Probabilistic Admissible Encoding on Elliptic Curves - 
                Towards PACE with Generalized Integrated Mapping
      
           Lukasz Krzywiecki,  Przemyslaw Kubiak,   Miroslaw Kutylowski  


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 Muller's
probabilistic square root algorithm we show a mapping that works efficiently for any 
finite field 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. 


paper presented at SOFSEM 2014
published in LNCS 8327, Springer Verlag, 395--406
DOI: 10.1007/978-3-319-04298-5_35