A new NTRU cryptosystem outperforms three highly secured NTRU-analog systems through an innovational algebraic structure

NTRU public key cryptosystem relies on computations that are efficiently performed with insignificant storage and time complexity. Many researchers were motivated to improve NTRU performance by replacing the original polynomial ring and mathematical structure with new modified algebraic structures, such as QTRU, OTRU, BITRU, and many others. In this work, a new NIRU-analog cryptosystem called QOBTRU is proposed based on a newly designed algebraic structure called Carternion algebra. QOBTRU is at least quadratic higher than the original NTRU in terms of computational and space complexity. It is intended to have an alternative security and performance attribute upon three chosen highly performed multidimensional NTRU-like cryptosystems, which are QTRU, OTRU, and BITRU. Their comparison with QOBTRU highlighted its strength over them. Some statistical and security analysis is performed to demonstrate its efficiency.