Fig. 1. Schematic of the encryption process

Fig. 2. Schematic of the decryption process

Fig. 3. Two original images and their encryption and decryption results. (a) (b) Original images Lena and Peppers; (c) fingerprint; (d) MFRP1; (e) phase key P1; (f) encrypted image; (g) (h) decrypted images Lena and Peppers obtained by correct keys

Fig. 4. Decrypted results of image Lena with incorrect keys. (a) Incorrect fingerprint; (b) decrypted result with the incorrect fingerprint; (c)-(f) decrypted results with the incorrect parameters of the chaotic map a0'=1.75+10-15, b0'=0.33+10-15, x0'=0.34+10-15, y0'=10-15; (g)-(h) decrypted results with the incorrect parameter of the Gyrator transform α1'=0.5+10-2, α2'=0.6+9×10-3; (i) decrypted result with the incorrect phase key P1

Fig. 5. Decrypted results of image Peppers with incorrect keys. (a) Incorrect fingerprint; (b) decrypted result with the incorrect fingerprint; (c)-(f) decrypted results with the incorrect parameters of the chaotic map a0'=1.75+10-15, b0'=0.33+10-15, x0'=0.34+10-15, y0'=10-15; (g)-(h) decrypted results with the incorrect parameter of the Gyrator transform α1'=0.5+10-2, α2'=0.6+9×10-3; (i) decrypted result with the incorrect phase key P2

Fig. 6. Histograms of the original image and encrypted image. (a) Original image Lena; (b) histogram of Lena; (c) original image Peppers; (d) histogram of Peppers; (e) encrypted image; (f) histogram of the encrypted image

Fig. 7. Encrypted images with different occlusion sizes. (a)-(d) Occlusion size is 12.5%, 25%, 37.5%, 50% respectively

Fig. 8. PSNR and CC curves of decrypted images versus different occlusion sizes. (a) Lena; (b) Peppers

Fig. 9. PSNR and CC curves of decrypted images versus different intensity of Gaussian noise. (a) Lena; (b) Peppers