The Mathematics of Bitcoin

Abstract

Bitcoin is among the first successful, fully implemented cryptocurrencies. As it slowly emerges into mainstream use, it is necessary to understand how a transaction works, involves an entirely digital currency. This paper provides an overview of a bitcoin transaction from the point of view of the user, looking at the details and security of an individual transaction, transaction blocks, and the Bitcoin public ledger, or block chain. It also discusses the mathematics implemented to secure and maintain the trust in the Bitcoin network. Security for the individual transaction is achieved through use of digital keys and digital signatures. Elliptic Curve Cryptography using the secp256k1 curve and Elliptic Curve Digital Signature Algorithm are the algorithms most commonly used in a bitcoin transaction. The Secure Hash Algorithm 256 (SHA256) condenses information in a one-way hash function. Double SHA256 insures the security of individual transactions and secures the block chain against tampering.