Objective

2

With the rapid development and popularity of the Internet and information technologies

computers and mobile phones have become an important part of the daily lives of people. Through these electronic devices

a large number of pictures that may contain private information are transmitted and stored. Image information security is becoming increasingly important. However

the use of traditional encryption algorithms (e.g.

data encryption standard

advanced encryption standard

and international data encryption algorithm) to encrypt images will result in low efficiency and poor security because of the data size and high redundancy among the pixels of digital images. An effective approach to deal with this issue is to develop secure and effective digital image encryption algorithms. The existing image algorithms can be categorized into pixel-permutation-based

chaotic-system-based

and bitplane-based methods. The image encryption algorithms of the pixel-permutation-based method change the pixel position to destroy adjacent pixel dependencies by performing the permutation operation on the pixel matrix

thereby generating noise-like and meaningless cipher images. However

only the encryption algorithms that use pixel permutation have weak resistance to statistical attacks and poor security. The image encryption algorithms of the chaotic-system-based method take advantage of the excellent intrinsic properties of a chaotic sequence

such as ergodicity

pseudorandomness

and sensitivity to initial conditional and control parameters

to enable diffusion and confusion encryption. These methods have a large key space

strong keystream adaptivity

and high security and often combine with other encryption methods to achieve effective image encryption. The image encryption algorithms of the bitplane-based method decompose the pixels into bit levels

implementing the permutation and diffusion operations on the bitplanes. Bitplane matrix transformation

selective encryption based on bitplane information distribution

and integrating bit-level encryption with pixel-level encryption are the typical bitplane encryption algorithms. The bitplane encryption operation can enhance the sensitivity of the algorithm to small changes in the original image

thus improving the capability to resist differential attack. Moreover

the bitplane permutation operation can change the position and value of a pixel simultaneously

thereby reducing the computational complexity of the image encryption algorithm. Most bitplane encryption algorithms have desirable encryption performance with only one round. Therefore

a novel image encryption algorithm with the bit-level synchronous permutation diffusion and pixel-level annular diffusion (called BSPDPAD) was proposed in this study to improve image encryption efficiency and security to solve the security problem of the selective encryption algorithms with the bitplane information distribution

the statistical attack problem of pixel permutation encryption algorithms

and the problem of sequential diffusion producing stop point mechanism and nonuniform plaintext sensitivity effectively.

Method

2

BSPDPAD uses the chaotic sequence generated by the piecewise linear chaotic map (PWLCM) to construct bit-level and pixel-level keystreams and simultaneously encrypts the image at the bit and pixel levels. At the bit-level encryption stage

BSPDPAD first generates two sets of chaotic sequences by iteratively executing the PWLCM. One set is used to block an image randomly

and the other set is decomposed into bitplanes to obtain the binary keystream sequences. For the four lower bitplanes that contain few information

only the circular shift operation is performed on them. However

for the four higher bitplanes that contain abundant information

exclusive disjunction of the binary elements of the four higher bitplanes with the binary elements of the four lower bitplanes and bit-level keystream is necessary in addition to the cyclic shift operation. Thus

BSPDPAD synchronously permutes and diffuses the four higher bitplanes with the binary keystream sequences and permutes the four lower bitplanes to achieve intra-block and inter-block diffusion. At the pixel-level encryption stage

BSPDPAD iterates the PWLCM again to generate a new keystream. We use the new keystream to perform horizontal sequential diffusion and vertical inversion diffusion of the intermediate encryption image

which completely underwent the bit-level encryption operation

thereby avoiding the problem of stop point mechanism and nonuniform plaintext sensitivity. In addition

the initial value of the PWLCM is modified according to the plain image information at the bit-level and pixel-level encryption stages to enhance the adaptation and the plaintext sensitivity of BSPDPAD.

Result

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Simulation experiments on several gray-scale images and color images show that the key space of BSPDPAD is more than 2

100

indicating that the BSPDPAD algorithm can effectively resist the exhaustive attack. The histogram of the cipher image tends to be evenly distributed

which can cover the distribution of image pixels well and ensure that the algorithm is effective against statistical attack and known cipher attack. The absolute value of the adjacent pixel correlation coefficient of the cipher image encrypted by the BSPDPAD is lower than that of the plaintext image and that of similar encryption algorithms. The entropy of the BSPDPAD ciphering image is close to the theoretical value of 8. Therefore

BSPDPAD has a strong capability to resist entropy attack. The key sensitivity analysis shows that BSPDPAD has satisfactory key sensitivity in the encryption and decryption phases. BSPDPAD also has high NPCR and UACI values

thereby indicating that BSPDPAD has strong plaintext sensitivity and high capability to resist differential attack. Moreover

color image encryption experiments show that BSPDPAD is also suitable for color image encryption

and its encryption performance is excellent. In summary

BSPDPAD is superior to other state-of-the-art encryption algorithms in terms of correlation

information entropy

key space

sensitivity

and capacity to resist multiple attacks. In addition

BSPDPAD has a better diffusion effect

which can obtain excellent encryption performance with only one round of encryption.

Conclusion

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By integrating bit-level selective encryption and pixel-level annular diffusion

BSPDPAD can effectively resist various attacks and exhibit high security. Therefore

BSPDPAD is suitable for all kinds of grayscale and color images and has a large potential application value in the image encryption field.