Robust Encryption-Compression Scheme Based on Multiple Parameter Discrete Fractional Fourier Transform for JPEG 2000

The concept of Fractional Fourier transform (FRFT) was first introduced by N. Wiener in 1929, in quantum mechanics, the FRFT was recognized as a ‘transform method’ by mathematical bodies after the work of Victor Namias in 1980 in which the concept of FRFT had introduced by considering fractional power of eigenfunctions of the ordinary FT. Encryption along with compression is the process used to secure any multimedia content processing with minimum data storage and transmission. The transforms play a vital role in optimizing any encryption-compression systems. Earlier the original information in the existing security system based on the fractional Fourier transform (FRFT) is protected by only a certain order of FRFT. In this article, a novel method for an encryption-compression scheme based on multiple parameters of discrete fractional Fourier transform (DFRFT) with random phase matrices is proposed. The performance analysis and salient features of the proposed encryption-compression scheme are discussed in detail. The multiple-parameter discrete fractional Fourier transform (MPDFRFT) possesses all the desired properties of discrete fractional Fourier transform. The MPDFRFT converts to the DFRFT when all of its order parameters are the same. We exploit the properties of multiple-parameter DFRFT and propose a novel encryption-compression scheme using the double random phase in the MPDFRFT domain for encryption and compression data. The proposed scheme provides two-way options for data encryption and compression as well. The proposed scheme with MPDFRFT significantly enhances the data security along with the image quality of decompressed images compared to DFRFT and FRFT and it shows consistent performance with different images. The numerical simulations demonstrate the validity and efficiency of this scheme based on Peak signal to noise ratio (PSNR) and compression ratio (CR) and the robustness of the schemes against bruit force attack is examined.