Image Encryption Algorithm Based on Compressive Sensing and Fractional DCT via Polynomial Interpolation
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.
KeywordsCompressive sensing fractional discrete cosine transform (DCT) via polynomial interpolation image encryption three-dimensional piecewise and nonlinear chaotic maps real-valued output
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This work was supported by National Natural Science Foundation of China (Nos. 61662047 and 61462061).
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