This paper proposed a novel color image encryption scheme based on multiple chaotic systems. The ergodicity property of chaotic system is utilized to perform the permutation process; a substitution
operation is applied to achieve the diffusion effect. In permutation stage, the 3D color plain-image matrix
is converted to a 2D image matrix, then two generalized Arnold maps are employed to generate hybrid chaotic sequences which are dependent on the plain-image’s content. The generated chaotic sequences are then applied to perform the permutation process. The encryption’s key streams not only depend on the
cipher keys but also depend on plain-image and therefore can resist chosen-plaintext attack as well as
known-plaintext attack. In the diffusion stage, four pseudo-random gray value sequences are generated by another generalized Arnold map. The gray value sequences are applied to perform the diffusion process by bitxoring operation with the permuted image row-by-row or column-by-column to improve the encryption rate. The security and performance analysis have been performed, including key space analysis, histogram analysis, correlation analysis, information entropy analysis, key sensitivity analysis, differential analysis etc. The experimental results show that the proposed image encryption scheme is highly secure thanks to its large key space and efficient permutation-substitution operation, and therefore it is suitable for practical image and video encryption.
Chaotic Block Image Scheme using Large Key Space and Message Digest AlgorithmCSCJournals
In this paper, chaotic block image scheme using large key space and message digest algorithm. Cat map intended for confusion and 2D-Sine Tent Composite map (2D-STCM) key generator intended for diffusion. Confusion is implemented by 2D Cat map with arbitrary block size. In the first tendency, 2D cat map use for local shuffling of indexes inside blocks, while in the second tendency, 2D cat map used for global shuffling of whole image indexes. The designed algorithm executes two confusions and one diffusion in each iteration. To increase the security level, the message digestion algorithm is used as a fingerprint for the plain image that creates the initial value of the key. After that 2D-STCM generates a large key stream. Diffusion implementation takes place by XOR operation; between a key stream and confused image. Experimental results, show that security level increases due to integration of confusion and diffusion. On the other side large key space and the high sensitivity of secret keys have been given a guarantee for the performance of the security. Performance measures reach to the top value among those in the similar researches. To verify the obtained results, authors implemented inverse chaos. All the tests are processed by MATLAB 2015a.
A new block cipher for image encryption based on multi chaotic systemsTELKOMNIKA JOURNAL
In this paper, a new algorithm for image encryption is proposed based on three chaotic systems which are Chen system,logistic map and two-dimensional (2D) Arnold cat map. First, a permutation scheme is applied to the image, and then shuffled image is partitioned into blocks of pixels. For each block, Chen system is employed for confusion and then logistic map is employed for generating subsititution-box (S-box) to substitute image blocks. The S-box is dynamic, where it is shuffled for each image block using permutation operation. Then, 2D Arnold cat map is used for providing diffusion, after that XORing the result using Chen system to obtain the encrypted image.The high security of proposed algorithm is experimented using histograms, unified average changing intensity (UACI), number of pixels change rate (NPCR), entropy, correlation and keyspace analyses.
Design a New Image Encryption using Fuzzy Integral Permutation with Coupled C...IJORCS
This document proposes a new image encryption algorithm combining DNA sequence addition and coupled chaotic maps. The algorithm has two parts: 1) A DNA sequence matrix is obtained by encoding image pixels and divided into blocks that are added using Sugeno fuzzy integral, 2) The modified color components are encrypted using coupled two-dimensional piecewise nonlinear chaotic maps to strengthen security. Experimental results on image databases show the algorithm effectively protects digital image security over the internet.
This document presents a digital image encryption technique based on a compound sine and cosine chaotic map. The map is used to generate random bits for encryption. The image is first converted to binary and separated into bit planes. Each bit plane is encrypted using XOR operations with bits from the chaotic map. Keys are generated from input ASCII codes which set initial conditions and parameters for the chaotic map, increasing security. Experiments were conducted encrypting color images in MATLAB to evaluate the encryption performance.
Chaos Image Encryption using Pixel shuffling cscpconf
This document proposes a chaos-based image encryption algorithm using pixel shuffling. It uses elements from a chaotic map like the Henon map or Lorentz map to shuffle the pixel positions of an image. The chaotic elements are divided into blocks corresponding to the RGB channels. Pixel positions are reordered according to the sorted indices of each block. Encryption scrambles the pixel positions, while decryption restores the original positions using the same chaotic map. Experimental results on brain and Lena images show the encrypted images have very low correlation with the originals. Slight key changes also result in completely different decryptions, demonstrating key sensitivity of the algorithm.
