The Math Behind Bitcoin

“One reason bitcoin can be confusing for beginners is that the technology behind it redefines the concept of ownership.

To own something in the traditional sense, be it a house or a sum of money, means either having personal custody of the thing or granting custody to a trusted entity such as a bank.

With bitcoin the case is different. Bitcoins themselves are not stored either centrally or locally and so no one entity is their custodian. They exist as records on a distributed ledger called the block chain, copies of which are shared by a volunteer network of connected computers. To “own” a bitcoin simply means having the ability to transfer control of it to someone else by creating a record of the transfer in the block chain. What grants this ability? Access to an ECDSA private and public key pair. What does that mean and how does that secure bitcoin?

Let’s have a look under the hood…”

http://www.coindesk.com/math-behind-bitcoin/