
Produces a fixed-size fingerprint of any input.
WHAT PROPERTIES MATTER
The same input always produces the same output A small change produces an entirely different output The input cannot be derived from the output Two inputs producing the same output are infeasible to find
WHAT IT IS USED FOR
Linking blocks Identifying transactions Proving work, in some designs
WHAT PUBLIC KEY CRYPTOGRAPHY PROVIDES
A key pair: one private and secret, one public and shareable.
WHAT SIGNING DOES
Produces proof that the holder of the private key authorised a message.
WHAT VERIFICATION DOES
Confirms that proof, using only the public key.
WHY THAT IS FUNDAMENTAL
It allows authorisation without any shared secret or central authority.
WHAT AN ADDRESS IS
Derived from a public key, usually by hashing.
WHAT A MERKLE TREE PROVIDES
Efficient proof that a transaction is included, without the whole block.
WHY THAT MATTERS
It allows light clients to verify inclusion cheaply.
WHAT ZERO-KNOWLEDGE PROOFS PROVIDE
Proving a statement is true without revealing why.
WHAT THAT ENABLES
Privacy, and compressing verification of many transactions into one proof.
