International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Weak Keys in MST1

Jens-Matthias Bohli
Maria Isabel Gonzalez Vasco
Consuelo Martínez
Rainer Steinwandt
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Abstract: The public key cryptosystem $MST_1$ has been introduced in~\cite{MaStTr00}. Its security relies on the hardness of factoring with respect to wild logarithmic signatures. To identify `wild-like' logarithmic signatures, the criterion of being totally-non-transversal has been proposed. We give tame totally-non-transversal logarithmic signatures for the alternating and symmetric groups of degree $\ge 5$. Hence, basing a key generation procedure on the assumption that totally-non-transversal logarithmic signatures are `wild like' seems critical. We also discuss the problem of recognizing `weak' totally-non-transversal logarithmic signatures, and demonstrate that another proposed key generation procedure based on permutably transversal logarithmic signatures may produce weak keys.
  title={Weak Keys in MST1},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / logarithmic signatures, group based cryptography, MST1},
  note={ 11838 received 31 May 2002},
  author={Jens-Matthias Bohli and Maria Isabel Gonzalez Vasco and Consuelo Martínez and Rainer Steinwandt},