# Differential evolution optimization of intertwining logistic map-DNA based image encryption technique

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## Abstract

Differential evolution (DE) is a powerful evolutionary algorithms, widely applied in different fields of science and engineering for solving the problem of optimization. Since image encryption has been viewed as an interesting research topic by many experts and innumerable methods to encrypt images have emerged, currently, the focus is on obtaining optimized images. The paper presents a novel image encryption scheme that uses intertwining logistic map (ILM), DNA encoding and DE optimization. The proposed approach is based on three phases: permutation involving ILM, diffusion engaging DNA and optimization using DE. Parameters like entropy, key sensitivity, secret key space, unified average change in intensity (UACI), correlation coefficient —vertical, horizontal and diagonal, and number of pixel change rate have been evaluated to test the efficiency of the proposed method. The paper also compares this performance with that of the genetic algorithms (GA), used previously for optimization. The significance of this approach is enhancing entropy, the essential characteristic of randomness, resisting against numerous statistical and differential attacks and generating good experimental results. The main contribution of this paper is to present the efficiency of DE in image optimization and exhibit how DE is better than GA.

## Keywords

ILM DE DNA Image encryption## Notes

### Compliance with ethical standards

### Conflict of interest

All the authors declare that the submitted manuscript and the authors do not have any conflict of interest.

