A non-associative lattice-based public key cryptosystem

In this paper we will prove that a lattice-based public key cryptosystem based on non-associative algebra is not only feasible but also arguably more secure than the existing lattice based cryptosystems such as NTRU, because its lattice does not fully fit within circular and convolutional modular lattice (CCML). The underlying algebraic structure of the proposed non-associative cryptosystem is the power-associative and alternative octonions algebra which can be defined over any Dedekind domain such as convolution polynomial ring. Besides the detailed specification of the proposed cryptosystem, we have proved that the security of the proposed scheme relies on the difficulty of the finding shortest vector in a certain kind of lattice. Since there is no isomorphic matrix representation for octonions, the only method for attacking the proposed cryptosystem and finding a spurious key for decryption is to form a lattice of dimension 16.N which is eight times larger than the NTRU lattice. By reducing the dimension of the underlying convolution polynomial ring (N) and using optimization techniques, we can increase the encryption and decryption speed, to a level equal to NTRU.