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On the Design and Optimization of a Quantum Polynomial-Time Attack on Elliptic Curve Cryptography

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Theory of Quantum Computation, Communication, and Cryptography (TQC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5106))

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Abstract

We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over GF(2m). We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of binary finite fields and by representing elliptic curve points using a technique based on projective coordinates. The depth of our proposed implementation is O(m 2), which is an improvement over the previous bound of O(m 3).

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Author information

Authors and Affiliations

  1. Department of Computer Science, and Institute for Quantum Information Science, University of Calgary, Calgary, AB, T2N 1N4, Canada

    Donny Cheung

  2. Department of Combinatorics and Optimization, and Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Dmitri Maslov

  3. Department of Computer Science, University of Bristol, Bristol, BS8 1UB, UK

    Jimson Mathew & Dhiraj K. Pradhan

Authors
  1. Donny Cheung
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  2. Dmitri Maslov
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  3. Jimson Mathew
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  4. Dhiraj K. Pradhan
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Editor information

Editors and Affiliations

  1. NTT Communication Science Laboratories, 3-1, Morinosato Wakamiya, Atsugi-shi, 243-0198, Kanagawa Pref., Japan

    Yasuhito Kawano

  2. Institute for Quantum Computing, University of Waterloo, N2L 3G1, Waterloo, ON, Canada

    Michele Mosca

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© 2008 Springer-Verlag Berlin Heidelberg

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Cheung, D., Maslov, D., Mathew, J., Pradhan, D.K. (2008). On the Design and Optimization of a Quantum Polynomial-Time Attack on Elliptic Curve Cryptography. In: Kawano, Y., Mosca, M. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2008. Lecture Notes in Computer Science, vol 5106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89304-2_9

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  • DOI: https://doi.org/10.1007/978-3-540-89304-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89303-5

  • Online ISBN: 978-3-540-89304-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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