Color Image Encryption Using Many-Parameter Discrete Fractional Fourier Transforms

Color images can be divided into three channels including red, green and blue channels. Each channel is independently processed using a random phase encoding and then converted into the fractional domain through the multiple-parameter discrete fractional Fourier transform (MPDFRFT) or random discrete fractional Fourier transform (RDFRFT). Subsequently, the same procedure is repeated again. After the second random phase encoding and the second MPDFRFT (or RDFRFT), the encrypted image is obtained. All parameters, including the power parameters, random phases and the random matrices in the definition of the RDFRFT, can be used as encryption keys. Errors in decryption keys will result in errors of decrypted images. Security of the proposed encryption schemes using MPDFRFT and RDFRFT can be enhanced as compared to the existing similar encryption scheme using the discrete fractional Fourier transform (DFRFT) because there are much more parameters in both of the MPDFRFT and RDFRFT than those in the DFRFT and, from computer experimental results, sensitivity to decryption key errors for the proposed methods are both higher than the existing DFRFT method.