Digital Images Phase Encryption Using Fractional Fourier Transform

Vilardy, Juan M.; Calderon, Jorge; Torres, Cesar; Mattos, Lorenzo

doi:10.1109/cerma.2006.38

Cited by 18 publications

(8 citation statements)

References 2 publications

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“…x (2) x (13) x (3) x (12) X(4) X(5) X(6) X(7) x (4) x (11) x (5) x ( x (6) x (9) x (7) x (8) X (12) X (13) X (14) X (15) x (2) x (5) x (3) x(4) …”

Section: Discussionunclassified

“…The introduction of independent parameters in discrete transforms provides an additional important propriety. For example, the independent parameters of the generalized versions of the DFT, DHT or DCT have been used in [1] as an additional secret key for watermarking and in [2] for encryption.…”

Section: Introduction and Background Materialsmentioning

confidence: 99%

“…The wide spread use of these transforms is mainly due to their practical usefulness and the existence of efficient algorithms for their fast computation. The success of these transforms has created a huge interest for their generalizations [1], [2] in order to solve more practical problems and meet the specifications of recent applications in multimedia and telecommunications. The introduction of independent parameters in discrete transforms provides an additional important propriety.…”

Section: Introduction and Background Materialsmentioning

confidence: 99%

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A new parametric transform

Bouguezel

Ahmad

Swamy

2008

2008 2nd International Conference on Signals, Circuits and Systems

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In this paper, a novel method for the parameterization of the Hadamard matrices is proposed. The resulting parametric Hadamard matrix of order N has N/2-1 independent parameters. It is a normalized matrix and its inverse can easily be obtained by taking the reciprocal of each of the N/2-1 independent parameters in the forward matrix and transposing the resulting matrix. The corresponding transform reduces to a new parametric integer transform when the independent parameters in the proposed matrix operator are all from the set, where m, n and l are chosen positive or negative integers. Other interesting special cases of the proposed transform can also be obtained. In addition, the proposed parametric transform can be computed using an algorithm having a very simple structure. This transform can be used in many transform-based applications. For example, it can be employed in watermarking and encryption where its independent parameters can be used as an additional secret key.

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“…x (2) x (13) x (3) x (12) X(4) X(5) X(6) X(7) x (4) x (11) x (5) x ( x (6) x (9) x (7) x (8) X (12) X (13) X (14) X (15) x (2) x (5) x (3) x(4) …”

Section: Discussionunclassified

Section: Introduction and Background Materialsmentioning

confidence: 99%

Section: Introduction and Background Materialsmentioning

confidence: 99%

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A new parametric transform

Bouguezel

Ahmad

Swamy

2008

2008 2nd International Conference on Signals, Circuits and Systems

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“…Both the DCT and KLT have more computational complexity than the slant transform. Therefore, the need arises for slant transform improvement schemes that yield performance comparable to that of the KLT and DCT without incurring their computational complexity [10][11][12][13][14][15][16][17][18][19][20]. Therefore, various generalizations of the WHTs and DFTs have been attempted.…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown that parametric transforms can have more flexibility and a wider range of applications compared to its original transform. For example, the independent parameters of the fractional discrete transform are used as an additional secret key for watermarking [5], encryption [4,17], error-correcting codes, etc. From this point of view, parametric transforms with matrices described in a unified form and based on a set of parameters become more and more important.…”

Section: Introductionmentioning

confidence: 99%

Fast parametric reciprocal-orthogonal jacket transforms

Lee

Zhang

Jiang

2014

EURASIP J. Adv. Signal Process.

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In this paper, we propose a new construction method for a novel class of parametric reciprocal-orthogonal jacket transform (PROJT) having 9 4 N parameters for a sequence length N = 2 r+1 that is a power of two, based on the reciprocal-orthogonal parametric (ROP) transform and block diagonal matrices. It is shown that the inverse transform of the proposed PROJT is conveniently obtained by the reciprocal of each elements of the forward matrix and transpose operation. What is more, an efficient algorithm for the computation of the PROJT has been developed with the aid of the matrix decomposition and Kronecker product. Further, the experiments show that the independent parameters in the proposed PROJT are successfully used as additional secret keys for image encryption, watermarking, and error-correcting codes.

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