An image encryption algorithm with a novel chaotic coupled mapped lattice and chaotic image scrambling technique

Behrang Chaboki, Ali Shakiba


In this paper, we build a novel chaotic coupled lattice mapping with positive Lyapunov exponent, and introduce a novel chaotic image scrambling mechanism. Then, we propose a chaotic image encryption algorithm which uses the introduced chaotic coupled lattice mapping to apply permutation by iteratively applying the introduced chaotic image scrambling mechanism, and diffusing the pixel values. We use a sorting approach rather than quantizing the chaotic floating-point values to construct the diffusion matrix. We also study the security of the proposed algorithm concerning several security measures including brute-force attack, differential attack, key sensitivity, and statistical attacks. Moreover, the proposed algorithm is robust against data loss and noise attacks.


Chaotic Coupled Lattice Mapping; Chaotic Image Scrambling; Chaotic Image Encryption

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N.~Zhou, S.~Pan, S.~Cheng, and Z.~Zhou, ``Image compression-encryption scheme

based on hyper-chaotic system and 2d compressive sensing,'' emph{Optics &

Laser Technology}, vol.~82, pp. 121--133, 2016.

X.~Chai, Z.~Gan, Y.~Chen, and Y.~Zhang, ``A visually secure image encryption

scheme based on compressive sensing,'' emph{Signal Processing}, vol. 134,

pp. 35--51, 2017.

J.~Dong, Y.~Chen, X.~Gu, and L.~Xie, ``Efficient and universal quantum key

distribution based on chaos and middleware,'' emph{International Journal of

Modern Physics B}, vol.~30, pp. 1,650,264--(20 pages), 2016.

N.~Zhou, Y.~Hu, L.~Gong, and G.~Li, ``Quantum image encryption scheme with

iterative generalized arnold transforms and quantum image cycle shift

operations,'' emph{Quantum Information Processing}, vol. 16 (6), p. Article

number: 164, 2017.

R.~Enayatifar, H.~Javedani~Sadaei, H.~Abdullah, M.~Li, and I.~Fauzi~Isnin, ``A

novel chaotic based image encryption using a hybrid model of deoxyribonucleic

acid and cellular automata,'' emph{Optics and Lasers in Engineering},

vol.~71, pp. 33--41, 2015.

J.~Chen, Z.-l. Zhu, L.-b. Zhang, Y.~Zhang, and B.-q. Yang, ``Exploiting

self-adaptive permutation–diffusion and dna random encoding for secure and

efficient image encryption,'' emph{Signal Processing}, vol. 142, pp.

--353, 2018.

Z.~Liu, L.~Xu, T.~Liu, H.~Chen, P.~Li, C.~Lin, and S.~Liu, ``Color image

encryption by using arnold transform and color-blend operation in discrete

cosine transform domains,'' emph{Optics Communications}, vol. 284, pp.

--128, 2011.

S.~You, Y.~Lu, W.~Zhang, B.~Yang, R.~Peng, and S.~Zhuang, ``Micro-lens array

based 3-d color image encryption using the combination of gravity model and

arnold transform,'' emph{Optics Communications}, vol. 355, pp. 419--426,

C.~Fu, J.-j. Chen, H.~Zuo, W.-h. Meng, Y.-f. Zhan, and Y.-w. Yu, ``A

chaos-based digital image encryption scheme with an improved diffusion

strategy,'' emph{Optics Express}, vol.~20, pp. 2363--2378, 2012.

G.~Ye and X.~Huang, ``Spatial image encryption algorithm based on chaotic map

and pixel frequency,'' emph{Science China Information Sciences}, vol.~61, p.

Article number: 058104, 2018.

Y.-Q. Zhang and X.-Y. Wang, ``A symmetric image encryption algorithm based on

mixed linear–nonlinear coupled map lattice,'' emph{Information Sciences},

vol. 273, pp. 329--351, 2014.

