Image Encryption Algorithm Based on Compressive Sensing and Fractional DCT via Polynomial Interpolation

Abstract

Based on compressive sensing and fractional discrete cosine transform (DCT) via polynomial interpolation (PI-FrDCT), an image encryption algorithm is proposed, in which the compression and encryption of an image are accomplished simultaneously. It can keep information secret more effectively with low data transmission. Three-dimensional piecewise and nonlinear chaotic maps are employed to obtain a generating sequence and the exclusive OR (XOR) matrix, which greatly enlarge the key space of the encryption system. Unlike many other fractional transforms, the output of PI-FrDCT is real, which facilitates the storage, transmission and display of the encrypted image. Due to the introduction of a plain-image-dependent disturbance factor, the initial values and system parameters of the encryption scheme are determined by cipher keys and plain-image. Thus, the proposed encryption scheme is very sensitive to the plain-image, which makes the encryption system more secure. Experimental results demonstrate the validity and the reliability of the proposed encryption algorithm.