Abstract
To protect image data privacy, a secure and fast image encryption algorithm using hyper-chaos based key generator and vector operation is proposed. Firstly, we introduce a novel post-process method to create a key matrix for significantly reducing the iterations of the hyperchaotic system from $W\,\,\times \,\,H$ /4 to $2W$ for an image size of $W\,\,\times \,\,H$ . And within the post-process, a random selector driven by the piecewise linear chaotic map ensures the good randomness and unpredictability of the generated key matrix. Secondly, the vector operation is employed to accelerate the cipher block chaining based diffusion process, so the plain image can be parallel encrypted row by row and column by column with high efficiency. Thirdly, we utilize a Logistic map to quickly produce an initial vector for the vectorized diffusion process. Finally, the proposed algorithm is evaluated by some common security and performance tests. Experimental results show that the cipher image can pass all tests of NIST SP 800–22 with $P$ -values $\gg ~0.01$ , its correlation coefficient between pixels is close to 0, and the entropy is greater than 7.999. Combined with other results of security tests, we can safely conclude that the proposed image encryption algorithm provides adequate protection against statistical, brute-force, chosen-plaintext, and other common types of attacks. In addition, the time complexity is in the order of ${O}$ ( $W+H$ ) and the average encryption time of 512 $\times $ 512 images is only 0.023s. The results indicate that our algorithm with high security and fast speed can meet the requirements of real-time confidential transmission of massive image data.
Highlights
With the vigorous development of information technology and online social media, digital images have become part of our daily living [1], [2]
We randomly generated a session key consisting of pre1=157, x1(1)=0.737, x2(1)=0.962, x3(1)=0.175, x4(1)=0.504 for hyperchaotic Lorenz system (HCLS), pre2=103, y(1)=0.357 for PWLCM, and pre3=54, z(1)=0.985 for Logistic map (LM)
The HCLS only iterates 2W times rather than W×H times to create a key matrix with the same size as the plain image (W and H are the width and height of the plain image respectively)
Summary
With the vigorous development of information technology and online social media, digital images have become part of our daily living [1], [2]. The encryption technique makes it possible for us to transmit massive image data without leaking any useful information whether in wireless or wired communications [7]. Block ciphers, such as 3DES and AES, are commonly adopted [11], [12], extensive practical results [13], [14] indicate that these algorithms designed for textual data cannot effectively encrypt images partially given the low processing speed due to the large amount and high redundancy of image data [15]. Many novel image orientated encryption algorithms have been proposed [16]– [19] with chaos-based image encryption being the most representative approach
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