This chapter covers prime fields, elliptic curves operations over real numbers and prime fields. These are the basic mathematical concepts that ECDSA signing is based on.

Bitcoin signatures use the Elliptic Curve Digital Signing Algorithm to secure unspent outputs and are encoded in the DER serialisation format.

Bitcoin addresses encode the information required for a wallet to spend to the correct key. Hierarchical Deterministic wallets use a child-key derivation algorithm to safely derive new addresses from the same root.

An introduction to building and signing your first transaction which spends to Pay-to-Public-Key-Hash outputs.

Signatures can commit to specific input and outputs, allowing other parts of the transaction to be modified by other parties.

An output script which can be spent by n-of-m signatures.

P2SH output scripts commit to a hashed locking script. The locking script preimage must be provided together with the unlocking script for such a P2SH output to be spent.

Absolute and relative timelocks prevent transactions from being broadcast before a certain time or blockheight. A timelock may be commited to by the transaction signature, or can be enforced by the previous output script.

Pay-to-witness output scripts are be spent with transactions with valid witnesses. Wallets which do not support native P2W transactions may send to outputs which wrap P2W scripts in P2SH outputs.

A closer lock at blocks and block headers, and their validation by nodes.

An introduction to the P2P messaging protocol between Bitcoin nodes on the network.

SPV clients follow the longest header chain with the most proof-of-work. They rely on specific transaction updates from full Bitcoin nodes, and perform merkle proofs to validate confirmation of these transactions.

We demonstrate a basic payment channel between two nodes which is enabled by revocable output scripts (RSMC's). Payment routing across multiple payment channels is made possible by hashed time-locked contracts (HTLC's).