Breaking an image encryption scheme based on Arnold map and Lucas series

Fairly recently, a novel image encryption based on Arnold scrambling and Lucas series has been proposed in the literature. The scheme design is based on permutation-substitution operations, where Arnold map is used to permute pixels for some T rounds, and Lucas sequence is used to mask the image and substitute pixel's values. The authors of the cryptosystem have claimed, after several statistical analyses, that their system is "with high efficiency" and resists chosen and known plaintext attacks. Negatively, in this paper we showed the opposite. The key space of the scheme under study could be reduced considerably after our equivalent keys analysis, and thus the system is breakable under reasonable brute force attack. After all, the design of the scheme has several weaknesses that make it weak against chosen and known plaintext attacks. Consequently, we do not recommend the use of this system for any cryptographic concern or security purpose.

[1]  S. Lian,et al.  Efficient image or video encryption based on spatiotemporal chaos system , 2009 .

[2]  Olivier Déforges,et al.  Cryptanalyzing an image encryption scheme using reverse 2-dimensional chaotic map and dependent diffusion , 2018, Multimedia Tools and Applications.

[3]  Rhouma Rhouma,et al.  Cryptanalysis of a spatiotemporal chaotic image/video cryptosystem , 2008 .

[4]  Xin-Wen Wu,et al.  On the Security of Permutation-Only Image Encryption Schemes , 2016, IEEE Transactions on Information Forensics and Security.

[5]  Jizhao Liu,et al.  A novel fast image encryption algorithm for embedded systems , 2019, Multimedia Tools and Applications.

[6]  Fatih Özkaynak,et al.  Analysis and improvement of a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system , 2014, Nonlinear Dynamics.

[7]  Chengqing Li,et al.  When an attacker meets a cipher-image in 2018: A Year in Review , 2019, J. Inf. Secur. Appl..

[8]  B Suresh.G.,et al.  Chaos Based Image Encryption , 2018 .

[9]  Wadii Boulila,et al.  A Novel Privacy Approach of Digital Aerial Images Based on Mersenne Twister Method with DNA Genetic Encoding and Chaos , 2020, Remote. Sens..

[10]  F. Dyson,et al.  Period of a Discrete Cat Mapping , 1992 .

[11]  Xuemin Zhang,et al.  Color image chaos encryption algorithm combining CRC and nine palace map , 2019, Multimedia Tools and Applications.

[12]  Fahad Bin Muhaya,et al.  Modified AES Using Chaotic Key Generator for Satellite Imagery Encryption , 2009, ICIC.

[13]  S. Agaian,et al.  NPCR and UACI Randomness Tests for Image Encryption , 2011 .

[14]  Jawad Ahmad,et al.  A Novel Hybrid Secure Image Encryption Based on Julia Set of Fractals and 3D Lorenz Chaotic Map , 2020, Entropy.

[15]  B. Subramanyan,et al.  Image Encryption Based on AES Key Expansion , 2011, 2011 Second International Conference on Emerging Applications of Information Technology.

[16]  Fatih Özkaynak,et al.  Brief review on application of nonlinear dynamics in image encryption , 2018, Nonlinear Dynamics.

[17]  Xin Ge,et al.  Cryptanalysis of a spatiotemporal chaotic image/video cryptosystem and its improved version , 2011 .

[18]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[19]  Nasharuddin Zainal,et al.  High Definition Image Encryption Algorithm Based on AES Modification , 2014, Wirel. Pers. Commun..

[20]  Wolfgang A. Halang,et al.  Cryptanalysis of an image encryption scheme based on a compound chaotic sequence , 2007, Image Vis. Comput..

[21]  Syeda Iram Batool,et al.  A novel image encryption scheme based on Arnold scrambling and Lucas series , 2019, Multimedia Tools and Applications.

[22]  Song Guo,et al.  A Selective Privacy-Preserving Approach for Multimedia Data , 2017, IEEE MultiMedia.

[23]  Faiq Gmira,et al.  A New Cryptosystem of Color Image Using a Dynamic-Chaos Hill Cipher Algorithm , 2019 .

[24]  Gonzalo Alvarez,et al.  Some Hints for the Design of Digital Chaos-Based Cryptosystems: Lessons Learned from Cryptanalysis , 2008, 0812.0765.

[25]  Lyle D. Broemeling,et al.  An Account of Early Statistical Inference in Arab Cryptology , 2011 .

[26]  Qiang Zhang,et al.  A novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system , 2013 .

[27]  S. Li,et al.  Cryptographic requirements for chaotic secure communications , 2003, nlin/0311039.

[28]  D. Kahn.  The codebreakers : the story of secret writing , 1968 .

[29]  Guanrong Chen,et al.  Cryptanalysis of RCES/RSES Image Encryption Scheme , 2004, IACR Cryptol. ePrint Arch..

[30]  Sankaradass Veeramalai,et al.  An efficient space filling curve based image encryption , 2018, Multimedia Tools and Applications.

[31]  Gonzalo Álvarez,et al.  Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems , 2003, Int. J. Bifurc. Chaos.

[32]  Jawad Ahmad,et al.  A Novel Secure Occupancy Monitoring Scheme Based on Multi-Chaos Mapping , 2020, Symmetry.

[33]  Khalid Satori,et al.  Benchmarking AES and chaos based logistic map for image encryption , 2013, 2013 ACS International Conference on Computer Systems and Applications (AICCSA).

[34]  Tony Crilly,et al.  The Golden Ratio and Fibonacci , 1999, The Mathematical Gazette.

[35]  Joe Nance,et al.  Periods of the discretized Arnold Cat Map and its extension to n dimensions , 2011, 1111.2984.

[36]  Yong Zhang,et al.  Security analysis of a chaos triggered image encryption scheme , 2019, Multimedia Tools and Applications.

[37]  Xiaofeng Liao,et al.  A novel robust dual diffusion/confusion encryption technique for color image based on Chaos, DNA and SHA-2 , 2018, Multimedia Tools and Applications.

[38]  Stefan Katzenbeisser,et al.  Depreciating Motivation and Empirical Security Analysis of Chaos-Based Image and Video Encryption , 2018, IEEE Transactions on Information Forensics and Security.

[39]  Shiguo Lian,et al.  Efficient video encryption scheme based on advanced video coding , 2007, Multimedia Tools and Applications.

[40]  Vladimir Igorevich Arnolʹd,et al.  Problèmes ergodiques de la mécanique classique , 1967 .

[41]  Xiaoyan Wang,et al.  Big Data Privacy Preserving in Multi-Access Edge Computing for Heterogeneous Internet of Things , 2018, IEEE Communications Magazine.

[42]  Simone Moretti,et al.  Optimisation of multimedia over wireless IP links via X-layer design: an end-to-end transmission chain simulator , 2010, Multimedia Tools and Applications.

[43]  Karl G. Larew.  The Codebreakers: The Story of Secret Writing. By David Kahn. (New York: Macmillan Company. 1967. Pp. xvi, 1164. $14.95.) , 1968 .

[44]  Mohamed Boussif,et al.  Images encryption algorithm based on the quaternion multiplication and the XOR operation , 2019, Multimedia Tools and Applications.

[45]  Haidar Raad Shakir,et al.  An image encryption method based on selective AES coding of wavelet transform and chaotic pixel shuffling , 2019, Multimedia Tools and Applications.

[46]  Kwok-Wo Wong,et al.  An image encryption scheme using reverse 2-dimensional chaotic map and dependent diffusion , 2013, Commun. Nonlinear Sci. Numer. Simul..