Image confusion and diffusion based on multi-chaotic system and mix-columnjournalBEEI
In this paper, a new image encryption algorithm based on chaotic cryptography was proposed. The proposed scheme was based on multiple stages of confusion and diffusion. The diffusion process was implemented twice, first, by permuting the pixels of the plain image by using an Arnold cat map and, the second time by permuting the plain image pixels via the proposed permutation algorithm. The confusion process was performed many times, by performing the XOR operation between the two resulted from permuted images, subtracted a random value from all pixels of the image, as well as by implementing the mix column on the resulted image, and by used the Lorenz key to obtain the encrypted image. The security analysis tests that used to exam the results of this encryption method were information entropy, key space analysis, correlation, histogram analysis UACI, and NPCR have shown that the suggested algorithm has been resistant against different types of attacks.
A CHAOTIC CONFUSION-DIFFUSION IMAGE ENCRYPTION BASED ON HENON MAPIJNSA Journal
This paper suggests chaotic confusion-diffusion image encryption based on the Henon map. The proposed chaotic confusion-diffusion image encryption utilizes image confusion and pixel diffusion in two levels. In the first level, the plainimage is scrambled by a modified Henon map for n rounds. In the second level, the scrambled image is diffused using Henon chaotic map. Comparison between the logistic map and modified Henon map is established to investigate the effectiveness of the suggested chaotic confusion-diffusion image encryption scheme. Experimental results showed that the suggested chaotic confusion-diffusion image encryption scheme can successfully encrypt/decrypt images using the same secret keys. Simulation results confirmed that the ciphered images have good entropy information and low correlation between coefficients. Besides the distribution of the gray values in the ciphered image has random-like behavior.
IRJET- LS Chaotic based Image Encryption System Via Permutation ModelsIRJET Journal
This document proposes an image encryption system using logistic sine map and permutation models. The system works as follows:
1. A plain image is converted to grayscale and decomposed into 8 bit planes.
2. Each bit plane is randomly scrambled.
3. A logistic sine map is used to generate a key to partially encrypt each bit plane.
4. The bits planes are then permuted to obtain the final encrypted image. Logistic sine maps are well-suited for this approach due to their sensitivity to initial parameter values and ability to generate seemingly random outputs. The system aims to increase security by efficiently scrambling and permuting the bit plane values of the input image.
Chaotic Block Image Scheme using Large Key Space and Message Digest AlgorithmCSCJournals
In this paper, chaotic block image scheme using large key space and message digest algorithm. Cat map intended for confusion and 2D-Sine Tent Composite map (2D-STCM) key generator intended for diffusion. Confusion is implemented by 2D Cat map with arbitrary block size. In the first tendency, 2D cat map use for local shuffling of indexes inside blocks, while in the second tendency, 2D cat map used for global shuffling of whole image indexes. The designed algorithm executes two confusions and one diffusion in each iteration. To increase the security level, the message digestion algorithm is used as a fingerprint for the plain image that creates the initial value of the key. After that 2D-STCM generates a large key stream. Diffusion implementation takes place by XOR operation; between a key stream and confused image. Experimental results, show that security level increases due to integration of confusion and diffusion. On the other side large key space and the high sensitivity of secret keys have been given a guarantee for the performance of the security. Performance measures reach to the top value among those in the similar researches. To verify the obtained results, authors implemented inverse chaos. All the tests are processed by MATLAB 2015a.
A new block cipher for image encryption based on multi chaotic systemsTELKOMNIKA JOURNAL
In this paper, a new algorithm for image encryption is proposed based on three chaotic systems which are Chen system,logistic map and two-dimensional (2D) Arnold cat map. First, a permutation scheme is applied to the image, and then shuffled image is partitioned into blocks of pixels. For each block, Chen system is employed for confusion and then logistic map is employed for generating subsititution-box (S-box) to substitute image blocks. The S-box is dynamic, where it is shuffled for each image block using permutation operation. Then, 2D Arnold cat map is used for providing diffusion, after that XORing the result using Chen system to obtain the encrypted image.The high security of proposed algorithm is experimented using histograms, unified average changing intensity (UACI), number of pixels change rate (NPCR), entropy, correlation and keyspace analyses.
