The generalized weighted fractional fourier transform and its application to image encryption

Jun Lang; Ran Tao; Yue Wang

doi:10.1109/CISP.2009.5301283

The generalized weighted fractional fourier transform and its application to image encryption

Jun Lang^*
, Ran Tao
, Yue Wang

^*Corresponding author for this work

School of Information and Electronics

Beijing Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Citations (Scopus)

Abstract

In this paper, Shih's weighted fractional Fourier transform is generalized to contain two 4D vector parameters ℳ, script N ∈ ℤ⁴ , which is denoted by Generalized Weighted Fractional Fourier Transform (GWFRFT). The proposed GWFRFT is shown to possess all of the desired properties for Shih's FRFT. In fact, the GWFRFT will reduce to Shih's FRFT when both ℳ, script N are zero vectors. The eigenvalue relationships between GWFRFT and two original FRFT definitions are discussed. To give an example of application, we exploit its multiple-parameter feature and propose the double random phase encoding in the GWFRFT domain for digital image encryption. The proposed encoding scheme in the GWFRFT domain can enhances data security.

Original language	English
Title of host publication	Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09
DOIs	https://doi.org/10.1109/CISP.2009.5301283
Publication status	Published - 2009
Event	2009 2nd International Congress on Image and Signal Processing, CISP'09 - Tianjin, China Duration: 17 Oct 2009 → 19 Oct 2009

Publication series

Name	Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09

Conference

Conference	2009 2nd International Congress on Image and Signal Processing, CISP'09
Country/Territory	China
City	Tianjin
Period	17/10/09 → 19/10/09

Keywords

Digital signal processing
Fractional fourier transform
Image encryption

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10.1109/CISP.2009.5301283

Cite this

Lang, J., Tao, R., & Wang, Y. (2009). The generalized weighted fractional fourier transform and its application to image encryption. In Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09 Article 5301283 (Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09). https://doi.org/10.1109/CISP.2009.5301283

@inproceedings{0ecd09c5bfc544d2b4b944d7285417dc,

title = "The generalized weighted fractional fourier transform and its application to image encryption",

abstract = "In this paper, Shih's weighted fractional Fourier transform is generalized to contain two 4D vector parameters ℳ, script N ∈ ℤ4 , which is denoted by Generalized Weighted Fractional Fourier Transform (GWFRFT). The proposed GWFRFT is shown to possess all of the desired properties for Shih's FRFT. In fact, the GWFRFT will reduce to Shih's FRFT when both ℳ, script N are zero vectors. The eigenvalue relationships between GWFRFT and two original FRFT definitions are discussed. To give an example of application, we exploit its multiple-parameter feature and propose the double random phase encoding in the GWFRFT domain for digital image encryption. The proposed encoding scheme in the GWFRFT domain can enhances data security.",

keywords = "Digital signal processing, Fractional fourier transform, Image encryption",

author = "Jun Lang and Ran Tao and Yue Wang",

year = "2009",

doi = "10.1109/CISP.2009.5301283",

language = "English",

isbn = "9781424441310",

series = "Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09",

booktitle = "Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09",

note = "2009 2nd International Congress on Image and Signal Processing, CISP'09 ; Conference date: 17-10-2009 Through 19-10-2009",

}

Lang, J, Tao, R & Wang, Y 2009, The generalized weighted fractional fourier transform and its application to image encryption. in Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09., 5301283, Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09, 2009 2nd International Congress on Image and Signal Processing, CISP'09, Tianjin, China, 17/10/09. https://doi.org/10.1109/CISP.2009.5301283

The generalized weighted fractional fourier transform and its application to image encryption. / Lang, Jun; Tao, Ran; Wang, Yue.
Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09. 2009. 5301283 (Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - The generalized weighted fractional fourier transform and its application to image encryption

AU - Lang, Jun

AU - Tao, Ran

AU - Wang, Yue

PY - 2009

Y1 - 2009

N2 - In this paper, Shih's weighted fractional Fourier transform is generalized to contain two 4D vector parameters ℳ, script N ∈ ℤ4 , which is denoted by Generalized Weighted Fractional Fourier Transform (GWFRFT). The proposed GWFRFT is shown to possess all of the desired properties for Shih's FRFT. In fact, the GWFRFT will reduce to Shih's FRFT when both ℳ, script N are zero vectors. The eigenvalue relationships between GWFRFT and two original FRFT definitions are discussed. To give an example of application, we exploit its multiple-parameter feature and propose the double random phase encoding in the GWFRFT domain for digital image encryption. The proposed encoding scheme in the GWFRFT domain can enhances data security.

AB - In this paper, Shih's weighted fractional Fourier transform is generalized to contain two 4D vector parameters ℳ, script N ∈ ℤ4 , which is denoted by Generalized Weighted Fractional Fourier Transform (GWFRFT). The proposed GWFRFT is shown to possess all of the desired properties for Shih's FRFT. In fact, the GWFRFT will reduce to Shih's FRFT when both ℳ, script N are zero vectors. The eigenvalue relationships between GWFRFT and two original FRFT definitions are discussed. To give an example of application, we exploit its multiple-parameter feature and propose the double random phase encoding in the GWFRFT domain for digital image encryption. The proposed encoding scheme in the GWFRFT domain can enhances data security.

KW - Digital signal processing

KW - Fractional fourier transform

KW - Image encryption

UR - https://www.scopus.com/pages/publications/73849142735

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DO - 10.1109/CISP.2009.5301283

M3 - Conference contribution

AN - SCOPUS:73849142735

SN - 9781424441310

T3 - Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09

BT - Proceedings of the 2009 2nd International Congress on Image and Signal Processing, CISP'09

T2 - 2009 2nd International Congress on Image and Signal Processing, CISP'09

Y2 - 17 October 2009 through 19 October 2009

ER -

The generalized weighted fractional fourier transform and its application to image encryption

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