Much of the data transmitted and stored today is both highly redundant and sensitive in terms of security. This includes applications that manage legal documents, medical records, software code, and scientific data. The typical approach to handling such data involves compressing it first, followed by encryption. Among the various compression algorithms, the relatively new Asymmetric Numeral Systems (ANS) is becoming increasingly popular within the IT sector. The paper explores possible applications of ANS in Cryptography. It presents the ANS algorithms and their properties that can be useful for security sensitive applications. The ANS with randomised states can be seen as the basic cryptographic tool that can be used to convert uniformly random sequences into an arbitrary probability distribution calibrated by appropriate selection of symbol spreads. The paper presents two generic joint compression and encryption (also called compcrypt). The first uses the sponge structure and the second follows the CBC mode. Security of the compcrypt algorithm is discussed. The main take away is that both the linear and differential analysis become less effective due to fact that the adversary needs to guess lengths of ANS encoding.