A Novel Parallelizable Chaotic Image Encryption Scheme Based on Elliptic Curves

Most of the computational time in many chaotic image encryption schemes is spent generating the required chaotic sequences. Since chaotic systems are defined by recurrence relations, they are often generated sequentially. In this paper, we propose a chaotic image encryption scheme which enables pixel-level parallelism to boost the computational speed of generating chaotic sequences. We use a group defined over elliptic curve (EC) points and the addition operator to generate a discrete chaotic sequence and use it to construct an image encryption scheme. The proposed scheme is designed such that encryption and decryption operations are highly parallelizable to take advantage of readily available parallel processing platforms such as GPU acceleration, DSPs and multi-core CPUs. Complexity analysis indicates that the proposed scheme is more efficient than existing EC-based image encryption schemes. Practical experiments on a quad-core CPU show that the proposed scheme can achieve a speedup of 3.93, confirming its superior parallelization efficiency in comparison with existing parallel image encryption schemes. We also provide detailed analysis of the immunity of the proposed scheme to all common cryptanalysis attacks. Results reveal that the proposed technique shows promising performance in terms of security and efficiency.

[1]  I. Pehlivan,et al.  Secure image encryption algorithm design using a novel chaos based S-Box , 2017 .

[2]  Juliano B. Lima,et al.  Encryption of medical images based on the cosine number transform , 2015, Signal Process. Image Commun..

[3]  Jiahui Liu,et al.  A parallel encryption algorithm of the logistic map for multicore with OpenMP , 2013, Ifost.

[4]  Igor E. Shparlinski,et al.  On the Uniformity of Distribution of Congruential Generators over Elliptic Curves , 2001, SETA.

[5]  Xiaofeng Liao,et al.  Color image encryption based on chaotic systems and elliptic curve ElGamal scheme , 2017, Signal Process..

[6]  Yu Zheng,et al.  A novel batch image encryption algorithm using parallel computing , 2020, Inf. Sci..

[7]  Tao Xiang,et al.  Parallel image encryption algorithm based on discretized chaotic map , 2008 .

[8]  Cecilio Pimentel,et al.  Image encryption using block cipher and chaotic sequences , 2019, Signal Process. Image Commun..

[9]  Azman Samsudin,et al.  A new hybrid digital chaotic system with applications in image encryption , 2019, Signal Process..

[10]  Tariq Shah,et al.  A novel scheme for image encryption using substitution box and chaotic system , 2017 .

[11]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

[12]  Zhongmeng Zhao,et al.  Efficient image encryption scheme with synchronous substitution and diffusion based on double S-boxes , 2018, Chinese Physics B.

[13]  Wei Xiang,et al.  Novel Medical Image Encryption Scheme Based on Chaos and DNA Encoding , 2019, IEEE Access.

[14]  Ahmed Gomaa Radwan,et al.  A novel image encryption system merging fractional-order edge detection and generalized chaotic maps , 2020, Signal Process..

[15]  Dariusz Burak,et al.  Parallelization of Image Encryption Algorithm Based on Game of Life and Chaotic System , 2017, ICAISC.

[16]  Elaine B. Barker,et al.  Recommendation for key management: , 2019 .

[17]  T. Lange,et al.  Certain Exponential Sums and Random Walks on Elliptic Curves , 2005, Canadian Journal of Mathematics.

[18]  Amany Sarhan,et al.  Parallel approaches to improve the speed of chaotic-maps-based encryption using GPU , 2021, Journal of Real-Time Image Processing.

[19]  Burton S. Kaliski,et al.  A Pseudo-Random Bit Generator Based on Elliptic Logarithms , 1986, CRYPTO.

[20]  Hossein Nezamabadi-pour,et al.  A novel parallel image encryption with chaotic windows based on logistic map , 2017, Comput. Electr. Eng..

[21]  P. L. Montgomery.  Speeding the Pollard and elliptic curve methods of factorization , 1987 .

[22]  Rozmie R. Othman,et al.  A new image encryption technique combining Elliptic Curve Cryptosystem with Hill Cipher , 2017, J. King Saud Univ. Comput. Inf. Sci..

[23]  Guangyi Wang,et al.  A novel parallel image encryption algorithm based on hybrid chaotic maps with OpenCL implementation , 2020, Soft Computing.

[24]  Khumanthem Manglem Singh,et al.  A robust image encryption scheme based on chaotic system and elliptic curve over finite field , 2017, Multimedia Tools and Applications.

[25]  Ghulam Muhammad,et al.  Framework for Efficient Medical Image Encryption Using Dynamic S-Boxes and Chaotic Maps , 2020, IEEE Access.

[26]  Elaine B. Barker.  Recommendation for Key Management, Part 1: General , 2016 .

[27]  Hejiao Huang,et al.  Image Encryption Using Josephus Problem and Filtering Diffusion , 2019, IEEE Access.

