In the traditional optical cryptosystems based on computational ghost imaging, a large number of phase-only masks or speckle patterns are generated to reconstruct the object image with high visual quality. At the same time, this kind of massive data, which is usually considered as the security keys to enhance the security of the cryptosystem, needs to be stored and transmitted and leads to low efficiency in practical applications. To address this issue, a computational ghost imaging method based on sparse reconstruction with the Barzilai-Borwein gradient projection is proposed from a new perspective of applying the compressive sensing technique in this paper. The measured intensities of the object image are collected by the means of traditional computational ghost imaging, while the security key composed of speckle patterns is compressed using compressive sensing and then transmitted in the secure channel in the proposed method. Consequently, the burden of key management such as storage and transmission can be considerably decreased. Moreover, when a significantly small part of the security key is shared in the secure channel, original information still can be authenticated without clear visualization by calculating the nonlinear correlation map between the object image and its reconstruction. The optical experiments illustrate the feasibility and effectiveness of the proposed method and demonstrate that it can provide an effective alternative for enriching the related research on computational ghost imaging techniques.