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 $(\Z/p\Z)^*$ 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