[Draft BIP] Quantum-Resistant Transition Framework for Bitcoin

The recent advancements in quantum computing and its potential impact on cryptographic security, particularly focusing on the comparison between RSA-2048 and ECDSA (P-256), have been a significant point of discussion. A study by Mosca et al., detailed in a ScienceDirect article, highlights that breaking ECDSA requires significantly less effort than RSA-2048, by approximately an order of magnitude. This revelation is paradoxical given that the longer bit lengths of RSA, originally intended to safeguard against classical attacks such as NFS on shorter RSA keys, inadvertently offer better resistance in the post-quantum era.

The analysis does not incorporate Gidney's findings, which could further alter the computational workload needed for a quantum attack. Gidney's research introduced a twenty-fold reduction in the number of qubits required for certain quantum operations, specifically targeting RSA-2048 through optimized circuit layouts. However, applying this improvement universally, including to algorithms like ECDSA, remains uncertain due to early quantum computers' likely specialization for specific circuits to maximize performance. Gidney's work, especially his proposals on error correction methods like the yoked surface code, shows potential applicability beyond RSA-2048, but their effectiveness across different cryptographic algorithms and quantum computing architectures is yet to be fully understood.

Moreover, the discussion extends to the suitability of various quantum computing architectures for breaking cryptographic schemes. Superconducting quantum computers, despite their faster operation, face scalability challenges due to lower stability. Conversely, architectures based on neutral atoms, as described in an arXiv paper, offer slower computational speeds but higher stability, suggesting they may be more effective for sustained, long-range cryptographic attacks against specific public keys.

Given these considerations, the importance of adopting a proactive approach towards cryptographic security in the quantum era is underscored. As Gidney concludes, it is crucial to ensure security measures do not solely rely on the slow progress of quantum computing technology, emphasizing the need for ongoing vigilance and adaptation in cryptographic practices to safeguard against future quantum threats.