Delaram Kahrobaei, Charalambos Koupparis, Vladimir Shpilrain
We propose a cryptosystem based on matrices over group rings and claim that it is secure against adaptive chosen ciphertext attack.
Maggie Habeeb, Delaram Kahrobaei, Charalambos Koupparis et al.
In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our protocol can be based on any group, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when our protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. Here we also suggest a particular non-commutative semigroup (of matrices) as the platform and show that security of the relevant protocol is based on a quite different assumption compared to that of the standard Diffie-Hellman protocol.
Delaram Kahrobaei, Charalambos Koupparis, Vladimir Shpilrain
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.
Delaram Kahrobaei, Charalambos Koupparis
The objective of this work is to survey several digital signatures proposed in the last decade using non-commutative groups and rings and propose a digital signature using non-commutative groups and analyze its security.