Computational ghost imaging (CGI) has demonstrated rapid developments in recent years [1], [2], [3]. It is different from traditional direct imaging methods, which uses the modulated patterns to illuminate target for obtaining bucket detector values containing the target information, and then uses the second-order correlation algorithm [4], [5], [6] to recover the target. Its special and novel imaging method have been found to be widely used in biomedicine [7], [8], [9], [10], imaging through atmospheric turbulence environment [11], [12], [13], [14], [15], [16], remote sensing [17], [18] in recent years. How to improve the efficiency of ghost imaging is very important for the real applications. In order to reduce the sampling rate and improve imaging efficiency, compressed sensing technology [19], [20] has been used in the CGI. And deep learning techniques  [21], [22], [23], [24], [25], [26], [27], [28] demonstrates great potentials to reduce the sampling rate of ghost imaging. Meanwhile, how to improve its imaging effect is also a very important topic in the CGI field. Polarization-difference based ghost imaging shows good anti-scattering effects [29], [30], [31], [32], [33], [34], [35]. By modulating Hadamard patterns [36], [37], [38], [39] to illuminate the target, the image quality can be improved greatly due to its orthogonality. Using random patterns to illuminate target, and then orthonormalize the acquired bucket detector values and patterns, can also greatly improve the image quality [40], [41].

The CGI is not only just for imaging, but can also be applied to image encryption [42], [43], [44]. Since the second-order correlation algorithm requires the illumination patterns and the bucket detector values to recovery target. So, it is very suitable for encrypted transmission  [45], [46], [47], in which we can send bucket detector values and illumination patterns in a public channel and a private channel, respectively  [48], [49]. By integrating metasurface technology and the secret sharing principle of visual cryptography (VC) [50], [51], the security of ghost imaging encryption is improved and extend the application of VC to more diversified scenarios. However, for the encrypted transmission of image, it is first necessary to consider security issues and send the key to recover image directly in the private channel. Once the data is stolen, it is insecure. Secondly, in image encryption transmission, the data transmitted in the private channel is as small as possible to send quickly, but these encryption schemes send large illumination patterns information in the private channel. Thirdly, such encryption schemes are too blunt and difficult to confuse eavesdroppers. Moreover, there are already attacks on this encryption scheme, and the attacker can confuse the receiver by sending forgery patterns to achieve the effect of the attack [52], [53], [54], which illustrates that traditional ghost imaging encryption scheme are no longer secure. In this regard, we have designed a CGI encryption scheme that hide illumination patterns information.

In this letter, we design an efficient, convenient, and strong resistance to eavesdropping CGI encryption scheme. In our scheme, the sender uses the KPs and original illumination patterns (fake patterns) to hide the data of real patterns (RPs), and the bucket detector values can be then obtained from the CGI. The sender sends fake patterns (FPs) and bucket detector values in the public channel. The receiver gets a key vector consisting of the KPs labels (sequence positions in KPs database), which sent by the sender in the private channel. The receiver can decrypt the FPs, and orthonormalize the data [40] and then restore the target. Our scheme transmits much less data in the private channel, and sends FPs and bucket detector values in the public channel, which has a great deceptive effect on eavesdroppers. Throughout the encrypted transmission scheme, we have designed the encryption and decryption algorithm, which is extremely convenient in the applications.