Cryptanalysis of a 2-party key establishment based on a semigroup action problem
Rainer Steinwandt Adriana Suárez Corona
Advances in Mathematics of Communications 2011, 5(1): 87-92 doi: 10.3934/amc.2011.5.87
An Advances in Mathematics of Communications article from 2007 proposes an informal 2-party key establishment along the lines of the classic Diffie-Hellman construction, but using a two-sided matrix semiring action. The article contains no formal security analysis, but a specific parameter choice has been considered. We describe a heuristic attack technique against the suggested instance, which for the published "challenge value" results in a complete session key recovery with only a minor computational effort.
keywords: semigroup action problem key establishment Cryptanalysis semiring.
Attribute-based group key establishment
Rainer Steinwandt Adriana Suárez Corona
Advances in Mathematics of Communications 2010, 4(3): 381-398 doi: 10.3934/amc.2010.4.381
Motivated by the problem of establishing a session key among parties based on the possession of certain credentials only, we discuss a notion of attribute-based key establishment. A number of new issues arise in this setting that are not present in the usual settings of group key establishment where unique user identities are assumed to be publicly available.
    After detailing the security model, we give a two-round solution in the random oracle model. As main technical tool we introduce a notion of attribute-based signcryption, which may be of independent interest. We show that the type of signcryption needed can be realized through the encrypt-then-sign paradigm. Further, we discuss additional guarantees of the proposed protocol, that can be interpreted in terms of deniability and privacy.
keywords: signcryption. attribute-based cryptography Group key establishment

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