A MULTI-DIMENSIONAL ALGEBRA FOR DESIGNING AN IMPROVED NTRU CRYPTOSYSTEM

The NTRU public key cryptosystem is essentially based on the Nth degree trun- cated polynomial ring Z[X]/XN−1 . By altering the Z[X]/XN−1 or its mathematical con- struction, many researchers have worked to improve NTRU. In this paper, we present a new multi-dimensional public key cryptosystem which depends on a commutative quaternion al- gebra with a new structure. The new structure is an alternative to NTRU called NTRTE. Some data are used for comparing the key security and message security of NTRTE with the original NTRU and QTRU cryptosystems. Based on a security assessment, the comparison reveals that NTRTE is more resistant to them.