Weighted Fractional-Order Transform Based on Periodic Matrix

Tieyu Zhao and Yingying Chi
Additional contact information
Tieyu Zhao: Information Science Teaching and Research Section, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Yingying Chi: Information Science Teaching and Research Section, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

Mathematics, 2021, vol. 9, issue 17, 1-20

Abstract: Tao et al. proposed the definition of the linear summation of fractional-order matrices based on the theory of Yeh and Pei. This definition was further extended and applied to image encryption. In this paper, we propose a reformulation of the definitions of Yeh et al. and Tao et al. and analyze them theoretically. The results show that many weighted terms are invalid. Therefore, we use the proposed reformulation to prove that the effective weighted terms depend on the period of the matrix. This also shows that the image encryption methods based on the weighted fractional-order transform will lead to the security risk of key invalidation. Finally, our hypothesis is verified by the unified theoretical framework of multiple-parameter discrete fractional-order transforms.

Keywords: fractional-order matrix; fractional Fourier transform; eigenvalue; image encryption (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/17/2073/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/17/2073/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:17:p:2073-:d:623192

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().