------, ``A new image encryption algorithm based on non-adjacent coupled map

lattices,'' emph{Applied Soft Computing}, vol.~26, pp. 10--20, 2015.

A.~Shakiba, ``A novel randomized one-dimensional chaotic chebyshev mapping for

chosen plaintext attack secure image encryption with a novel chaotic breadth

first traversal,'' emph{Multimedia Tools and Applications}, 2019.

------, ``A randomized {CPA}-secure asymmetric-key chaotic color image

encryption scheme based on the chebyshev mappings and one-time pad,''

emph{Journal of King Saud University-Computer and Information Sciences},

K.~Kaneko, ``{Period-Doubling of Kink-Antikink Patterns, Quasiperiodicity in

Antiferro-Like Structures and Spatial Intermittency in Coupled Logistic

Lattice*): Towards a Prelude of a “Field Theory of Chaos”},''

emph{Progress of Theoretical Physics}, vol.~72, no.~3, pp. 480--486, 09

K.~Briggs, ``An improved method for estimating liapunov exponents of chaotic

time series,'' emph{Physics Letters A}, vol. 151, no. 1-2, pp. 27--32, 1990.

M.~Wang, X.~Wang, Y.~Zhang, and Z.~Gao, ``A novel chaotic encryption scheme

based on image segmentation and multiple diffusion models,'' emph{Optics &

Laser Technology}, vol. 108, pp. 558--573, 2018.

X.~Deng, C.~Liao, C.~Zhu, and Z.~Chen, ``Image encryption algorithms based on

chaos through dual scrambling of pixel position and bit,'' emph{J. Commun},

vol.~3, p. 025, 2014.

X.~Huang, ``Image encryption algorithm using chaotic chebyshev generator,''

emph{Nonlinear Dynamics}, vol.~67, no.~4, pp. 2411--2417, 2012.

M.~J. Rostami, A.~Shahba, S.~Saryazdi, and H.~Nezamabadi-pour, ``A novel

parallel image encryption with chaotic windows based on logistic map,''

emph{Computers & Electrical Engineering}, vol.~62, pp. 384--400, 2017.

X.~Wang, Q.~Wang, and Y.~Zhang, ``A fast image algorithm based on rows and

columns switch,'' emph{Nonlinear Dynamics}, vol.~79, no.~2, pp. 1141--1149,

X.~Wu, K.~Wang, X.~Wang, and H.~Kan, ``Lossless chaotic color image

cryptosystem based on {DNA} encryption and entropy,'' emph{Nonlinear

Dynamics}, vol.~90, no.~2, pp. 855--875, 2017.

G.~Ye, C.~Pan, X.~Huang, Z.~Zhao, and J.~He, ``A chaotic image encryption

algorithm based on information entropy,'' emph{International Journal of

Bifurcation and Chaos}, vol.~28, no.~01, p. 1850010, 2018.

G.~Ye and K.-W. Wong, ``An efficient chaotic image encryption algorithm based

on a generalized arnold map,'' emph{Nonlinear dynamics}, vol.~69, no.~4, pp.

--2087, 2012.

Y.~Zhang, ``The unified image encryption algorithm based on chaos and cubic

s-box,'' emph{Information Sciences}, vol. 450, pp. 361--377, 2018.

Z.~Eslami and A.~Bakhshandeh, ``An improvement over an image encryption method

based on total shuffling,'' emph{Optics Communications}, vol. 286, pp.

--55, 2013.

P.~Cheng, H.~Yang, P.~Wei, and W.~Zhang, ``A fast image encryption algorithm

based on chaotic map and lookup table,'' emph{Nonlinear Dynamics}, vol.~79,

no.~3, pp. 2121--2131, 2015.

K.-w. Wong, ``A fast chaotic cryptographic scheme with dynamic look-up table,''

emph{Physics Letters A}, vol. 298, no.~4, pp. 238--242, 2002.

J.~Wu, X.~Liao, and B.~Yang, ``Image encryption using 2d h{'e}non-sine map and

{DNA} approach,'' emph{Signal Processing}, vol. 153, pp. 11--23, 2018.

