Quantum Computing And Bitcoin Security

Rapid progress in quantum computing is predicted by some to have crucial ramifications in domains using public-key cryptography, such as the Bitcoin ecosystem.

Bitcoin’s “asymmetric cryptography” is based on the principle of “one-way function,” implying that a public key can be easily derived from its corresponding private key but not vice versa. This is because classical algorithms require an astronomical amount of time to perform such computations and consequently are impractical. However, Peter Shor’s polynomial-time quantum algorithm run on a sufficiently-advanced quantum computer could perform such derivations and thus falsify digital signatures.

Potential Risks Posed By Quantum Computing

For a better understanding of risk levels introduced by advanced quantum computing, we restrict ourselves to simple person-to-person payments. These can be divided into two categories, each affected differently by quantum computing:

  1. Pay to public key (p2pk): Here, the public key is directly obtainable from the wallet address. A quantum computer could potentially be used to derive the private key, thus allowing an adversary to spend funds at the address.
  2. Pay to public key hash (p2pkh): Here, the address is composed of a hash of the public key and hence, is not directly obtainable. It is revealed only at the moment of initiation of a transaction. Hence, as long as funds have never been transferred from a p2pkh address, the public key is not known and the private key cannot be derived even using a quantum computer. However, if funds are ever transferred from a p2pkh address, the public key is revealed. Hence, to limit exposure of the public key, such addresses should never be used more than once.

While avoiding reuse of a p2pkh address can limit vulnerability, there might still arise situations where a quantum-capable adversary can successfully commit fraud. The act of transferring coins even from a “safe” address, reveals the public key. From that moment until the transaction is mined, an adversary has a window of opportunity to steal funds.

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