How Would Quantum Computing Impact the Security of Bitcoin by Enhancing Our Ability to Solve the Elliptic Curve Discrete Logarithm Problem?
16 Pages Posted: 27 Aug 2018
Date Written: August 2018
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
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