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Mathematical Problems in Engineering
Volume 2019, Article ID 4789194, 10 pages
Review Article

The Weighted Fractional Fourier Transform and Its Application in Image Encryption

1Information and Computational Science, Northeastern University at Qinhuangdao, Qinhuangdao 064000, China
2State Key Laboratory of Tunable Laser Technology Research, Institute of Optic-Electronics, Harbin Institute of Technology, Harbin 150001, China

Correspondence should be addressed to Tieyu Zhao; moc.361@3123y30ytz

Received 15 February 2019; Revised 11 April 2019; Accepted 28 April 2019; Published 12 May 2019

Academic Editor: Nazrul Islam

Copyright © 2019 Tieyu Zhao and Qiwen Ran. 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.


With the rapid development of information, the requirements for the security and reliability of cryptosystems have become increasingly difficult to meet, which promotes the development of the theory of a class of fractional Fourier transforms. In this paper, we present a review of the development and applications of the weighted fractional Fourier transform (WFRFT) in image encryption. Relationships between the algorithms are established using the generalized permutation matrix group in theoretical analysis. In addition, the advantages and potential weaknesses of each algorithm in image encryption are analyzed and discussed. It is expected that this review will provide a clear picture of the current developments of the WFRFT in image encryption and may shed some light on future developments.