Design a New Image Encryption using Fuzzy Integral Permutation with Coupled C...IJORCS
This document proposes a new image encryption algorithm combining DNA sequence addition and coupled chaotic maps. The algorithm has two parts: 1) A DNA sequence matrix is obtained by encoding image pixels and divided into blocks that are added using Sugeno fuzzy integral, 2) The modified color components are encrypted using coupled two-dimensional piecewise nonlinear chaotic maps to strengthen security. Experimental results on image databases show the algorithm effectively protects digital image security over the internet.
This document presents a digital image encryption technique based on a compound sine and cosine chaotic map. The map is used to generate random bits for encryption. The image is first converted to binary and separated into bit planes. Each bit plane is encrypted using XOR operations with bits from the chaotic map. Keys are generated from input ASCII codes which set initial conditions and parameters for the chaotic map, increasing security. Experiments were conducted encrypting color images in MATLAB to evaluate the encryption performance.
Chaos Image Encryption using Pixel shuffling cscpconf
This document proposes a chaos-based image encryption algorithm using pixel shuffling. It uses elements from a chaotic map like the Henon map or Lorentz map to shuffle the pixel positions of an image. The chaotic elements are divided into blocks corresponding to the RGB channels. Pixel positions are reordered according to the sorted indices of each block. Encryption scrambles the pixel positions, while decryption restores the original positions using the same chaotic map. Experimental results on brain and Lena images show the encrypted images have very low correlation with the originals. Slight key changes also result in completely different decryptions, demonstrating key sensitivity of the algorithm.
Image confusion and diffusion based on multi-chaotic system and mix-columnjournalBEEI
In this paper, a new image encryption algorithm based on chaotic cryptography was proposed. The proposed scheme was based on multiple stages of confusion and diffusion. The diffusion process was implemented twice, first, by permuting the pixels of the plain image by using an Arnold cat map and, the second time by permuting the plain image pixels via the proposed permutation algorithm. The confusion process was performed many times, by performing the XOR operation between the two resulted from permuted images, subtracted a random value from all pixels of the image, as well as by implementing the mix column on the resulted image, and by used the Lorenz key to obtain the encrypted image. The security analysis tests that used to exam the results of this encryption method were information entropy, key space analysis, correlation, histogram analysis UACI, and NPCR have shown that the suggested algorithm has been resistant against different types of attacks.
A CHAOTIC CONFUSION-DIFFUSION IMAGE ENCRYPTION BASED ON HENON MAPIJNSA Journal
This paper suggests chaotic confusion-diffusion image encryption based on the Henon map. The proposed chaotic confusion-diffusion image encryption utilizes image confusion and pixel diffusion in two levels. In the first level, the plainimage is scrambled by a modified Henon map for n rounds. In the second level, the scrambled image is diffused using Henon chaotic map. Comparison between the logistic map and modified Henon map is established to investigate the effectiveness of the suggested chaotic confusion-diffusion image encryption scheme. Experimental results showed that the suggested chaotic confusion-diffusion image encryption scheme can successfully encrypt/decrypt images using the same secret keys. Simulation results confirmed that the ciphered images have good entropy information and low correlation between coefficients. Besides the distribution of the gray values in the ciphered image has random-like behavior.
IRJET- LS Chaotic based Image Encryption System Via Permutation ModelsIRJET Journal
This document proposes an image encryption system using logistic sine map and permutation models. The system works as follows:
1. A plain image is converted to grayscale and decomposed into 8 bit planes.
2. Each bit plane is randomly scrambled.
3. A logistic sine map is used to generate a key to partially encrypt each bit plane.
4. The bits planes are then permuted to obtain the final encrypted image. Logistic sine maps are well-suited for this approach due to their sensitivity to initial parameter values and ability to generate seemingly random outputs. The system aims to increase security by efficiently scrambling and permuting the bit plane values of the input image.
This document proposes a new image encryption scheme based on chaotic encryption. It provides a fast encryption algorithm using a pseudorandom key stream generator based on coupled chaotic maps. Only the most important image components identified using discrete wavelet transform are encrypted. Statistical analysis shows the encrypted images have uniform histograms and negligible pixel correlations, resisting cryptanalysis attacks. The partial encryption also reduces computation time for applications with bandwidth and power constraints like mobile devices.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
METHOD FOR A SIMPLE ENCRYPTION OF IMAGES BASED ON THE CHAOTIC MAP OF BERNOULLIijcsit
In this document, we propose a simple algorithm for the encryption of gray-scale images, although the
scheme is perfectly usable in color images. Prior to encryption, the proposed algorithm includes a pair of
permutation processes, inspired by the Bernoulli mapping. The permutation disperses the image
information to hinder the unauthorized recovery of the original image. The image is encrypted using the
XOR function between a sequence generated from the same Bernoulli mapping and the image data,
obtained after two permutation processes. Finally, for the verification of the algorithm, the gray-scale Lena
pattern image was used; calculating histograms for each stage alongside of the encryption process. The
histograms prove dispersion evolution for pattern image during whole algorithm.
