Image Encryption Algorithm Based on a Chaotic Iterative Process

Affiliation(s)

Group for Automatic Mesh Generation and Advanced Methods, Gamma3 Project (UTT-INRIA), University of.

Network & Information Security, Ecole Supérieure d’Informatique, Electronique, Automatique.

Group for Automatic Mesh Generation and Advanced Methods, Gamma3 Project (UTT-INRIA), University of.

Network & Information Security, Ecole Supérieure d’Informatique, Electronique, Automatique.

ABSTRACT

The paper describes a symmetric encryption algorithm based on bit permutations and using an iterative process combined with a chaotic function. The main advantages of such a cryptosystem is its ability to encrypt securely bit sequences and assuring confusion, diffusion and indistinguishability properties in the cipher. The algorithm is applied on the image encryption where the plain-image is viewed as binary sequence. The results of statistical analysis about randomness, sensitivity and correlation on the cipher-images show the relevance of the proposed cryptosystem.

The paper describes a symmetric encryption algorithm based on bit permutations and using an iterative process combined with a chaotic function. The main advantages of such a cryptosystem is its ability to encrypt securely bit sequences and assuring confusion, diffusion and indistinguishability properties in the cipher. The algorithm is applied on the image encryption where the plain-image is viewed as binary sequence. The results of statistical analysis about randomness, sensitivity and correlation on the cipher-images show the relevance of the proposed cryptosystem.

Cite this paper

M. François, T. Grosges, D. Barchiesi and R. Erra, "Image Encryption Algorithm Based on a Chaotic Iterative Process,"*Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 1910-1920. doi: 10.4236/am.2012.312262.

M. François, T. Grosges, D. Barchiesi and R. Erra, "Image Encryption Algorithm Based on a Chaotic Iterative Process,"

References

[1] R. L. Rivest, A. Shamir and L. Adleman, “A Method for Obtaining Digital Signatures and Public-Key Cryptosystems,” Communication ACM, Vol. 21, No. 2, 1978, pp. 120-126. doi:10.1145/359340.359342

[2] B. Schneier and P. Sutherland, “Applied Cryptography: Protocols, Algorithms, and Source Code in C,” John Wiley & Sons, Inc., Hoboken, 1995.

[3] NIST, “Announcing the Advanced Encryption Standard (AES),” 2001. http://csrc.nist.gov/CryptoToolkit/aes/

[4] C. C. Chang, M. S. Hwang and T. S. Chen, “A New Encryption Algorithm for Image Cryptosystems,” Journal of Systems and Software, Vol. 58, No. 2, 2001, pp. 83-91. doi:10.1016/S0164-1212(01)00029-2

[5] G. Chen, Y. Mao and C. K. Chui, “A Symmetric Image Encryption Scheme Based on 3D Chaotic Cat Maps,” Chaos Solitons and Fractals, Vol. 21, No. 3, 2004, pp. 749-761. doi:10.1016/j.chaos.2003.12.022

[6] Z. Zhu, W. Zhang, K. Wong and H. Yu, “A Chaos-Based Symmetric Image Encryption Scheme Using a Bit-Level Permutation,” Information Sciences, Vol. 181, No. 6, 2011, pp. 1171-1186. doi:10.1016/j.ins.2010.11.009

[7] N. K. Pareek, V. Patidar and K. K Sud, “Image Encryption Using Chaotic Logistic Map, Image and Vision Computing,” Vol. 24, No. 9, 2006, pp. 926-934. doi:10.1016/j.imavis.2006.02.021

[8] Y. Wang, K. W. Wong, X. Liao, T. Xiang and G. Chen, “A Chaos-Based Image Encryption Algorithm with Variable Control Parameters,” Chaos Solitons and Fractals, Vol. 41, No. 4, 2009, pp. 1773-1783. doi:10.1016/j.chaos.2008.07.031

[9] A. K. Acharya, “Image Encryption Using a New Chaos Based Encryption Algorithm,” Proceedings of the International Conference on Communication, Computing and Security, New York, 12-14 February 2011, pp. 577-581. doi:10.1145/1947940.1948060

[10] A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray and S. Vo, “Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications,” Special Publication 800-22 Revision 1a, National Institute of Standards and Technology, 2010.

