This work presents a simple, easy to implement secure invertible data hiding method utilizing the advantages of both cryptography and steganography. The secret message to embed is first encrypted using CAESAR cipher method, and this encrypted message is further compressed using Huffman encoding. These encoded bits are embedded inside a host image thus creating the stego image. Data hiding method used here is the Histogram shifting method. In this method the maximum point and the minimum point of the histogram of an image is selected and slightly modifies the pixel intensities to embed data into the image. In the conventional Histogram shifting data hiding method the embedding capacity is limited by the peak value of the histogram. This proposed technique can overcome this limitation by compressing the input secret data bits to hide, thereby making possible to embed more data. Also encrypting the secret data before compression gives an add-on advantage of increased security to the secret message. Finally the stego image is compressed before transmission which allows efficient utilization of the allotted band width. The performance of this method is tested by plotting capacity versus PSNR value of the marked image. Experimental results show that this method gives improved visual quality of the marked image. Also this method gives high capacity and PSNR value when compared to other conventional data hiding methods.