Paper title: Novel Crypting Methods Based on Singular Values Decomposition
Published in: Issue 2, (Vol. 10) / 2016Download
Publishing date: 2016-10-20
Pages: 15-20
Author(s): HOUAS Amrane, SOUALHI Sara, MOKHTARI Zouhir
Abstract. With the rapid development of multimedia exchanges, it is necessary to dispose secure systems to protect data and ensure the security of transfer. Two encryption schemes are proposed in this letter where the second is obtained by a simple modification on the first. The construction of the proposed schemes is based on the Singular Values Decomposition (SVD) which allows us to compress data by liminating a number of singular values. So by these schemes instead to send an encrypted image, we send a set of three or six encrypting images. Both of schemes are applied on (PNG) images in different levels and their efficiency is tested by calculating MSE, NPSR and MAE. Numerical results and the reconstructed images are discussed.
Keywords: Cryptography, Compression, Singular Values Decomposition, Attaks

1. Alfalou, Ayman, and al. "Simultaneous fusion, compression, and encryption of multiple images." Optics express 19.24 (2011): 24023-24029.

2. Cheng-Chi, and al. "A new visual cryptography with multi-level encoding." Journal of Visual Languages & Computing 25.3 (2014): 243-250.

3. Kıymaz, Onur, and Şeref Mirasyedioğlu. "A new symbolic computational approach to singular initial value problems in the second-order ordinary differential equations." Applied mathematics and computation 171.2 (2005): 1218-1225.

4. Le Bihan, Nicolas, and Stephen J. Sangwine. "Jacobi method for quaternion matrix singular value decomposition." Applied mathematics and computation 187.2 (2007): 1265-1271.

5. Mohamed, Faraoun Kamel. "A parallel block-based encryption schema for digital images using reversible cellular automata." Engineering Science and Technology, an International Journal 17.2 (2014): 85-94.

6. Mokhtari, Zouhir, and Khaled Melkemi. "A New Watermarking Algorithm Based on Entropy Concept." Acta applicandae mathematicae 116.1 (2011): 65-69.

7. Naor, Moni, and Adi Shamir. "Visual cryptography." Advances in Cryptology—EUROCRYPT'94. Springer Berlin Heidelberg, 1995. 5. Cheng-Chi Lee, Hong-Hao Chen, Lee,

8. Naor, Moni, and Adi Shamir. "Visual cryptography II: Improving the contrast via the cover base." Security protocols. Springer Berlin Heidelberg, 1997.

9. Rufai, Awwal Mohammed, Gholamreza Anbarjafari, and Hasan Demirel. "Lossy image compression using singular value decomposition and wavelet difference reduction." Digital Signal Processing 24 (2014): 117-123.

10. Sahlan, M. Nosrati, and E. Hashemizadeh. "Wavelet Galerkin method for solving nonlinear singular boundary value problems arising in physiology." Applied Mathematics and Computation 250 (2015): 260-269.

11. Shih, Y-T., C-S. Chien, and C-Y. Chuang. "An adaptive parameterized block-based singular value decomposition for image de-noising and compression." Applied Mathematics and Computation 218.21 (2012): 10370-10385.

12. Wazwaz, Abdul-Majid. "A new method for solving singular initial value problems in the second-order ordinary differential equations." Applied Mathematics and Computation 128.1 (2002): 45-57.

13. Yadani, Kenichi, Koichi Kondo, and Masashi Iwasaki. "A singular value decomposition algorithm based on solving hyperplane constrained nonlinear systems." Applied Mathematics and Computation 216.3 (2010): 779-790.

Back to the journal content
Creative Commons License
This article is licensed under a
Creative Commons Attribution-ShareAlike 4.0 International License.
Home | Editorial Board | Author info | Archive | Contact
Copyright JACSM 2007-2020