Massoud Sokouti - Department of Electrical and Computer Engineering, Shahid Beheshti University, Tehran, Iran
Ali Zakerolhosseini - Department of Electrical and Computer Engineering, Shahid Beheshti University, Tehran, Iran
Babak Sokouti - Biotechnology Research Center Tabriz University of Medical Sciences, Tabriz, Iran

We propose a probabilistic and multi-dimensional public key cryptosystem based on the GGH public key cryptosystem using polynomial rings and quaternion algebra.The new method encrypts four data vectors in each encryption session using quaternion algebraic structure and polynomialrings. The new method is faster than GGH in producing publickey but it is slow in encryption and decryption since it uses quaternion algebraic structure and polynomial rings. The new method strengths the GGH cryptosystem while using quaternion algebraic structure. Quaternion algebra is a non-commutative algebra and it makes this cipher much more resistant to some lattice based attacks.

GGH, Polynomial rings, Public key cryptography, Lattice attacks, Encryption, Quaternion algebra