Q.~Yin and C.~Wang, ``A new chaotic image encryption scheme using breadth-first

search and dynamic diffusion,'' emph{International Journal of Bifurcation

and Chaos}, vol.~28, no.~04, p. 1850047, 2018.

W.~Liu, K.~Sun, and C.~Zhu, ``A fast image encryption algorithm based on

chaotic map,'' emph{Optics and Lasers in Engineering}, vol.~84, pp. 26--36,

A.~Kadir, A.~Hamdulla, and W.-Q. Guo, ``Color image encryption using skew tent

map and hyper chaotic system of 6th-order cnn,'' emph{Optik-International

Journal for Light and Electron Optics}, vol. 125, no.~5, pp. 1671--1675,

Y.~Wu, Y.~Zhou, J.~P. Noonan, and S.~Agaian, ``Design of image cipher using

latin squares,'' emph{Information Sciences}, vol. 264, pp. 317--339, 2014.

H.~Hermassi, R.~Rhouma, and S.~Belghith, ``Improvement of an image encryption

algorithm based on hyper-chaos,'' emph{Telecommunication Systems}, vol.~52,

no.~2, pp. 539--549, 2013.

C.-Y. Song, Y.-L. Qiao, and X.-Z. Zhang, ``An image encryption scheme based on

new spatiotemporal chaos,'' emph{Optik-International Journal for Light and

Electron Optics}, vol. 124, no.~18, pp. 3329--3334, 2013.

Y.~Zhou, L.~Bao, and C.~P. Chen, ``Image encryption using a new parametric

switching chaotic system,'' emph{Signal processing}, vol.~93, no.~11, pp.

--3052, 2013.

Y.~Zhang and D.~Xiao, ``An image encryption scheme based on rotation matrix

bit-level permutation and block diffusion,'' emph{Communications in

Nonlinear Science and Numerical Simulation}, vol.~19, no.~1, pp. 74--82,

K.~Gupta and S.~Silakari, ``Novel approach for fast compressed hybrid color

image cryptosystem,'' emph{Advances in Engineering Software}, vol.~49, pp.

--42, 2012.

H.~Liu, X.~Wang emph{et~al.}, ``Image encryption using {DNA} complementary

rule and chaotic maps,'' emph{Applied Soft Computing}, vol.~12, no.~5, pp.

--1466, 2012.

X.~Wei, L.~Guo, Q.~Zhang, J.~Zhang, and S.~Lian, ``A novel color image

encryption algorithm based on {DNA} sequence operation and hyper-chaotic

system,'' emph{Journal of Systems and Software}, vol.~85, no.~2, pp.

--299, 2012.

C.~Huang and H.~Nien, ``Multi chaotic systems based pixel shuffle for image

encryption,'' emph{Optics Communications}, vol. 282, no.~11, pp. 2123--2127,

R.~Rhouma, S.~Meherzi, and S.~Belghith, ``{OCML}-based colour image

encryption,'' emph{Chaos, Solitons & Fractals}, vol.~40, no.~1, pp.

--318, 2009.

L.~Xu, Z.~Li, J.~Li, and W.~Hua, ``A novel bit-level image encryption algorithm

based on chaotic maps,'' emph{Optics and Lasers in Engineering}, vol.~78,

pp. 17--25, 2016.

N.~Zhou, H.~Jiang, L.~Gong, and X.~Xie, ``Double-image compression and

encryption algorithm based on co-sparse representation and random pixel

exchanging,'' emph{Optics and Lasers in Engineering}, vol. 110, pp. 72--79,

B.~Norouzi, S.~Mirzakuchaki, S.~M. Seyedzadeh, and M.~R. Mosavi, ``A simple,

sensitive and secure image encryption algorithm based on hyper-chaotic system

with only one round diffusion process,'' emph{Multimedia tools and

applications}, vol.~71, no.~3, pp. 1469--1497, 2014.

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