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Group key management based on semigroup actions
In this work we provide a suite of protocols for group key management based
on general semigroup actions. Construction of the key is made in a distributed
and collaborative way. Examples are provided that may in some cases enhance the
security level and communication overheads of previous existing protocols.
Security against passive attacks is considered and depends on the hardness of
the semigroup action problem in any particular scenario.Comment: accepted for publication in Journal of algebra and its application
Public Key Cryptography based on Semigroup Actions
A generalization of the original Diffie-Hellman key exchange in
found a new depth when Miller and Koblitz suggested that such a protocol could
be used with the group over an elliptic curve. In this paper, we propose a
further vast generalization where abelian semigroups act on finite sets. We
define a Diffie-Hellman key exchange in this setting and we illustrate how to
build interesting semigroup actions using finite (simple) semirings. The
practicality of the proposed extensions rely on the orbit sizes of the
semigroup actions and at this point it is an open question how to compute the
sizes of these orbits in general and also if there exists a square root attack
in general. In Section 2 a concrete practical semigroup action built from
simple semirings is presented. It will require further research to analyse this
system.Comment: 20 pages. To appear in Advances in Mathematics of Communication
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