18,326 research outputs found
Public Key Exchange Using Matrices Over Group Rings
We offer a public key exchange protocol in the spirit of Diffie-Hellman, but
we use (small) matrices over a group ring of a (small) symmetric group as the
platform. This "nested structure" of the platform makes computation very
efficient for legitimate parties. We discuss security of this scheme by
addressing the Decision Diffie-Hellman (DDH) and Computational Diffie-Hellman
(CDH) problems for our platform.Comment: 21 page
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 Protocols over Twisted Dihedral Group Rings
Key management is a central problem in information security. The development of quantum computation could make the protocols we currently use unsecure. Because of that, new structures and hard problems are being proposed. In this work, we give a proposal for a key exchange in the context of NIST recommendations. Our protocol has a twisted group ring as setting, jointly with the so-called decomposition problem, and we provide a security and complexity analysis of the protocol. A computationally equivalent cryptosystem is also proposed
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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