Method for encrypting and decrypting image based on multi-order fractional Fourier transform
A fractional Fourier and image technology, applied in the field of information security, can solve the problem that the fractional Fourier transform order is not fully utilized, and achieve the effect of improving security and expanding the key space.
Inactive Publication Date: 2010-06-16
BEIJING INSTITUTE OF TECHNOLOGYGY
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[0004] However, the existing digital image encryption system based on Fractional Fourier Transform is just a simple extension of the traditional Fourier Transform-based secure communication system, which uses Fractional Fourier Transform or Fractional Fourier Domain to replace the Fourier transform or Fourier domain, the order of the fractional Fourier transform is not fully utilized
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[0036] A kind of image encryption and decryption method based on multi-order fractional Fourier transform that the present invention proposes comprises image encryption (such as figure 1 shown) and image decryption (as figure 2 shown), the specific implementation steps are as follows:
[0037] 1. Encryption steps
[0038] (1) Divide the rows and columns of the original image by N times and M times respectively, and obtain M×N sub-images S of equal size (a-1)N+b , a=1, 2,..., M, b=1, 2,..., N;
[0039] (2) The sub-image S obtained by step (1) (a-1)N+b The column vector of do M times interpolation and p 2[(a-1)N+b]-1 Order inverse discrete fractional Fourier transform, row vector for N-fold interpolation and p 2[(a-1)N+b] Order inverse discrete fractional Fourier transform, get Y (a-1)N+b ;
[0040] (3) According to formula (2), Y obtained by step (2) (a-1)N+b The encrypted image is obtained by sequential addition.
[0041] 2. Decryption steps
[0042] (1) Extract the...
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The invention relates to a method for encrypting and decrypting an image based on multi-order fractional Fourier transform, which belongs to the technical field of information security. The method selects discrete sampling-type discrete fractional Fourier transform as a basic tool; at an encryption end of a system, an original image is equally divided into a plurality of sub-images with the same size; interpolation and discrete fractional Fourier transform of different orders are respectively performed on the row and the column of each sub-image; and the transformed images are superposed to obtain an encrypted image; and at the decryption end of the system, the original image is recovered effectively by establishing a linear equation. The method makes full use of the characteristics of the order change of the fractional Fourier transform, and can be combined with other encrypting methods, thereby expanding key space and improving the security of the system relative to the conventionalimage encrypting technology on the basis of the fractional Fourier transform. The method of the invention also can be used for encrypting double images or a plurality of images, which provides a new way for the design of future image encryption technology.
Description
technical field [0001] The invention relates to an image encryption and decryption method based on multi-order fractional Fourier transform, belonging to the technical field of information security. Background technique [0002] Image information is vivid and vivid, and it is one of the important means for people to express information. At present, with the rapid development of network technology, digital image information has been widely used in military, medical, financial and other fields. However, while network technology makes information transmission more convenient, it also inevitably brings hidden dangers to information security. At present, the illegal theft, tampering, and dissemination of image information are becoming more and more rampant. Therefore, technologies to protect the security of digital image content have emerged as the times require. [0003] The concept of fractional Fourier transform was proposed as early as 1929, applied in the field of optics i...
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Inventor 陶然孟祥意王越
Owner BEIJING INSTITUTE OF TECHNOLOGYGY