Elliptic Curve Digital Signatures and Their Application in the Bitcoin Crypto-currency Transactions

Abstract

The Elliptic Curve Digital Signature Algorithm (ECDSA), defines a technique for generating and validating digital signatures. We start by reviewing the mathematics behind the Digital Signature Algorithm (DSA) and its elliptic curve analogue (ECDSA). Secondly, we describe how the ECDSA is used in Bitcoin technology. Bitcoin is a type of crypto-currency that has been in existence since 2009. It was introduced by Satoshi Nakamoto (possibly a pseudonym) in their much cited paper [8]. Its design and distribution is not controlled by any central organization. Despite this, Bitcoin has defied all odds to become a phenomenal currency widely accepted by thousands of merchants worldwide. At the time of writing this article, 1 unit of Bitcoin (1 BTC) has a value of approximately USD 5,500. The internal workings of Bitcoins is based on elliptic curve digital signatures and is not well understood by many people including a large percentage of Bitcoin users. The the second part of this article we make give an overview to illuminate how the internal nuts and bolts of Bitcoin works.