A New Chaos Based Image Encryption and Decryption using a Hash FunctionIRJET Journal
This document proposes a new chaos-based image encryption and decryption scheme using Arnold's cat map for pixel permutation and the Lorenz system for diffusion. A hash function, specifically MurmurHash3, is used to generate the permutation and diffusion keys. This helps accelerate the diffusion process and reduces the number of cipher cycles needed compared to previous schemes. The encryption process involves first permuting the pixel positions using the cat map, with control parameters determined by the hash value of the original image. Then diffusion is performed using the Lorenz system to generate the keystream. Decryption follows the reverse process using the same keys. Security analysis demonstrates the scheme has a large key space and the encrypted images pass various statistical tests, indicating the
The document describes a new GIS tool that classifies lands around selected monuments using texture analysis and machine learning. The tool extracts sub-images around the monument, calculates texture features using GLCM, and classifies the lands using minimum distance classification to identify flat areas for constructing buildings like museums or visitor centers. Key steps include feature extraction using GLCM, calculating metrics like entropy and correlation, and classifying new images based on closest texture feature vectors in the training database.
A DIGITAL COLOR IMAGE WATERMARKING SYSTEM USING BLIND SOURCE SEPARATIONcsandit
An attempt is made to implement a digital color image-adaptive watermarking scheme in
spatial domain and hybrid domain i.e host image in wavelet domain and watermark in spatial
domain. Blind Source Separation (BSS) is used to extract the watermark The novelty of the
presented scheme lies in determining the mixing matrix for BSS model using BFGS (Broyden–
Fletcher–Goldfarb–Shanno) optimization technique. This method is based on the smooth and
textured portions of the image. Texture analysis is carried based on energy content of the
image (using GLCM) which makes the method image adaptive to embed color watermark.
The performance evaluation is carried for hybrid domain of various color spaces like YIQ, HSI
and YCbCr and the feasibility of optimization algorithm for finding mixing matrix is also
checked for these color spaces. Three ICA (Independent Component Analysis)/BSS algorithms
are used in extraction procedure ,through which the watermark can be retrieved efficiently . An
effort is taken to find out the best suited color space to embed the watermark which satisfies the
condition of imperceptibility and robustness against various attacks.
A new approach of colour image encryption based on henon like chaotic mapAlexander Decker
1. This document presents a new approach for color image encryption based on the Henon-like chaotic map. The algorithm separates the RGB components of an image, encrypts one component using a Henon chaotic map to generate a random bitstream, and then performs a bitwise XOR with the original pixel values of that component.
2. The Henon map is a discrete dynamical system that exhibits chaotic behavior. This property of sensitivity to initial conditions is leveraged to generate encryption keys. The proposed algorithm uses a Henon-like map containing a frequency control parameter to maintain chaotic behavior.
3. Experimental results demonstrate the encryption achieves a uniform distribution of pixel values and differences in histograms between plain and cipher images, indicating the
New Chaotic Substation and Permutation Method for Image Encryptiontayseer Karam alshekly
New Chaotic Substation and Permutation Method for Image Encryption is introduced based on combination between Block Cipher and chaotic map. The new algorithm encrypts and decrypts a block of 500 byte. Each block is firstly permuted by using the hyper-chaotic map and then the result is substituted using 1D Bernoulli map. Finally the resulted block is XORed with the key block. The proposed cipher image subjected to number of tests which are the security analysis (key space analysis and key sensitivity analysis) and statistical attack analysis (histogram, correlation, and differential attack and information entropy) and all results show that the proposed encryption scheme is secure because of its large key space; it’s highly sensitivity to the cipher keys and plain-images.
Performance analysis of transformation and bogdonov chaotic substitution base...IJECEIAES
In this article, a combined Pseudo Hadamard transformation and modified Bogdonav chaotic generator based image encryption technique is proposed. Pixel position transformation is performed using Pseudo Hadamard transformation and pixel value variation is made using Bogdonav chaotic substitution. Bogdonav chaotic generator produces random sequences and it is observed that very less correlation between the adjacent elements in the sequence. The cipher image obtained from the transformation stage is subjected for substitution using Bogdonav chaotic sequence to break correlation between adjacent pixels. The cipher image is subjected for various security tests under noisy conditions and very high degree of similarity is observed after deciphering process between original and decrypted images.