[28]  Sean Hallgren,et al.  Linear Congruential Generators Over Elliptic Curves , 2001 .

[29]  Hegui Zhu,et al.  2D Logistic-Modulated-Sine-Coupling-Logistic Chaotic Map for Image Encryption , 2019, IEEE Access.

[30]  Xiaojuan Zhang,et al.  Parallel Image Encryption Technology Based on Cellular Automaton , 2020, 2020 IEEE Sixth International Conference on Big Data Computing Service and Applications (BigDataService).

[31]  Ayman Alharbi,et al.  Efficient Image Encryption Scheme Using Henon Map, Dynamic S-Boxes and Elliptic Curve Cryptography , 2020, IEEE Access.

[32]  Safya Belghith,et al.  A novel image encryption scheme based on substitution-permutation network and chaos , 2016, Signal Process..

[33]  Robert A. J. Matthews,et al.  On the Derivation of a "Chaotic" Encryption Algorithm , 1989, Cryptologia.

[34]  Zhongmeng Zhao,et al.  An efficient chaotic image encryption based on alternate circular S-boxes , 2014, Nonlinear Dynamics.

[35]  Dolendro Singh Laiphrakpam,et al.  Medical image encryption based on improved ElGamal encryption technique , 2017 .

[36]  Yushu Zhang,et al.  Medical image encryption algorithm based on Latin square and memristive chaotic system , 2019, Multimedia Tools and Applications.

[37]  Berry Schoenmakers,et al.  Cryptanalysis of the Dual Elliptic Curve Pseudorandom Generator , 2006, IACR Cryptol. ePrint Arch..

[38]  Saeed Mozaffari,et al.  Parallel image encryption with bitplane decomposition and genetic algorithm , 2018, Multimedia Tools and Applications.

[39]  Sezgin Kaçar,et al.  A novel parallel image encryption algorithm based on chaos , 2019, Cluster Computing.

[40]  Shahryar Toughi,et al.  An image encryption scheme based on elliptic curve pseudo random and Advanced Encryption System , 2017, Signal Process..

[41]  Fatih Özkaynak,et al.  An Image Encryption Algorithm Based on Chaotic Selection of Robust Cryptographic Primitives , 2020, IEEE Access.

[42]  Mohammad-Reza Feizi-Derakhshi,et al.  A novel image encryption algorithm based on polynomial combination of chaotic maps and dynamic function generation , 2019, Signal Process..

[43]  Kwok-Wo Wong,et al.  A random number generator based on elliptic curve operations , 2004 .

[44]  Tariq Shah,et al.  Generalized Majority Logic Criterion to Analyze the Statistical Strength of S-Boxes , 2012 .

[45]  Yicong Zhou,et al.  Cosine-transform-based chaotic system for image encryption , 2019, Inf. Sci..

[46]  Xue Ouyang,et al.  An Image Encryption Method Based on Elliptic Curve Elgamal Encryption and Chaotic Systems , 2019, IEEE Access.

[47]  Naveed Ahmed Azam,et al.  A novel image encryption scheme based on an elliptic curve , 2019, Signal Process..

[48]  Xuesong Wang,et al.  Digital Image Encryption Algorithm Based on Elliptic Curve Public Cryptosystem , 2018, IEEE Access.

[49]  Hongyu Zhao,et al.  Fast image encryption algorithm based on parallel computing system , 2019, Inf. Sci..

[50]  Alfred Menezes,et al.  Guide to Elliptic Curve Cryptography , 2004, Springer Professional Computing.

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

[52]  Saleh Ibrahim,et al.  Efficient key-dependent dynamic S-boxes based on permutated elliptic curves , 2021, Inf. Sci..

[53]  Guangchun Luo,et al.  A parallel image encryption algorithm based on chaotic Duffing oscillators , 2017, Multimedia Tools and Applications.

[54]  Dariusz Burak,et al.  Parallelization of Image Encryption Algorithm Based On Chaotic Neural Networks , 2016, ICAISC.

[55]  Yi Cao,et al.  A parallel image encryption algorithm based on the piecewise linear chaotic map and hyper-chaotic map , 2018, Nonlinear Dynamics.

[56]  Xing-yuan Wang,et al.  Cryptanalysis of a parallel sub-image encryption method with high-dimensional chaos , 2013, Nonlinear Dynamics.

[57]  Akif Akgul,et al.  S-Box Based Image Encryption Application Using a Chaotic System without Equilibrium , 2019, Applied Sciences.

[58]  Ruisong Ye,et al.  Cryptanalysis and improvement of medical image encryption using high-speed scrambling and pixel adaptive diffusion , 2020, Signal Process..

[59]  Xingyuan Wang,et al.  Fast image encryption algorithm based on parallel permutation-and-diffusion strategy , 2020, Multimedia Tools and Applications.