Quantum Algorithm for Solving the Discrete Logarithm Problem in the Class Group of an Imaginary Quadratic Field and Security Comparison of Current Cryptosystems at the Beginning of Quantum Computer Age

  • Arthur Schmidt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3995)


In this paper, we present a quantum algorithm which solves the discrete logarithm problem in the class group of an imaginary quadratic number field. We give an accurate estimation of the qubit complexity for this algorithm. Based on this result and analog results for the factoring and the discrete logarithm problem in the point group of an elliptic curve, we compare the run-times of cryptosystems which are based on problems above. Assuming that the size of quantum computers will grow slowly, we give proposals which cryptosystem should be used if middle-size quantum computers will be built.


Elliptic Curve Quantum Computer Elliptic Curf Quantum Algorithm Discrete Logarithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Arthur Schmidt
    • 1
  1. 1.Fachbereich Informatik, Fachgebiet Kryptographie und ComputeralgebraTechnische Universität DarmstadtDarmstadtGermany

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