A new alternative to NTRU cryptosystem based on highly dimensional algebra with dense lattice structure

Ntru public key is a cryptosystem with hard mathematical structure and short key size relies in its security on the hardness of lattice based cryptosystems. its smallest key size made it highly performed system and grant it an advantageous over other numbers theoretical based cryptosystems. due to shamir's conclusion about the dnon commutative computations in encryption and decryption processes of any cryptosystem leads to turn it into a highly lattice attack resist system. in this paper,a new alternative non associative,non-commutative multidimensional system is proposed under the same principle of ntru cryptosystem. it is called hxdtru,where its operations taken place in a specially designed high dimensional algebra called hexadecnion algebra. the proposed system is implemented,and its security and efficiency are analyzed.