Properties of gsw and their applications

In CRYPTO´13, Gentry et al. proposed a fully homomorphic encryption scheme, called GSW. We find that the scheme has three special properties, which are not sufficiently recognized and applied in current literatures. Property 1: Noise grows asymmetrically in multiplication. Property 2: Small noise in MultConst(C, α) . Property 3: Fixed noise bound when α is a power of 2 in MultConst(C, α) . We made use of property 1 to the Yi´s private searching on streaming data protocol, called YBVX. Compared with YBVX, the four mainly aspects of efficiency in our protocol had been improved, the computation complexity of the sever decreased from O(ml² + μ)multi. + O(ml² + μ)add.+O(μd)enc. +O(μ)ADD. t o O(m +μ)multi. + O(m +μ)add.+ O(μd)enc.+O(μ) ADD; the space complexity decreased from O(ml² + μd) to O(m + μd) ; the communication complexity decreased from O(ml)+O(d|D|k) to O(m)+O(d|D|k) ; the computation complexity of the client decreased from O(ml)dec.+O(d | D |) enc to O(m)dec.+ O(d | D |)enc. what´s more, the above three properties can have a variety of applications, ranging from improving the property of cryptographic prototypes to protocol building.