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

  • Donny Cheung
  • Dmitri Maslov
  • Jimson Mathew
  • Dhiraj K. Pradhan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5106)


We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over GF(2 m ). 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).


Elliptic Curve Elliptic Curf Quantum Algorithm Quantum Circuit Elliptic Curve Cryptography 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Donny Cheung
    • 1
  • Dmitri Maslov
    • 2
  • Jimson Mathew
    • 3
  • Dhiraj K. Pradhan
    • 3
  1. 1.Department of Computer Science, and Institute for Quantum Information ScienceUniversity of CalgaryCalgaryCanada
  2. 2.Department of Combinatorics and Optimization, and Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  3. 3.Department of Computer ScienceUniversity of BristolBristolUK

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