[11] Y. Wu, J. Noonan and S. Agaian, “Npcr and Uaci Randomness Tests for Image Encryption,” Cyber Journals: Multidisciplinary, Journals in Science and Technology, Journal of Selected Areas in Telecommunications (JSAT), 2011, pp. 31-38.

[12] G. álvarez and S. Li, “Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems,” International Journal of Bifurcation and Chaos, Vol. 16, No. 8, 2006, pp. 2129-2151.

[13] T. Gao and Z. Chen, “Image Encryption Based on a New Total Shuffling Algorithm,” Chaos, Solitons and Fractals, Vol. 38, No. 1, 2008, pp. 213-220. doi:10.1016/j.chaos.2006.11.009

[14] X. Wang and J. Zhang, “An Image Scrambling Encryption Using Chaos-Controlled Poker Shuffle Operation,” Proceedings of International Symposium on Biometrics and Security Technologies, Islamabad, 23-24 April 2008, pp. 1-6.

[1] R. L. Rivest, A. Shamir and L. Adleman, “A Method for Obtaining Digital Signatures and Public-Key Cryptosystems,” Communication ACM, Vol. 21, No. 2, 1978, pp. 120-126. doi:10.1145/359340.359342

[2] B. Schneier and P. Sutherland, “Applied Cryptography: Protocols, Algorithms, and Source Code in C,” John Wiley & Sons, Inc., Hoboken, 1995.

[3] NIST, “Announcing the Advanced Encryption Standard (AES),” 2001. http://csrc.nist.gov/CryptoToolkit/aes/

[4] C. C. Chang, M. S. Hwang and T. S. Chen, “A New Encryption Algorithm for Image Cryptosystems,” Journal of Systems and Software, Vol. 58, No. 2, 2001, pp. 83-91. doi:10.1016/S0164-1212(01)00029-2

[5] G. Chen, Y. Mao and C. K. Chui, “A Symmetric Image Encryption Scheme Based on 3D Chaotic Cat Maps,” Chaos Solitons and Fractals, Vol. 21, No. 3, 2004, pp. 749-761. doi:10.1016/j.chaos.2003.12.022

[6] Z. Zhu, W. Zhang, K. Wong and H. Yu, “A Chaos-Based Symmetric Image Encryption Scheme Using a Bit-Level Permutation,” Information Sciences, Vol. 181, No. 6, 2011, pp. 1171-1186. doi:10.1016/j.ins.2010.11.009

[7] N. K. Pareek, V. Patidar and K. K Sud, “Image Encryption Using Chaotic Logistic Map, Image and Vision Computing,” Vol. 24, No. 9, 2006, pp. 926-934. doi:10.1016/j.imavis.2006.02.021

[8] Y. Wang, K. W. Wong, X. Liao, T. Xiang and G. Chen, “A Chaos-Based Image Encryption Algorithm with Variable Control Parameters,” Chaos Solitons and Fractals, Vol. 41, No. 4, 2009, pp. 1773-1783. doi:10.1016/j.chaos.2008.07.031

[9] A. K. Acharya, “Image Encryption Using a New Chaos Based Encryption Algorithm,” Proceedings of the International Conference on Communication, Computing and Security, New York, 12-14 February 2011, pp. 577-581. doi:10.1145/1947940.1948060

[10] A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray and S. Vo, “Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications,” Special Publication 800-22 Revision 1a, National Institute of Standards and Technology, 2010.

[11] Y. Wu, J. Noonan and S. Agaian, “Npcr and Uaci Randomness Tests for Image Encryption,” Cyber Journals: Multidisciplinary, Journals in Science and Technology, Journal of Selected Areas in Telecommunications (JSAT), 2011, pp. 31-38.

[12] G. álvarez and S. Li, “Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems,” International Journal of Bifurcation and Chaos, Vol. 16, No. 8, 2006, pp. 2129-2151.

[13] T. Gao and Z. Chen, “Image Encryption Based on a New Total Shuffling Algorithm,” Chaos, Solitons and Fractals, Vol. 38, No. 1, 2008, pp. 213-220. doi:10.1016/j.chaos.2006.11.009

[14] X. Wang and J. Zhang, “An Image Scrambling Encryption Using Chaos-Controlled Poker Shuffle Operation,” Proceedings of International Symposium on Biometrics and Security Technologies, Islamabad, 23-24 April 2008, pp. 1-6.