Elliptic Curve Cryptography for Bitcoin Security

Abstract

Mathematics has addressed many a complex problem in the past and is consistently providing avenues for present day security problems too. This time, we understand the interesting Mathematics powering the security structure for Bitcoin. The complex Mathematics that goes on, provides much more and ensures a critical component in the security apparatus implemented in the Bitcoin protocol. The solution is addressed by the Elliptic Curve representation and the science of cryptography fortified by Elliptic Curve Cryptography (ECC). We attempt to present the Elliptic curve secp256k1  and its relation to security enforced for the bitcoin network. For easier understanding, the order 113 is identified to present this integration.