# Trace zero varieties in cryptography : optimal representation and index calculus

Massierer, Maike. Trace zero varieties in cryptography : optimal representation and index calculus. 2014, Doctoral Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_10782

We also investigate the hardness of the discrete logarithm problem in trace zero subgroups. For this purpose, we propose an index calculus algorithm to compute discrete logarithms in these groups, following the approach of Gaudry for index calculus in abelian varieties of small dimension. We make the algorithm explicit for small values of $n$ and study its complexity as well as its practical performance with the help of our own Magma implementation. Finally, we compare this approach with other possible attacks on the discrete logarithm problem in trace zero subgroups and draw some general conclusions on the suitability of these groups for cryptographic systems.}