Optical encryption for multi-user based on computational ghost imaging with Hadamard modulation

In multi-user applications, one of the thorny problems for a cryptographic algorithm is how to distribute the keys and reduce the amount of transmitted data without crosstalk and security risks. Based on Hadamard modulated Computational Ghost Imaging (CGI), we propose an optical encryption scheme for multi-user, in which a common ciphertext is public for all users and one user owns a unique key to index the row sequence of Hadamard basis for decryption. Therefore, the channel resources are saved because the ciphertext does not need to be transmitted. Compared with the conventional CGI-based random intensity modulation encryption, the scheme not only reduces the amount of transmitted key data but also enhances the quality of decrypted images, which benefits from the order of Hadamard basis rather than its distribution being taken as the key. Theoretical analysis and numerical simulations are conducted to prove the feasibility and property of the scheme.