How Would Quantum Computing Impact the Security of Bitcoin by Enhancing Our Ability to Solve the Elliptic Curve Discrete Logarithm Problem?

Abstract

Bitcoin, being the most widely used cryptocurrency, should have no security vulnerabilities. When users transfer Bitcoin, they must ‘sign off’ on the transaction using a private key generated by the elliptic curve digital signature algorithm (ECDSA). Calculating a user’s private key from their public key is known as the elliptic curve discrete logarithm problem (ECDLP). The only known method to solve this problem on classical computers is through brute-force, which takes exponential time. However, quantum computers can run a modified version of Shor’s algorithm to solve the ECDLP in polynomial time, thus posing a threat to the security of ECDSA. In this paper, I explain what makes the ECDLP intractable and run an experiment to estimate the time taken to solve the ECDLP on a classical computer. I then describe the modified version of Shor’s algorithm which can solve the ECDLP and compare it to brute forcing a solution on a classical computer. My research has shown that in the advent of quantum computers with sufficient qubits, the signature algorithm used in Bitcoin needs an update. Finally, I suggest a quantum-resistant alternative to ECDSA – Lamport Signatures.

Keywords: Bitcoin, Quantum Computing, Security, Elliptic Curve Discrete Logarithm Problem, Safety/Security in Digital Systems