Weak Keys in MST1

Jens-Matthias Bohli; Maria Isabel Gonzalez Vasco; Consuelo Martinez; Rainer Steinwandt

Paper 2002/070

Weak Keys in MST1

Jens-Matthias Bohli, Maria Isabel Gonzalez Vasco, Consuelo Martinez, and Rainer Steinwandt

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.

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: logarithmic signatures group based cryptography MST1
Contact author(s): mvasco @ orion ciencias uniovi es
History: 2002-06-03: received
Short URL: https://ia.cr/2002/070
License: CC BY

BibTeX

@misc{cryptoeprint:2002/070,
      author = {Jens-Matthias Bohli and Maria Isabel Gonzalez Vasco and Consuelo Martinez and Rainer Steinwandt},
      title = {Weak Keys in MST1},
      howpublished = {Cryptology ePrint Archive, Paper 2002/070},
      year = {2002},
      note = {\url{https://eprint.iacr.org/2002/070}},
      url = {https://eprint.iacr.org/2002/070}
}