IRJET- An Acute Method of Encryption & Decryption by using Histograms and Che...IRJET Journal
This document proposes an image encryption technique using histograms and cheat images. It involves permuting the input image and a cheat image using a logistic map and secret key parameters. The encrypted image is generated using the permuted values. For decryption, the same process is applied in reverse using the cheat image and secret key. The technique is analyzed for security through statistical analysis, differential attacks, sensitivity analysis, and entropy measures, showing it effectively encrypts images and is robust against attacks.
Performance Improvement of Vector Quantization with Bit-parallelism HardwareCSCJournals
Vector quantization is an elementary technique for image compression; however, searching for the nearest codeword in a codebook is time-consuming. In this work, we propose a hardware-based scheme by adopting bit-parallelism to prune unnecessary codewords. The new scheme uses a “Bit-mapped Look-up Table” to represent the positional information of the codewords. The lookup procedure can simply refer to the bitmaps to find the candidate codewords. Our simulation results further confirm the effectiveness of the proposed scheme.
AN ENHANCED SEPARABLE REVERSIBLE DATA HIDING IN ENCRYPTED IMAGES USING SIDE M...Editor IJMTER
This paper proposes a scheme for Enhanced Separable Reversible Data Hiding in
Encrypted images Using Side Match. In the first step the original image is encrypted using an
encryption key. Then additional data is embedded into the image by modifying a small portion of the
encrypted image using a data hiding key. With an encrypted image containing additional data, if a
receiver has the data hiding key, he can extract the additional data. If the receiver has the encryption
key, he can decrypt the image, but cannot extract the additional data. If the receiver has both the data
hiding key and encryption key, he can extract the additional data and recover the original content by
exploiting the spatial correlation in natural images. The accuracy of data extraction is improved by
using a better scheme for measuring the smoothness of the received image, and uses the Side Match
scheme to further decrease the error rate of extracted bits.
The document summarizes a proposed user-friendly image sharing scheme that uses JPEG-LS prediction and LSB matching functions. The scheme encodes a secret image into meaningful shadow images using different prime numbers for different blocks, as determined by JPEG-LS prediction. It hides the prime number indicators in the least significant bits of pixels using LSB matching to prevent image degradation. The experimental results showed the reconstructed image quality was higher than previous schemes, making it suitable for applications requiring high quality images like medicine, military, or art.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
HYBRIDIZATION OF DCT BASED STEGANOGRAPHY AND RANDOM GRIDSIJNSA Journal
The document discusses a hybrid approach to steganography and visual cryptography for improved data security. It proposes combining principles of steganography, which hides data in a cover media, and visual cryptography, which encrypts images in a way that can be decrypted by human vision without algorithms. Specifically, it describes generating two random grids from a secret image that reveal the image when overlaid but hide it individually. The random grids are created by inverting or substituting pixels based on the secret image. This hybrid approach aims to provide stronger security than either technique alone by incorporating advantages of both.
Enhancement and Analysis of Chaotic Image Encryption Algorithms cscpconf
The focus of this paper is to improve the level of security and secrecy provided by the chaotic
map based image encryption.An encryption algorithm based on the Logistic and the Henon
maps is proposed. The algorithm uses chaotic iteration to generate the encryption keys, and
then carries out the XOR and cyclic shift operations on the plain text to change the values of
image pixels. Chaotic Map Lattice based image encryption algorithm suggested by Pisarchik is
also examined which is based on Logistic map alone. In experiments, the corresponding results
showed the proposed method is a promising scheme for image encryption in terms of security
and secrecy. At the end, we show the results of a security analysis and a comparison of both
schemes
This document describes an image encryption and decryption technique using chaos algorithms. It uses the chaotic properties of the Henon map and Arnold cat map. The Henon map is used to generate pseudo-random key values for pixel shuffling. Pixel positions of the input image are first shuffled using the Arnold cat map. Then they are shuffled again using the sorted key values from the Henon map. This encrypts the image. Decryption reverses the process to recover the original pixel values and image. Experimental results show the encrypted image is secure and the original image can be recovered accurately using the correct key during decryption. The technique provides efficient and secure encryption of images for transmission.
