How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
Abstract
We significantly reduce the cost of factoring integers and computing discrete logarithms in finite fields on a quantum computer by combining techniques from Shor 1994, GriffithsNiu 1996, Zalka 2006, Fowler 2012, EkeråHåstad 2017, Ekerå 2017, Ekerå 2018, GidneyFowler 2019, Gidney 2019. We estimate the approximate cost of our construction using plausible physical assumptions for largescale superconducting qubit platforms: a planar grid of qubits with nearestneighbor connectivity, a characteristic physical gate error rate of $10^{3}$, a surface code cycle time of 1 microsecond, and a reaction time of 10 microseconds. We account for factors that are normally ignored such as noise, the need to make repeated attempts, and the spacetime layout of the computation. When factoring 2048 bit RSA integers, our construction's spacetime volume is a hundredfold less than comparable estimates from earlier works (Fowler et al. 2012, Gheorghiu et al. 2019). In the abstract circuit model (which ignores overheads from distillation, routing, and error correction) our construction uses $3 n + 0.002 n \lg n$ logical qubits, $0.3 n^3 + 0.0005 n^3 \lg n$ Toffolis, and $500 n^2 + n^2 \lg n$ measurement depth to factor $n$bit RSA integers. We quantify the cryptographic implications of our work, both for RSA and for schemes based on the DLP in finite fields.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.09749
 Bibcode:
 2019arXiv190509749G
 Keywords:

 Quantum Physics
 EPrint:
 26 pages, 10 figures, 5 tables