Probabilistic Admissible Encoding on Elliptic Curves - Towards PACE with Generalized Integrated Mapping

  • Łukasz Krzywiecki
  • Przemysław Kubiak
  • Mirosław Kutyłowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8327)


We consider admissible encodings on an elliptic curve, that is, the hash functions that map bitstrings to points of the curve. We extend the framework of admissible encodings, known from CRYPTO 2010 paper, to some class of non-deterministic mapping algorithms. Using Siguna Müller’s probabilistic square root algorithm we show a mapping that works efficiently for any finite field \(\mathbb{F}_q\) of characteristic greater than 3, and that is immune to timing attacks. Thereby we remove limitations of the mappings analyzed in the CRYPTO 2010 paper. Consequently, we remove limitations of a so called PACE Integrated Mapping protocol, which has recently been standardized by ICAO, and is used to protect contactless identity documents against unauthorized access.


indifferentiability admissible encoding non-deterministic square root algorithm finite field elliptic curve 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Łukasz Krzywiecki
    • 1
  • Przemysław Kubiak
    • 1
  • Mirosław Kutyłowski
    • 1
  1. 1.Institute of Mathematics and Computer ScienceWrocław University of TechnologyPoland

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