Compression schemes can be divided into two categories, lossy and lossless, but this paper presents lossless data compression models and the original data can be correctly recovered from the data compressed material. Some mathematical results are assumed; the results of probability tests are assumed and used to evaluate the compression techniques we will discuss. To learn more about math concepts for some of the topics in this article, see [2, 3]. First, we look at several ideas in information theory that provide a standard for the development of lossless data compression schemes are briefly reviewed. We next look at several ways to model data that lead to efficient data compression encryption schemes.