Symmetric information exchange system based on ring isomorphism (Q2103813)

In the paper under review, the authors suggest algorithms for exchanging messages between subscribers based on the properties of associative-commutative rings with unity and systems of linear Diophantine equations over such rings. They also present algorithms for constructing finite rings whose additive groups are full-cycle, and algorithms for constructing isomorphisms between a ring of \(k\)-th order whose additive group is full-cycle and the residue ring \(Z_k\) modulo \(k\). In my opinion, the hard problem behind the security of the proposed scheme is not convincing. It is difficult in modern cryptography to present a scheme without provable security, and the proposed scheme does not have one. Therefore, the proposed protocol in its actual form is not enough to convince the cryptography community to accept the scheme as a secure one.