The design and engineering of original cryptographic solutions is a major concern to provide secure information systems. In a previous study, we have described a generator based on chaotic iterations, which uses the well-known XORshift generator. By doing so, we have improved the statistical performances of XORshift and make it behave chaotically, as defined by Devaney. The speed and security of this former generator have been improved in a second study, to make its usage more relevant in the Internet security context. In this paper, these contributions are summarized and a new version of the generator is introduced. It is based on a new Lookup Table implying a large improvement of speed. A comparison and a security analysis between the XORshift and these three versions of our generator are proposed, and various new statistical results are given. Finally, an application in the information hiding framework is presented, to give an illustrative example of the use of such a generator in the Internet security field.