Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • 6 - Breaking cryptosystems

  • from Part I - Areas of application
  • Alexander M. Dalzell, AWS Center for Quantum Computing, Sam McArdle, AWS Center for Quantum Computing, Mario Berta, RWTH Aachen University, Przemyslaw Bienias, AWS Center for Quantum Computing, Chi-Fang Chen, University of California, Berkeley, András Gilyén, HUN-REN Alfréd Rényi Institute of Mathematics, Connor T. Hann, AWS Center for Quantum Computing, Michael J. Kastoryano, University of Copenhagen, Emil T. Khabiboulline, National Institute of Standards and Technology, Aleksander Kubica, Yale University, Grant Salton, Amazon Quantum Solutions Lab, Samson Wang, Caltech, Fernando G. S. L. Brandão, AWS Center for Quantum Computing
  • Book:
    Quantum Algorithms
    Published online:
    03 May 2025
    Print publication:
    24 April 2025, pp 98-110
    • Chapter
      • You have access
      • Open access
    • PDF
    • Export citation

  • Summary

    This chapter covers the potential use of quantum algorithms for cryptanalysis, that is, the breaking and weakening of cryptosystems. We discuss Shor’s algorithm for factoring and discrete logarithm, which render widely used public-key cryptosystems vulnerable to attack, given access to a sufficiently large-scale quantum computer. We present resource estimates from the literature for running Shor’s algorithm, and we discuss the outlook for postquantum cryptography, which aims to replace existing cryptosystems while being resistant to quantum attack. We also cover quantum approaches for weakening the security of cryptosystems based on Grover’s search algorithm.

  • 12 - Quantum Fourier transform

  • from Part II - Quantum algorithmic primitives
  • Alexander M. Dalzell, AWS Center for Quantum Computing, Sam McArdle, AWS Center for Quantum Computing, Mario Berta, RWTH Aachen University, Przemyslaw Bienias, AWS Center for Quantum Computing, Chi-Fang Chen, University of California, Berkeley, András Gilyén, HUN-REN Alfréd Rényi Institute of Mathematics, Connor T. Hann, AWS Center for Quantum Computing, Michael J. Kastoryano, University of Copenhagen, Emil T. Khabiboulline, National Institute of Standards and Technology, Aleksander Kubica, Yale University, Grant Salton, Amazon Quantum Solutions Lab, Samson Wang, Caltech, Fernando G. S. L. Brandão, AWS Center for Quantum Computing
  • Book:
    Quantum Algorithms
    Published online:
    03 May 2025
    Print publication:
    24 April 2025, pp 225-227
    • Chapter
      • You have access
      • Open access
    • PDF
    • Export citation

  • Summary

    This chapter covers the quantum Fourier transform, which is an essential quantum algorithmic primitive that efficiently applies a discrete Fourier transform to the amplitudes of a quantum state. It features prominently in quantum phase estimation and Shor’s algorithm for factoring and computing discrete logarithms.