Security of the Secp256k1 Elliptic Curve used in the Bitcoin Blockchain

Abstract

The article delves into the intricate characteristics and security properties of the secp256k1 elliptic curve used for the generation of addresses in the Bitcoin blockchain. The Bitcoin blockchain is a decentralized digital ledger that records all transactions made with Bitcoin cryptocurrency. In this work, the secp256k1 elliptic curve and its parameters and the method of generating private and public keys using random numbers are described. While the private key allows for the signing of transactions to spend Bitcoin, the corresponding public key and address enable others to verify transactions and send funds to that specific address on the blockchain, ensuring security, authenticity, and privacy in the decentralized network. The attacks on the use of secp256k1 for generating the bitcoin addresses like the Brute force attack, twist attack, fault attacks, and side channel attacks in the implementation of the elliptic curve are discussed. By maintaining the security and integrity of secp256k1, we can ensure that cryptographic operations, such as digital signatures and key exchanges, remain uncompromised. If the curve's security were compromised, malicious users could potentially derive private keys from public keys, leading to unauthorized transactions, double-spending, or other malicious activities. The security of implementation can be enhanced by ensuring cryptographic libraries and software implementations that utilize secp256k1 undergo thorough testing and validation to ensure correct and secure operations. The important attacks on blockchain technology like the 51% attack, Sybil attack, Double Spending attack, and Smart Contract vulnerabilities are discussed. Through a comprehensive exploration, readers will gain insights into why this particular elliptic curve was chosen for use in Bitcoin's cryptographic protocols, highlighting its role in ensuring the robustness and integrity of the blockchain ecosystem.