IMAGE ENCRYPTION BASED ON DIFFUSION AND MULTIPLE CHAOTIC MAPSIJNSA Journal
This document proposes an image encryption algorithm that uses diffusion and multiple chaotic maps. It begins by generating subkeys using chaotic logistic maps. The image is then encrypted using one subkey via logistic map transformation, diffusing the image. Additional subkeys are generated from four chaotic maps by hopping through various map orbits. The image is treated as a 1D array via raster and zigzag scanning, divided into blocks, and those blocks undergo position permutation and value transformation controlled by the chaotic subkeys, fully encrypting the image. Decryption reverses the process using the same subkeys.
IRJET- An Image Cryptography using Henon Map and Arnold Cat MapIRJET Journal
The document proposes a new symmetric image encryption algorithm based on the Henon chaotic system and Arnold Cat map. The algorithm uses Henon map to generate pseudo-random key values for pixel encryption and Arnold Cat map for pixel shuffling. Encryption involves XORing pixel values with keys and shuffling pixels, while decryption reverses these processes to recover the original image using the same keys.
The document proposes and evaluates a new digital image security scheme that uses Residue Number System (RNS) encoding/decoding and a modified Arnold transform algorithm. Key points:
- The encryption process encodes the plain image into residual images using RNS, then encrypts them by applying the modified Arnold transform multiple times.
- The decryption process decrypts the cipher image by applying the inverse Arnold transform, then decodes the residual images back into the plain image using RNS and the Chinese Remainder Theorem.
- Experimental results on images of different sizes show the scheme can encrypt/decrypt without information loss. Security analysis indicates resistance to statistical attacks like histograms and strong sensitivity to encryption keys.
The document proposes and evaluates a new digital image security scheme that uses Residue Number System (RNS) encoding/decoding and a modified Arnold transform algorithm. Key points:
- The encryption process encodes the plain image into residual images using RNS, then encrypts them using the modified Arnold transform.
- The decryption process decrypts the cipher image using the inverse Arnold transform, then decodes the residual images back into the plain image using RNS and the Chinese Remainder Theorem.
- Experimental results on test images of different sizes and formats show the scheme can effectively encrypt and decrypt without information loss. Security analysis also indicates resistance to statistical attacks like histograms and strong sensitivity to encryption keys.
Color Image Encryption and Decryption Using Multiple Chaotic MapsIJTET Journal
Owing to advances in communication technology, a bulk of visual digital data is being stored and transmitted over the internet now-a-days. Particularly millions and millions of images transfer through the network per day as per the statistics and a result, the security of image data is an important requirement. Image encryption algorithm is used to provide this security. In this paper, an image encryption algorithm based on confusion diffusion architecture that uses dynamic key space is proposed. An internal key generator is used to generate the initial seeds for the overall encryption scheme is proposed. With these initial seeds logistic map generates pseudo random numbers then these numbers are converted into permutation order for permutation. The diffusion bits are generated in parallel using the logistic map and manipulated with pixels confused. The image pixels are iteratively confused and diffused using permutation order and diffusion bits respectively to produce cipher image in minimum number of rounds. This paper proposes a new kind of initial seed generation that utilizes the combo of logistic and tent maps. Even all external seeds are same. The internal seeds will be totally different. This ensures the key sensitivity. The simulation results and analysis confirm that the satisfactory level of security is achieved in three rounds and overall encryption time is saved.
This document proposes a new image encryption scheme based on chaotic encryption. It provides a fast encryption algorithm using a pseudorandom key stream generator based on coupled chaotic maps. Only the most important image components identified using discrete wavelet transform are encrypted. Statistical analysis shows the encrypted images have uniform histograms and negligible pixel correlations, resisting cryptanalysis attacks. The partial encryption also reduces computation time for applications with bandwidth and power constraints like mobile devices.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
METHOD FOR A SIMPLE ENCRYPTION OF IMAGES BASED ON THE CHAOTIC MAP OF BERNOULLIijcsit
In this document, we propose a simple algorithm for the encryption of gray-scale images, although the
scheme is perfectly usable in color images. Prior to encryption, the proposed algorithm includes a pair of
permutation processes, inspired by the Bernoulli mapping. The permutation disperses the image
information to hinder the unauthorized recovery of the original image. The image is encrypted using the
XOR function between a sequence generated from the same Bernoulli mapping and the image data,
obtained after two permutation processes. Finally, for the verification of the algorithm, the gray-scale Lena
pattern image was used; calculating histograms for each stage alongside of the encryption process. The
histograms prove dispersion evolution for pattern image during whole algorithm.
