Finding the secret key in Bitcoin: A review on mathematical approaches to Elliptic Curve Discrete Logarithm Problem

Abstract

With the popular usage of Bitcoin safety in making payments or transactions becomes a topic of concern In brief the security chiefly relies on the easiness of finding the secret key/ private key in Bitcoin To a large extent this depends on how easy it is to resolve an Elliptic Curve Discrete Logarithm Problem (ECDLP) With that in mind the main focus of this paper is to review any mathematical approaches and their variants that can theoretically tackle an ECDLP in Bitcoin The objective is to discuss the security of Bitcoin by studying methods of uncovering the private key On the other hand the existence of non-mathematical approaches provides an alternative to figure out the private key faster Notably they work only in the presence of implementation vulnerabilities Even so in consideration of the influence that non-mathematical approaches may bring about this paper also includes an outline of some of the frequently mentioned ones Last but not least results indicated that using Bitcoin for payments or transactions appears to be secure at this stage but the development of quantum computers may alter the situation in the future By taking this into account this paper ends up with a comment on the impact of quantum computers on Bitcoin

Date of Award	2019
Original language	English
Supervisor	Po-Yi Huang (Supervisor)