Abstract
A new image encryption and decryption algorithm based on chaotic map and dynatomic modular curve is proposed in this paper. Firstly, the definition of dynatomic modular curve and its periodic points are introduced, and a property of the dynatomic modular curve is proved. Secondly, the relationship between the Logistic map and the dynatomic modular curve is discussed. Finally, the encryption algorithm which is composed of permutation of pixels and substitution is given. In order to eliminate sufficiently the relation between adjacent pixels in the image, pixel values of the original image are sorted as index function, which derives from Logistic map and dynatomic modular curve. And XOR operation is performed between the scrambled pixel sequence and projective transformation sequence. Simulation experiments and nonparametric hypothesis test demonstrate that the proposed algorithm is secure to resist different types of attacks and it can be applied to real-time encryption.
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References
Chen G, Mao YB, Chui CK (2004) A sysmmetric image encryption scheme based on 3D chaotic cat maps. Chaos, Solution & Fractals 12:749–761
Chen WH, Luo S, Zheng WX (2016) Impulsive synchronization of reaction-diffusion neural networks with mixed delays and its application to image encryption. IEEE Transactions on Neural Networks and Learning Systems 33(1):300–303
Chhotaray A, Biswas S, Chhotaray SK, Rath GS (2015) An image encryption technique using orthonormal matrices and chaotic maps. Proceeding of 3rd International conference on advanced computing. Networking and Informatics 9(44):355–362
Cong-Xu Z, Ke-Hui S (2012) Cryptanalysis and improvement of a class of hyper-chaos based image encryption algorithms. Acta Phys Sin 61(12):1–12
Fu Z, Sun X, Liu Q, Zhou L, Shu J (2015) Achieving efficient cloud Search services: multi-keyword ranked Search over encrypted cloud data supporting Parallel computing. IEICE Trans Commun E98-B(1):190–200
R. Hartshorne (1977) Algebraic geometry. Springer-Verlag, New York. GraduateTexts in Mathematics, 52
Hua T, Chen J, Pei D, Zhang W, Zhou N (2015) Quantum image encryption algorithm based on image correlation decomposition. Int J Theor Phys 54:526–537
Huang X (2012) Image encryption algorithm using chaotic chebyshev generator. Nonlinear Dyn 67:2411–2417
Huang CK, Liao CW, Hsu SL, Jeng YC (2013) Implementation of gray image encryption with pixel shuffling and gray-level encryption by single chaotic system. Telecommun Systems 52(2):563–571
Kamara S, Lauter K (2010) Cryptographic cloud storage. In: Financial cryptography and data security. Springer. pp. 136–149
Kwok HS, Tang WKS (2007) A fast image encryption system based on chaotic maps with finite precision representation. Chaos, Solution & Fractals 32:1518–1529
Li S, Zheng X (2002) Cryptanalysis of a chaotic image encryption method. Proceedings of the IEEE International Conference on Circuits and Systems 2:708–711
Lin T, Xingyuan W (2012) A bit-level image encryption algorithm based on spatiotemporal chaotic system and self-adaptive. Opt Commun 2012:940276
Liu L, Miao S (2016) A new image encryption algorithm based on logistic chaotic map with varying parameter. Spring 5(1):1–12
Liu H, Wang X (2010) Color image encryption based on onetime keys and robust chaotic maps. Comput Math Appl 59(10):3320–3327
Manjunath Prasad, K.L. Sudha (2011) Chaos image encryption using pixel shuffling. Computer Science & Information Technology 1(12):169–179
Parvin Z, Seyedarabi H, Shamsi M (2016) A new secure and sensitive image encryption scheme based on new substitution with chaotic function. Multimedia Tools and Applications 75(17):10631–10648
Qin C, Zhang X (2015) Reversible data hiding in encrypted image with privacy protection for image content. J Vis Commun Image Represent 31:154–164
Qin C, Chang C-C, Chiu Y-P (2014) A novel joint data-hiding and compression scheme based on SMVQ and image Inpainting. IEEE Trans Image Process 23(3):969–978
Rajput AS, Sharma M (2015) A novel image encryption and authentication scheme using chaotic maps. Advances in intelligent informatics. Springer International Publishing Switzerland 26:277–286
Sharath Kumar HS, Panduranga HT, Naveen Kumar SK (2013) A two stage combinational approach for image encryption. Advances in Computing & Information Technology.Conference paper (AISC,volume 177):843–849
Joseph H. Silverman (2007) The arithmetic of dynamical systems. Springer Science + Business Media, LLC.148–158
Sivakumar T, Venkatesan R (2016) A new image encryption method based on Knight’s travel path and true random number. Journal of Information Science and Engineering, Jan 32(1):133–152
Wang X-Y, Feng C, Tian W (2009) A new compound mode of confusion and diffusion for block encryption of image based on chaos. Commun Nonlinear Sci Numer Simul 15(9):2479–2485
Wang H, Xu J-P, Sheng X-S, Zan P (2014) Discrete chaotic synchronization and It’s application in image encryption. LSMS/ICSEE2014, part 2. CCIS 462:264–272
Xia Z, Wang X, Sun X, Wang Q (2016) A secure and dynamic multi-keyword ranked Search scheme over encrypted cloud data. IEEE Transactions On Parallel And Distributed Systems 27(2):340–352
Ye G, Wong K-W (2012) An efficient chaotic image encryption algorithm based on a generalized Arnold map. Nonlinear Dyn 69:2079–2087
Yuan H-M, Liu Y, Gong L-H, Wang J (2017) A new image cryptosystem based on 2D hyper-chaotic system. Multimedia Tools and Applications 76(6):8087–8108
Zhang S, Gao T (2016) An image encryption scheme based on DNA coding and permutation of hyper-image. Multimedia Tools and Applications 75(24):17157–17170
Zhang Q, Xue X, Wei X (2012) A novel image encryption algorithm based on DNA subsequence operation. Sci World J 2012:286741
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This work was supported by the National Key Research and Development Program of China 2016YFB0800601.
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Li, B., Liao, X. & Jiang, Y. A novel image encryption scheme based on logistic map and dynatomic modular curve. Multimed Tools Appl 77, 8911–8938 (2018). https://doi.org/10.1007/s11042-017-4786-7
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DOI: https://doi.org/10.1007/s11042-017-4786-7