461 research outputs found
Cryptanalysis of some protocols using matrices over group rings
We address a cryptanalysis of two protocols based on the supposed difficulty
of discrete logarithm problem on (semi) groups of matrices over a group ring.
We can find the secret key and break entirely the protocols
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
Public key protocols over the ring E_p(m)
In this paper we use the nonrepresentable ring E_p(m) to introduce public key cryptosystems in noncommutative settings and based on the Semigroup Action Problem and the Decomposition Problem respectively.The second author was supported by Ministerio de Economia y Competitividad grant MTM2014-54439 and Junta de Andalucia FQM0211
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