A New Chaos Based Image Encryption and Decryption using a Hash FunctionIRJET Journal
This document proposes a new chaos-based image encryption and decryption scheme using Arnold's cat map for pixel permutation and the Lorenz system for diffusion. A hash function, specifically MurmurHash3, is used to generate the permutation and diffusion keys. This helps accelerate the diffusion process and reduces the number of cipher cycles needed compared to previous schemes. The encryption process involves first permuting the pixel positions using the cat map, with control parameters determined by the hash value of the original image. Then diffusion is performed using the Lorenz system to generate the keystream. Decryption follows the reverse process using the same keys. Security analysis demonstrates the scheme has a large key space and the encrypted images pass various statistical tests, indicating the
The document describes a new GIS tool that classifies lands around selected monuments using texture analysis and machine learning. The tool extracts sub-images around the monument, calculates texture features using GLCM, and classifies the lands using minimum distance classification to identify flat areas for constructing buildings like museums or visitor centers. Key steps include feature extraction using GLCM, calculating metrics like entropy and correlation, and classifying new images based on closest texture feature vectors in the training database.
A DIGITAL COLOR IMAGE WATERMARKING SYSTEM USING BLIND SOURCE SEPARATIONcsandit
An attempt is made to implement a digital color image-adaptive watermarking scheme in
spatial domain and hybrid domain i.e host image in wavelet domain and watermark in spatial
domain. Blind Source Separation (BSS) is used to extract the watermark The novelty of the
presented scheme lies in determining the mixing matrix for BSS model using BFGS (Broyden–
Fletcher–Goldfarb–Shanno) optimization technique. This method is based on the smooth and
textured portions of the image. Texture analysis is carried based on energy content of the
image (using GLCM) which makes the method image adaptive to embed color watermark.
The performance evaluation is carried for hybrid domain of various color spaces like YIQ, HSI
and YCbCr and the feasibility of optimization algorithm for finding mixing matrix is also
checked for these color spaces. Three ICA (Independent Component Analysis)/BSS algorithms
are used in extraction procedure ,through which the watermark can be retrieved efficiently . An
effort is taken to find out the best suited color space to embed the watermark which satisfies the
condition of imperceptibility and robustness against various attacks.
A new approach of colour image encryption based on henon like chaotic mapAlexander Decker
1. This document presents a new approach for color image encryption based on the Henon-like chaotic map. The algorithm separates the RGB components of an image, encrypts one component using a Henon chaotic map to generate a random bitstream, and then performs a bitwise XOR with the original pixel values of that component.
2. The Henon map is a discrete dynamical system that exhibits chaotic behavior. This property of sensitivity to initial conditions is leveraged to generate encryption keys. The proposed algorithm uses a Henon-like map containing a frequency control parameter to maintain chaotic behavior.
3. Experimental results demonstrate the encryption achieves a uniform distribution of pixel values and differences in histograms between plain and cipher images, indicating the
New Chaotic Substation and Permutation Method for Image Encryptiontayseer Karam alshekly
New Chaotic Substation and Permutation Method for Image Encryption is introduced based on combination between Block Cipher and chaotic map. The new algorithm encrypts and decrypts a block of 500 byte. Each block is firstly permuted by using the hyper-chaotic map and then the result is substituted using 1D Bernoulli map. Finally the resulted block is XORed with the key block. The proposed cipher image subjected to number of tests which are the security analysis (key space analysis and key sensitivity analysis) and statistical attack analysis (histogram, correlation, and differential attack and information entropy) and all results show that the proposed encryption scheme is secure because of its large key space; it’s highly sensitivity to the cipher keys and plain-images.
Performance analysis of transformation and bogdonov chaotic substitution base...IJECEIAES
In this article, a combined Pseudo Hadamard transformation and modified Bogdonav chaotic generator based image encryption technique is proposed. Pixel position transformation is performed using Pseudo Hadamard transformation and pixel value variation is made using Bogdonav chaotic substitution. Bogdonav chaotic generator produces random sequences and it is observed that very less correlation between the adjacent elements in the sequence. The cipher image obtained from the transformation stage is subjected for substitution using Bogdonav chaotic sequence to break correlation between adjacent pixels. The cipher image is subjected for various security tests under noisy conditions and very high degree of similarity is observed after deciphering process between original and decrypted images.
IRJET- An Acute Method of Encryption & Decryption by using Histograms and Che...IRJET Journal
This document proposes an image encryption technique using histograms and cheat images. It involves permuting the input image and a cheat image using a logistic map and secret key parameters. The encrypted image is generated using the permuted values. For decryption, the same process is applied in reverse using the cheat image and secret key. The technique is analyzed for security through statistical analysis, differential attacks, sensitivity analysis, and entropy measures, showing it effectively encrypts images and is robust against attacks.
