520 research outputs found
Classification of finite congruence-simple semirings with zero
Our main result states that a finite semiring of order >2 with zero which is
not a ring is congruence-simple if and only if it is isomorphic to a `dense'
subsemiring of the endomorphism semiring of a finite idempotent commutative
monoid.
We also investigate those subsemirings further, addressing e.g. the question
of isomorphy.Comment: 16 page
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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