Although the learning with errors(LWE)-based full homomorphic encryption scheme was the first example of deviation from the original Gentry's blueprint, the scheme did not give detailed conversion process of circuit layer structure, and must rely on bootstrapping technique to achieve full homomorphism.Therefore, through modifying the re-linearization technique proposed by the above scheme, a technique called non-matrix key switching is presented, which includes key switching with re-linearization and pure key switching. The complex matrix operations of existing key switching technique are removed. Combining this technique with modulus switching, a(leveled) fully homomorphic encryption scheme without bootstrapping from LWE is constructed. In order to make circuit layer structure clear, the scheme gives detailed refresh door operation. Finally, we use bootstrapping to upgrade arithmetic circuit to any layer, and make the homomorphic computing capability of the scheme have nothing to circuit depth.
