Ehsan Malekian - Faculty of Electrical and Computer Engineering,Shahid Beheshti University, Evin, Tehran, Iran
Ali Zakerolhosseini - Faculty of Electrical and Computer Engineering,Shahid Beheshti University, Evin, Tehran, Iran

In this paper, a classic example of a public key cryptosystem with non-associative algebra has been presented in order to show that the non-associative algebra also has the potential to be used in the public key cryptosystems. The proposed scheme is similar to the NTRU public key cryptosystem and can be regarded as a multi-dimensional and probabilistic cryptosystem in which the basic operations are very fast and efficient. The underlying algebra in the proposed scheme is based on the octonions algebra defined over the convolution polynomial ring with coefficients in GF(3)[X]. The most important conclusion of the proposed scheme is that the basic concept behind the NTRU cryptosystem is an abstract concept and it can be generalized to an algebra broader than Dedekind domain.

Non-associative Public Key Cryptosystem, NTRU, CTRU, Lattice based Cryptosystems