Fig. 1. Modified Gerchberg-Saxton algorithm flowchart in Gyrator transform domain

Fig. 2. Authentication system encryption schematic

Fig. 3. Schematic diagram of the authentication system

Fig. 4. Original images in high-level authentication. (a) Pepper; (b) Cameraman; (c) Pirate; (d) Baboon

Fig. 5. High-level authentication results. (a) φh1; (b) φh2

Fig. 6. Iterative encoding results. (a) Hyper-chaotic random amplitude constraint; (b) phase distribution of coded image E of high-level authentication; (c) average γ_CC variation versus the iteration number of the primary MGSA; (d) authentication key POM₂; (e) authentication key POM₁; (f) average γ_CC variation versus the iteration number of the secondary MGSA

Fig. 7. Original images in low-level authentication. (a) Barbara; (b) Couple; (c) Starfish; (d) Ship

Fig. 8. Low-level authentication results. (a) φl1; (b) φl2

Fig. 9. 3D γ_NCC distributions of low-level noise-like authentication images [Fig. 8(e)--(h)]. (a) Barbara; (b) Couple; (c) Starfish; (d) Ship

Fig. 10. 3D γ_NCC distributions when the false low-level authentication key is used. (a) Barbara; (b) Couple; (c) Starfish; (d) Ship

Fig. 11. Occlusion attack experiment. (a) Actual image; (b) authentication result; (c) authentication result when occluding 25%; (d) authentication result when occluding 50%

Fig. 12. MSE changing with noise intensity factor ξ and the authentication image obtained with ξ=0.4,ξ=0.8