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Weak Keys in MST1

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Abstract

The public key cryptosystem MST1 has been introduced by Magliveras et al. [12] (Public Key Cryptosystems from Group Factorizations. Jatra Mountain Mathematical Publications). 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 present tame totally-non-transversal logarithmic signatures for the alternating and symmetric groups of degree ≥ 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.

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Authors and Affiliations

  1. Institut für Algorithmen und Kognitive Systeme, Arbeitsgruppe Systemsicherheit, Prof. Dr. Th. Beth, Universität Karlsruhe, 76128, Karlsruhe, Germany

    Jens-Matthias Bohli & Rainer Steinwandt

  2. A´rea de Matemática Aplicada, Universidad Rey Juan Carlos, c/Tulipán, s/n, 28933, Madrid, Móstoles, Spain

    María Isabel González Vasco

  3. Departamento de Matemáticas, Universidad de Oviedo, c/Calvo Sotelo, s/n, 33007, Oviedo, Spain

    Consuelo Martínez

Authors
  1. Jens-Matthias Bohli
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  2. Rainer Steinwandt
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  3. María Isabel González Vasco
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  4. Consuelo Martínez
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Corresponding author

Correspondence to María Isabel González Vasco.

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Communicated by: P. Wild

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Bohli, JM., Steinwandt, R., Vasco, M.I.G. et al. Weak Keys in MST1. Des Codes Crypt 37, 509–524 (2005). https://doi.org/10.1007/s10623-004-4040-y

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  • DOI: https://doi.org/10.1007/s10623-004-4040-y

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