Notes

Hashing function
A blockchain is a distributed ledger in which transactions are hashed and digitally signed to produce a hash, through a cryptographic one-way function, of the transaction.[161] Each block in the blockchain, from the start of the chain (the "genesis block") to the end, contains a reference to the previous block in the chain. The hash of a previous block is then of the hash of the previous block, which is part of the hash of the genesis block. The chain is secure since it is mathematically proven that it is extremely difficult, if not impossible, to generate a hash of the genesis block that is identical to the hash of the block, and therefore any change to the block would change the hash. This offers immunity against double spending, a critical property of any payment system.

Since the hashing algorithm is a one-way function, it is computationally very difficult, if not impossible, to find the previous block's hash. There is however no practical way to keep track of every block in the chain, so some form of block-chaining is used. A typical implementation makes a chain of block-hashing functions, each by a different miner, and provides a peer-to-peer network between nodes that can verify and relay transactions and blocks. By keeping a copy of the blockchain available to each node, each node in the network has the same copy of the blockchain, and ensures against over-reliance on any one node.

Transaction validation

The function executed by the bitcoin client during a transaction validation is straightforward: first a cryptographic hash is created through an one-way hash function of a set of attributes of the transaction (see below). In addition, a signature verifying a hash with the private key corresponding to the public key embedded in the bitcoin address (see Address attributes) of the receiving address, has to be generated.

The bitcoin software verifies the signature, ensuring that the private key used to create it belongs to the address it purports to belong to.

Signature validation

The signing of messages with digital signature algorithms requires a private key known only to the sender of the message. The most common digital signature algorithm used to generate transaction-level signatures with Bitcoin is the elliptic curve digital signature algorithm (ECDSA). ECDSA is based on one or more points on an elliptic curve, using the generalised ElGamal signature scheme. ECDSA enables the usage of elliptic curve Diffie–Hellman key exchange,
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