How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits

Craig Gidney; Martin Ekerå

doi:10.22331/q-2021-04-15-433

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits

Craig Gidney¹ and Martin Ekerå^2,3

¹Google Inc., Santa Barbara, California 93117, USA
²KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
³Swedish NCSA, Swedish Armed Forces, SE-107 85 Stockholm, Sweden

Published:	2021-04-15, volume 5, page 433
Eprint:	arXiv:1905.09749v3
Doi:	https://doi.org/10.22331/q-2021-04-15-433
Citation:	Quantum 5, 433 (2021).

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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, Griffiths-Niu 1996, Zalka 2006, Fowler 2012, Ekerå-Håstad 2017, Ekerå 2017, Ekerå 2018, Gidney-Fowler 2019, Gidney 2019. We estimate the approximate cost of our construction using plausible physical assumptions for large-scale superconducting qubit platforms: a planar grid of qubits with nearest-neighbor 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 (Van Meter et al. 2009, Jones et al. 2010, 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.

► BibTeX data

@article{Gidney2021howtofactorbit,
  doi = {10.22331/q-2021-04-15-433},
  url = {https://doi.org/10.22331/q-2021-04-15-433},
  title = {How to factor 2048 bit {RSA} integers in 8 hours using 20 million noisy qubits},
  author = {Gidney, Craig and Eker{\aa{}}, Martin},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {433},
  month = apr,
  year = {2021}
}

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How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits

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