Such a transaction is similar to sending money from one bank account to another. Moving Bitcoins from one address to another is called a transaction. By means of a simple procedure, the user's computer calculates a random Bitcoin address (related to the public key) as well as a secret (private key) that is required in order to perform transactions from this address. Unlike the banking system where it is the responsibility of a bank to provide customers with a bank account, a Bitcoin user is responsible for generating his own (random) address. Bitcoin is a decentralized system for transferring value. To understand the impact of quantum computers on Bitcoin, we will start with a brief summary about how Bitcoin transactions work. This means that anyone with a sufficiently large quantum computer could use this algorithm to derive a private key from its corresponding public key, and thus, falsify any digital signature. However, in 1994, the mathematician Peter Shor published a quantum algorithm that can break the security assumption of the most common algorithms of asymmetric cryptography. All known (classical) algorithms to derive the private key from the public key require an astronomical amount of time to perform such a computation and are therefore not practical. This principle dictates that the public key can be easily derived from the private key but not the other way around. The security of asymmetric cryptography is based on a mathematical principle called a “one-way function”.
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This scheme is very common in the financial industry to prove authenticity and integrity of transactions. This allows individuals to produce a digital signature (using their private key) that can be verified by anyone who has the corresponding public key. As the name suggests, the private key is kept as secret, while the public key is made publicly available. In asymmetric cryptography, a private-public key pair is generated in such a manner that the two keys have a mathematical relation between them. We will therefore not discuss this in detail, but only explain the aspects that are relevant for the analysis in this article.
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A great amount of digital ink has been spilled on the topic of how quantum computers pose an existential threat to currently used asymmetric cryptography.