## References

- Abdullah AH, Enayatifar R, Lee M (2012) A hybrid genetic algorithm and chaotic function model for image encryption. AEU Int J Electron Commun 66(10):806–816CrossRefGoogle Scholar
- Adleman LM (1994) Molecular computation of solutions to combinatorial problems. Science 266(5187):1021–1024CrossRefGoogle Scholar
- Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurc Chaos 6(8):2129–2151MathSciNetzbMATHCrossRefGoogle Scholar
- Bisht A, Jaroli P, Dua M, Dua S (2018) Symmetric multiple image encryption using multiple new one-dimensional chaotic functions and two-dimensional cat map. In: IEEE international conference on inventive research in computing applications (ICIRCA). Coimbatore, pp 676–682Google Scholar
- Bisht A, Dua M, Dua S (2019a) A novel approach to encrypt multiple images using multiple chaotic maps and chaotic discrete fractional random transform. J Ambient Intell Hum Comput 10(9):3519–3531CrossRefGoogle Scholar
- Bisht A, Dua M, Dua S, Jaroli P (2019) A color image encryption technique based on bit-level permutation and alternate logistic maps. J Intell SystGoogle Scholar
- Chen G, Mao Y, Chui CK (2004) A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solitons Fractals 21(3):749–761MathSciNetzbMATHCrossRefGoogle Scholar
- Chen J, Zhou J, Wong K (2011) A modified chaos-based joint compression and encryption scheme. IEEE Trans Circuits Syst II Express Briefs 58(2):110–114CrossRefGoogle Scholar
- Chen Y-Y, Hsia C-H, Jhong S-Y, Lin H-J (2018) Data hiding method for AMBTC compressed images. J Ambient Intell Hum Comput 208:1–9Google Scholar
- Enayatifar R, Abdullah AH, Isnin IF (2014) Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence. Opt Lasers Eng 56:83–93CrossRefGoogle Scholar
- Enayatifar R, Sadaei HJ, Abdullah AH, Lee M, Isnin IF (2015) A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata. Opt Lasers Eng 71:33–41CrossRefGoogle Scholar
- Enayatifar R, Abdullah AH, Isnin IF, Altameem A, Lee M (2017) Image encryption using a synchronous permutation-diffusion technique. Opt Lasers Eng 90:146–154CrossRefGoogle Scholar
- Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurc Chaos 8(6):1259–1284MathSciNetzbMATHCrossRefGoogle Scholar
- Gómez J, Dasgupta D, González F (2003) Using adaptive operators in genetic search. In: Genetic and evolutionary computation conference, 2724, pp 1580–1581Google Scholar
- Guesmi R, Farah M, Kachouri A, Samet M (2016) A novel chaos-based image encryption using DNA sequence operation and secure hash algorithm SHA-2. Nonlinear Dyn 83(3):1123–1136MathSciNetzbMATHCrossRefGoogle Scholar
- Head T, Rozenberg G, Bladergroen R, Breek C, Lommerse P, Spaink H (2000) Computing with DNA by operating on plasmids. Biosystems 57(2):87–93CrossRefGoogle Scholar
- Ilonen J, Kamarainen J-K, Lampinen J (2003) Differential evolution training algorithm for feed-forward neural networks. Neural Process Lett 17(1):93–105CrossRefGoogle Scholar
- Jaroli P, Dua AB, Dua S (2018) A color image encryption using four dimensional differential equations and arnold chaotic map. In: IEEE international conference on inventive research in computing applications (ICIRCA). Coimbatore, pp 869–876Google Scholar
- Joshi R, Sanderson A (1999) Minimal representation multisensor fusion using differential evolution. IEEE Trans Syst Man Cybern Part A Syst Hum 29(1):63–76CrossRefGoogle Scholar
- Julstrom BA (1995) What have you done for me lately? Adapting operator probabilities in a steady-state genetic algorithm. In: 6th international conference on genetic algorithm (ICGA). CINII, pp 81–87Google Scholar
- Khade PN, Narnaware PM (2012) 3D chaotic functions for image encryption. IJCSI Int J Comput Sci Issues 9(3):1–6Google Scholar
- Khan JS, Rehman AU, Ahmad J, Habib Z (2015) A new chaos-based secure image encryption scheme using multiple substitution boxes. In: Conference on information assurance and cyber security (CIACS), pp 16–21Google Scholar
- Khan FA, Ahmed J, Khan JS, Ahmad JC, Khan MA (2017) A novel image encryption based on Lorenz equation, Gingerbreadman chaotic map and S8 permutation. J Intell Fuzzy Syst 33(6):3753–3765CrossRefGoogle Scholar
- Kumar M, Kumar S, Budhiraja R, Das MK, Singh S (2016) Intertwining logistic map and cellular automata based color image encryption model. In: IEEE international conference on computational techniques in information and communication technologies (ICCTICT). New Delhi, pp 618–623Google Scholar
- Li S, Chen G, Cheung A, Bhargava B, Lo K (2007) On the design of perceptual mpeg-video encryption algorithms. IEEE Trans Circ Syst Video Technol 17(2):214–223CrossRefGoogle Scholar
- Liu H, Wang X (2010) Color image encryption based on one-time keys and robust chaotic maps. Comput Math Appl 59(10):3320–3327MathSciNetzbMATHCrossRefGoogle Scholar
- Liu H, Wang X (2011) Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt Commun 284(16–17):3895–3903CrossRefGoogle Scholar
- Liu H, Wang X, Kadir A (2012a) Image encryption using DNA complementary rule and chaotic maps. Appl Soft Comput 12(5):1457–1466CrossRefGoogle Scholar
