Notes

Procedure
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Each block of the blockchain is formed of a hash of the previous block's contents. This information is assembled into a single data structure: a Merkle tree, a type of binary tree in which each non-leaf node has a single child and a single parent and each leaf node has zero or more child nodes but no parent node. Each block also has a cryptographic hash of it contents, which serves to link it to the previous block.

A Merkle tree has the property that any node (with the exception of the leaves) contains a hash of a much shorter binary representation of its value. Hashing the contents of a block produces a 128-bit value, enough space to find any node in the tree in time, and the hash produces a 64-bit value that links the block to the previous block.: 219 The idea is that it is easy to verify that a node's child nodes' data is correct, but that it takes a lot of work to verify that the data in the node has not changed from that in the previous block.

The blocks are linked together using their hashes. The block in the first block can be calculated simply by hashing the hash of the block in the first block, producing the required magic hash value. Hashing the hashes together requires a hash function – a function with an input of any length, which outputs a fixed-size value. This process is called double hashing: the hashes of the block hashes are hashed together into a new hash, which is itself hashed to produce the required block hash. This process is repeated for all the blocks, linking blocks together.

It is possible to verify the blocks without downloading the entire blockchain: any node connected to the network can verify that the current hash of the block has the required value by comparing it to the other nodes' hashes, which must have the same value for the block to be valid. By doing this, one can calculate the entire block chain without downloading all the blocks from all the nodes.: 220

Security

In his paper, Nakamoto introduced the concept of mining in Bitcoin. The process is generally optional, although new bitcoins can only be created by mining. Mining is done by solving a complex proof-of-work problem with the sole intention of adding a block of transactions to the blockchain. The problem is to find a nonce, which is a number between 1 and a number that depends on the number of coins in circulation, such that the hash of the block's
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