The authors propose a new cryptographic primitive for public key cryptography based on non-commutative finite groups. For this purpose they use finite non-commutative rings of the four-dimensional vectors over the ground field $\mathrm{GF}(p)$, where $p$ is a prime with suitable vector multiplication. They claim that their construction produces computationally difficult problem (it resembles the discrete logarithm problem) and prove that the key space is large enough. The positive aspect of their algorithm is that they can derive the public key from the private one a constant times faster than in the analogous schemas implemented using elliptic curves while maintaining the same security level. The article contains the necessary algebraic justifications of the proposed problem and algorithm, but its cryptanalysis is omitted.
Reviewer: Vladimír Lacko (Košice)