Optical image encryption technology based on joint transform correlation (JTC) has attracted increasing attention from researchers. We propose a multi-user secure communication system based on the special properties of JTC. Multiple users utilize their own fingerprints to encrypt the plain-text in the encryption process, and each user must be first authenticated at the beginning of the decryption process. Only users with legitimate identities can perform the decryption process, whereas unauthorized users with false identities cannot, so the security of the system is greatly improved. Furthermore, we propose a multi-user double-image encryption method, which can better meet the needs of different security environments. Considering the possibility of overlapping images at the output end, we prove that a JTC-based image encryption system can avoid overlapping images at the output when the distance between the input images is 3W (W is the side length of a square image), which provides a theoretical foundation for further research. Finally, a numerical simulation demonstrates the effectiveness and feasibility of the proposed idea.Entropy 2019, 21, 850 2 of 17 Vilardy et al. analyzed JTC encryption methods and found that it is possible to significantly improve the quality of the decrypted image by introducing a simple nonlinear operation in the encrypted function that contains the joint power spectrum [13][14][15]. Moreover, the JTC system has been applied to different transformation domains, such as the fractional Fourier transform domain [16], Fresnel transform domain [17], and chaotic maps [18,19], which greatly expanded the application of JTC. As is known, cryptography and cryptanalysis are complementary to each other. Therefore, attack schemes against JTC encryption system are proposed [20][21][22][23][24][25][26]. At the same time, the researchers introduced authentication to improve the security of the system [27][28][29][30].In the JTC encryption system, the common feature is that the classified information is controlled by one user. However, in some cases, this information cannot be owned by one user alone. The classified information can be obtained only if two or more users are present simultaneously. In the current study, a multi-user encryption system is proposed based on JTC. The proposed cryptosystem is uniquely useful in practical applications such as co-signing important documents, the control of nuclear buttons, access to certain crucial information, and so on.The remainder of this paper is organized as follows. Section 2 proves the feasibility of the proposed scheme through mathematical theory and the analysis of potential risks. Multi-user double image encryption is proposed, and the position distribution of the output image is analyzed in Section 3. Simulation results are shown in Section 4. Finally, the conclusions are presented in Section 5.
The Proposed CryptosystemOn he basis of JTC, the current report proposes a multi-user encryption system with fingerprint keys. Different system users utilize ...