We propose QTRU, a probabilistic and multi-dimensional public key cryptosystem based on the NTRU public key cryptosystem using quaternion algebra. QTRU encrypts four data vectors in each encryption session and the only other major difference between NTRU and QTRU is that the underlying algebraic structure has been changed to a non-commutative algebraic structure. As a result, QTRU inherits the ...

A multi-dimensional QTRU public-key cryptosystem improves NTRU by replacing the original ring in quaternion algebra. In this paper, we introduce QMNTR an improvement of using a new mathematical structure two public keys and five private keys. This modification has enhanced key system to be more robust secure.

In this paper we will construct a lattice-based public-key cryptosystem using non-commutative quaternion algebra, and since its lattice does not fully fit within Circular and Convolutional Modular Lattice (CCML), we prove it is arguably more secure than the existing lattice-based cryptosystems such as NTRU. As in NTRU, the proposed public-key cryptosystem relies for its inherent securi...