A new cryptographic method for cloud computing

We propose a noise-free efficient fully homomorphic encryption scheme based on a new homomorphic and probabilistic transform between the ring Z/2Z (ring of the residual integers modulo 2) and the ring of the Lipschitz integers. Our cryptosystem is capable of processing clear messages in the form of bits at input and providing ciphertexts in the form of Lipschitz quaternion matrices modulo a large even integer n in a non-deterministic way. The security of the present cryptosystem is based on the difficulty of solving a system of multivariate polynomial equations in a non-commutative ring. This cryptosystem makes it possible to further reduce the multiplication computation time in fully homomorphic encryption algorithms, as it makes it possible to minimize the size of a secret key and to reduce the expansion of ciphertexts.