Data compression combined with effective encryption is a common requirement of data storage and transmission. Low cost of these operations is often a high priority in order to increase transmission speed and reduce power usage. This requirement is crucial for battery-powered devices with limited resources, such as autonomous remote sensors or implants. Well-known and popular encryption techniques are frequently too expensive. This problem is on the increase as machine-to-machine communication and the Internet of Things are becoming a reality. Therefore, there is growing demand for finding trade-offs between security, cost and performance in lightweight cryptography. This article discusses Asymmetric Numeral Systems -- an innovative approach to entropy coding which can be used for compression with encryption. It provides compression ratio comparable with arithmetic coding at similar speed as Huffman coding, hence, this coding is starting to replace them in new compressors. Additionally, by perturbing its coding tables, the Asymmetric Numeral System makes it possible to simultaneously encrypt the encoded message at nearly no additional cost. The article introduces this approach and analyzes its security level. The basic application is reducing the number of rounds of some cipher used on ANS-compressed data, or completely removing additional encryption layer if reaching a satisfactory protection level.