- Liu L, Zhang Q, Wei X (2012b) A RGB image encryption algorithm based on DNA encoding and chaos map. Comput Electr Eng 38(5):1240–1248CrossRefGoogle Scholar
- Masuda N, Jakimoski G, Aihara K, Kocarev L (2006) Chaotic block ciphers: from theory to practical algorithms. IEEE Trans Circuits Syst I Regul Pap 53(6):1341–1352MathSciNetzbMATHCrossRefGoogle Scholar
- Ott E, Grebogi C, Yorke JA (1990) Controlling chaos. Phys Rev Lett:2837MathSciNetzbMATHCrossRefGoogle Scholar
- Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417CrossRefGoogle Scholar
- Rhouma R, Safya B (2008) Cryptanalysis of a new image encryption algorithm based on hyper-chaos. Phys Lett A 372(38):5973–5978zbMATHCrossRefGoogle Scholar
- Sneha PS, Sankar S, Kumar AS (2019) A chaotic colour image encryption scheme combining Walsh-Hadamard transform and Arnold-Tent maps. J Ambient Intell Hum Comput 2019:1–20Google Scholar
- Solak E, Çokal C (2011) Algebraic break of image ciphers based on discretized chaotic map lattices. Inf Sci 181(1):227–233MathSciNetCrossRefGoogle Scholar
- Solak E, Çokal C, Yildiz OT, Biyikoglu T (2010) Cryptanalysis of fridrich’s chaotic image encryption. Int J Bifurc Chaos 20(5):1405–1413MathSciNetzbMATHCrossRefGoogle Scholar
- Storn R (1995) Differrential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report, International Computer Science Institute 11Google Scholar
- Storn R (1996) On the usage of differential evolution for function optimization. In: Proceedings of North American fuzzy information processing, pp 519–523Google Scholar
- Suneja K, Dua S, Dua M (2019) A review of chaos based image encryption. In: IEEE 3rd international conference on computing methodologies and communication (ICCMC). Erode, pp 693–698Google Scholar
- Suri S, Vijay R (2017) A bi-objective genetic algorithm optimization of chaos-DNA based hybrid approach. J Intell Syst 28(2):333–346CrossRefGoogle Scholar
- Suri S, Vijay R (2019) A synchronous intertwining logistic map-DNA approach for color image encryption. J Ambient Intell Hum Comput 10(6):2277–2290CrossRefGoogle Scholar
- Tuson A, Ross P (1998) Adapting operator settings in genetic algorithms. Evol Comput 6(2):161–184CrossRefGoogle Scholar
- Wang l, Luan D (2013) A novel image encryption algorithm using chaos and reversible cellular automata. Commun Nonlinear Sci Numer Simul 18(11):3075–3085MathSciNetzbMATHCrossRefGoogle Scholar
- Wang X, Xu D (2014) Image encryption using genetic operators and intertwining logistic map. Nonlinear Dyn 78(4):2975–2984MathSciNetCrossRefGoogle Scholar
- Wang X-Y, Yang L, Liu R, Kadir A (2010) A chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn 62(3):615–621MathSciNetzbMATHCrossRefGoogle Scholar
- Wang X, Teng L, Qin X (2012) A novel colour image encryption algorithm based on chaos. Signal Process 92(4):1101–1108MathSciNetCrossRefGoogle Scholar
- Wang X, Liu L, Zhang Y (2015a) A novel chaotic block image encryption algorithm based on dynamic random growth technique. Opt Lasers Eng 66:10–18CrossRefGoogle Scholar
- Wang X-Y, Gu S-X, Zhang Y-Q (2015b) Novel image encryption algorithm based on cycle shift and chaotic system. Opt Lasers Eng 68:126–134CrossRefGoogle Scholar
- Wang X-Y, Zhang Y-Q, Bao X-M (2015c) A novel chaotic image encryption scheme using DNA sequence operations. Opt Lasers Eng 73:53–61CrossRefGoogle Scholar
- Wang X, Feng L, Zhao H (2019) Fast image encryption algorithm based on parallel computing system. Inf Sci 486:340–358CrossRefGoogle Scholar
- Xiao G, Lu M, Lai XQ (2006) New field of cryptography: DNA cryptography. Chin Sci Bull 51(12):1413–1420MathSciNetzbMATHCrossRefGoogle Scholar
- Zhang Y (2015) Cryptanalysis of a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Optik 126(2):223–229CrossRefGoogle Scholar
- Zhang Y, Fu LH (2012) Research on DNA cryptography. In: Sen J (ed) Applied cryptography and network security. Rijeka, Intechopen, pp 357–376Google Scholar
- Zhang Y-Q, Wang X-Y (2014) A symmetric image encryption algorithm based on mixed linear–nonlinear coupled map lattice. Inf Sci 273:329–351CrossRefGoogle Scholar
- Zhang Y-Q, Wang X-Y (2015) A new image encryption algorithm based on non-adjacent coupled map lattices. Appl Soft Comput 26:10–20CrossRefGoogle Scholar
- Zhang Q, Guo L, Wei X (2010a) Image encryption using DNA addition combining with chaotic maps. Math Comput Model 52(11–12):2028–2035MathSciNetzbMATHCrossRefGoogle Scholar
- Zhang Q, Wang Q, Wei X (2010b) A novel image encryption scheme based on dna coding and multi-chaotic maps. Adv Sci Lett 3(4):447–451CrossRefGoogle Scholar
- Zhang Y, Li C, Li Q, Zhang D, Shu S (2012) Breaking a chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn 69(3):1091–1096MathSciNetzbMATHCrossRefGoogle Scholar
- Zhang Q, Guo L, Wei X (2013) A novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Optik Int J Light Electron Opt 124(18):3596–3600CrossRefGoogle Scholar
- Zhang Y-Q, Wang X-Y, Liu J, Chi Z-L (2016) An image encryption scheme based on the MLNCML system using DNA sequences. Opt Lasers Eng 82:95–103CrossRefGoogle Scholar
- Zheng X, Xu J, Li W (2009) Parallel DNA arithmetic operation based on n-moduli set. Appl Math Comput 212(1):177–184MathSciNetzbMATHGoogle Scholar