Asymmetric Multiple-Image Encryption Based on Octonion Fresnel Transform and Sine Logistic Modulation Map Li, Jianzhong;
A novel asymmetric multiple-image encryption method using an octonion Fresnel transform (OFST) and a two-dimensional Sine Logistic modulation map (2D-SLMM) is presented. First, a new multiple-image information processing tool termed the octonion Fresneltransform is proposed, and then an efficient method to calculate the OFST of an octonion matrix is developed. Subsequently this tool is applied to process multiple plaintext images, which are represented by octonion algebra, holistically in a vector manner. The complex amplitude, formed from the components of the OFST-transformed original images and modulated by a random phase mask (RPM), is used to derive the ciphertext image by employing an amplitude- and phase-truncation approach in the Fresnel domain. To avoid sending whole RPMs to the receiver side for decryption, a random phase mask generation method based on SLMM, in which only the initial parameters of the chaotic function are needed to generate the RPMs, is designed. To enhance security, the ciphertext and two decryption keys produced in the encryption procedure are permuted by the proposed SLMM-based scrambling method. Numerical simulations have been carried out to demonstrate the proposed scheme`s validity, high security, and high resistance to various attacks.
P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767-769 (1995).
G. H. Situ and J. J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584-1586 (2004).
N. K. Nischal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235, 253-259 (2004).
N. Singh and A. Sinha, “Optical image encryption using improper Hartley transforms and chaos,” Optik 121, 918-925 (2010).
M. R. Abuturab, “Securing color information using Arnold transform in gyrator transform domain,” Optics and Lasers in Engineering 50, 772-779 (2012).
I. H. Lee and M. Cho, “Double random phase encryption based orthogonal encoding technique for color images,” J. Opt. Soc. Korea 18, 129-133 (2014).
J. C. Zheng and X. Q. Li, “Image authentication using only partial phase information from a double-random-phase-encrypted image in the Fresnel domain,” J. Opt. Soc. Korea 19, 241-247 (2015).
L. S. Sui, K. K. Duan, J. L. Liang, and X. H. Hei, “Asymmetric double-image encryption based on cascaded discrete fractional random transform and logistic maps,” Opt. Express 22, 10605-10621 (2014).
U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181-3186 (2006).
X. Peng, H. Z. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31, 3261-3263 (2006).
M. R. Abuturab, “An asymmetric single-channel color image encryption based on Hartley transform and gyrator transform,” Optics and Lasers in Engineering 69, 49-57 (2015).
W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35,118-120 (2010).
X. L. Ding, Q. Yuan, and L. B. Zhang, “Known-public key attack on asymmetric optical image cryptosystem,” Laser Technology 38, 561-564 (2014). (in Chinese)
X. Wang and D. M. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078-1081 (2012).
W. Chen and X. D. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913-3917 (2011).
I. Mehra and N. K. Nishchal, “Optical asymmetric image encryption using gyrator wavelet transform,” Opt. Commun. 354, 344-352 (2015).
G. Situ and J. J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306-1308 (2005).
I. H. Lee and M. J Cho, “Double random phase encryption using orthogonal encoding for multiple-image transmission,” J. Opt. Soc. Korea 18, 201-206 (2014).
X. Wang and D. M. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284,148-152 (2011).
L. S. Sui, K. K. Duan, J. L. Liang, Z. Q. Zhang, and H. N. Meng, “Asymmetric multiple-image encryption based on coupled logistic maps in fractional Fourier transform domain,” Optics and Lasers in Engineering 62, 139-152 (2014).
M. R. Abuturab, “Generalized Arnold map-based optical multiple color-image encoding in gyrator transform domain,” Opt. Commun. 343, 157-171 (2015).
N. Singh and A. Sinha, “Optical image encryption using Hartley transform and logistic map,” Opt. Commun. 282, 1104-1109 (2009).
X. L. Wang, H. C Zhai, Z. L. Li, and Q. Ge, “Double random-phase encryption based on discrete quaternion fourier-transforms,” Optik 122, 1856-1859 (2011).
B. C. Chanyal, “Classical geometrodynamics with zorn vector-matrix algebra for Gravito-Dyons,” Reports on Mathematical Physics 76, 1-20 (2015).
H. Y. Gao and K. M. Lam, “From quaternion to octonion: feature-based image saliency detection,” in Proc. ICASSP (Florence, Italy, May 2014), pp. 2808-2812.
Y. Wang, C. Quan, and C. J. Tay, “Optical color image encryption without information disclosure using phase-truncated Fresnel transform and a random amplitude mask,” Opt. Commun. 344, 147-155 (2015).
R. Tudela, E. M. Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
Z. Y. Hua, Y. C. Zhou, C. M. Pun, and C. L. Philip Chen, “2D sine logistic modulation map for image encryption,” Information Sciences 297, 80-94 (2015).
C. Flaut and V. Shpakivskyi, “De Moivre’s formula and Euler’s formula for octonions,” arXiv preprint arXiv:1405.5655 (2014).
G. H. Huang and X. M. Li, “Color palmprint feature extraction and recognition algorithm based on octonion,” Computer Engineering 38, 28-33 (2012). (in Chinese)
J. Liu, H. Jin, L. Ma, Y. Li, and W. Jin, “Optical color image encryption based on computer generated hologram and chaotic theory,” Opt. Commun. 307, 76-79 (2013).
M. Z. He, Q. F. Tan, L. C. Cao, Q. S. He, and G. F. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17, 22462-22473 (2009).
C. B. Li, Data Structure (Tsinghua University Press, Beijing, PRC, 2013), Chapter 9. (in Chinese)
K. Xu, F. Wang, and H. Y. Wang, “Lightweight and informative traffic Metrics for data center monitoring,” Journal of Network and Systems Management 20, 226-243 (2012).