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Math. Comput. Appl. 2017, 22(2), 28; doi:10.3390/mca22020028

An Algorithm Based on GSVD for Image Encryption

Department of Islamic Education, University of Kufa, 31001 Al-Najaf, Iraq
Department of Mathematics, University of Kufa, 31001 Al-Najaf, Iraq
Department of Computer Science, University of Kufa, 31001 Al-Najaf, Iraq
Authors to whom correspondence should be addressed.
Received: 28 January 2017 / Revised: 10 March 2017 / Accepted: 17 March 2017 / Published: 28 March 2017
Download PDF [327 KB, uploaded 28 March 2017]


This paper represents a new image encryption algorithm based on modifying generalized singular value decomposition (GSVD) by decomposing the plain-image into two segments using GSVD with an exchanged key-image to produce the cipher-image. The exchanged key-image is used as an encrypting and decrypting image. Mathematically, this procedure is represented by transforming the plain-image’s matrix into two different matrices and applying the GSVD with the exchanged key-image’s matrix to obtain the cipher-image’s matrix. The two encoded segments can be kept in several places or assigned to a group of authorized persons. No one can obtain the information of the image easily without the knowledge of the decrypting key. This proposed algorithm is represented as one of the digital image encryption techniques used to enhance the security of images that have been sent between recipients.
Keywords: encryption; singular value decomposition; generalized singular value decomposition; image encryption encryption; singular value decomposition; generalized singular value decomposition; image encryption
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Al-Kufi, M.A.H.J.; Hashim, H.R.; Hussein, A.M.; Mohammed, H.R. An Algorithm Based on GSVD for Image Encryption. Math. Comput. Appl. 2017, 22, 28.

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