Digital double random amplitude image encryption method based on the symmetry property of the parametric discrete Fourier transform

2018 ◽  
Vol 27 (02) ◽  
pp. 1 ◽  
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Image Encryption ◽  
Symmetry Property ◽  
Amplitude Image ◽  
Encryption Method

scholarly journals Image Encryption Using Chaotic Cat Mapping in the Discrete Fourier Transform

2018 ◽  
Vol 18 ◽  
pp. 7389-7397
Author(s):  
Mohammed Alzain
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Image Encryption ◽  
Experimental Results ◽  
Transform Domain ◽  
Two Dimensional ◽  
Encrypted Image ◽  
Image Cryptosystem ◽  
Fourier Transform Domain

The paper presents an secure image using the two dimensional chaotic cat mapping  (2D-CCM) in the Discrete Fourier Transform domain (DFT). The ciphering phase begins by applying the DFT on the plainimage to be encrypted and the resulted Fourier transformed image are scrambled using the 2D-CCM and finally an inverse DFT is applied to obtain the final encrypted image. The decryption phase applies a reverse  procedure to get the original plainimage. A set of encryption test experiments are employed to inspect the proposed DFT based 2D-CCM image cryptosystem. The experimental results verified and confirmed the superiority of the proposed DFT based 2D-CCM image cryptosystem.

scholarly journals Comparison of Discrete Fourier Transform and Fast Fourier Transform with Reduced Number of Multiplication and Addition Operations

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Digital Signal Processing ◽  
Fast Fourier Transform ◽  
Discrete Fourier Transform ◽  
Symmetry Property ◽  
Digital Signal ◽  
Basic Structure ◽  
Phase Factor ◽  
Normal Order

Fast Fourier Transform is an advanced algorithm for computing Discrete Fourier Transform efficiently. Although the results available from the operation of Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) are same, but exploiting the periodicity and symmetry property of phase factor Fast Fourier Transform computes the Discrete Fourier Transform using reduced number of multiplication and addition operations. The basic structure used in the operations of Fast Fourier Transform is the Butterfly structure. For the implementation of Fast Fourier Transform the two methods are used such as decimation in time (DIT) and decimation in frequency (DIF). Both the methods give same result but for decimation in time of Fast Fourier Transform bit reversed inputs are applied and for decimation in frequency of Fast Fourier Transform normal order inputs are applied, and the result is reversed again. In this paper, operations for DFT and FFT have been discussed and shown with examples. It is found that generalized formula for FFT have been described same in the books, but the expressions in the intermediate computations for the first decimation and second decimation are different in the various books of Digital Signal Processing. The expressions in the intermediate computation of FFT described in different books are broadly compared in this paper

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