Performance Improvement of Vector Quantization with Bit-parallelism HardwareCSCJournals
Vector quantization is an elementary technique for image compression; however, searching for the nearest codeword in a codebook is time-consuming. In this work, we propose a hardware-based scheme by adopting bit-parallelism to prune unnecessary codewords. The new scheme uses a “Bit-mapped Look-up Table” to represent the positional information of the codewords. The lookup procedure can simply refer to the bitmaps to find the candidate codewords. Our simulation results further confirm the effectiveness of the proposed scheme.
AN ENHANCED SEPARABLE REVERSIBLE DATA HIDING IN ENCRYPTED IMAGES USING SIDE M...Editor IJMTER
This paper proposes a scheme for Enhanced Separable Reversible Data Hiding in
Encrypted images Using Side Match. In the first step the original image is encrypted using an
encryption key. Then additional data is embedded into the image by modifying a small portion of the
encrypted image using a data hiding key. With an encrypted image containing additional data, if a
receiver has the data hiding key, he can extract the additional data. If the receiver has the encryption
key, he can decrypt the image, but cannot extract the additional data. If the receiver has both the data
hiding key and encryption key, he can extract the additional data and recover the original content by
exploiting the spatial correlation in natural images. The accuracy of data extraction is improved by
using a better scheme for measuring the smoothness of the received image, and uses the Side Match
scheme to further decrease the error rate of extracted bits.
The document summarizes a proposed user-friendly image sharing scheme that uses JPEG-LS prediction and LSB matching functions. The scheme encodes a secret image into meaningful shadow images using different prime numbers for different blocks, as determined by JPEG-LS prediction. It hides the prime number indicators in the least significant bits of pixels using LSB matching to prevent image degradation. The experimental results showed the reconstructed image quality was higher than previous schemes, making it suitable for applications requiring high quality images like medicine, military, or art.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
HYBRIDIZATION OF DCT BASED STEGANOGRAPHY AND RANDOM GRIDSIJNSA Journal
The document discusses a hybrid approach to steganography and visual cryptography for improved data security. It proposes combining principles of steganography, which hides data in a cover media, and visual cryptography, which encrypts images in a way that can be decrypted by human vision without algorithms. Specifically, it describes generating two random grids from a secret image that reveal the image when overlaid but hide it individually. The random grids are created by inverting or substituting pixels based on the secret image. This hybrid approach aims to provide stronger security than either technique alone by incorporating advantages of both.
Enhancement and Analysis of Chaotic Image Encryption Algorithms cscpconf
The focus of this paper is to improve the level of security and secrecy provided by the chaotic
map based image encryption.An encryption algorithm based on the Logistic and the Henon
maps is proposed. The algorithm uses chaotic iteration to generate the encryption keys, and
then carries out the XOR and cyclic shift operations on the plain text to change the values of
image pixels. Chaotic Map Lattice based image encryption algorithm suggested by Pisarchik is
also examined which is based on Logistic map alone. In experiments, the corresponding results
showed the proposed method is a promising scheme for image encryption in terms of security
and secrecy. At the end, we show the results of a security analysis and a comparison of both
schemes
This document describes an image encryption and decryption technique using chaos algorithms. It uses the chaotic properties of the Henon map and Arnold cat map. The Henon map is used to generate pseudo-random key values for pixel shuffling. Pixel positions of the input image are first shuffled using the Arnold cat map. Then they are shuffled again using the sorted key values from the Henon map. This encrypts the image. Decryption reverses the process to recover the original pixel values and image. Experimental results show the encrypted image is secure and the original image can be recovered accurately using the correct key during decryption. The technique provides efficient and secure encryption of images for transmission.
IMAGE ENCRYPTION BASED ON DIFFUSION AND MULTIPLE CHAOTIC MAPSIJNSA Journal
This document proposes an image encryption algorithm that uses diffusion and multiple chaotic maps. It begins by generating subkeys using chaotic logistic maps. The image is then encrypted using one subkey via logistic map transformation, diffusing the image. Additional subkeys are generated from four chaotic maps by hopping through various map orbits. The image is treated as a 1D array via raster and zigzag scanning, divided into blocks, and those blocks undergo position permutation and value transformation controlled by the chaotic subkeys, fully encrypting the image. Decryption reverses the process using the same subkeys.
IRJET- An Image Cryptography using Henon Map and Arnold Cat MapIRJET Journal
The document proposes a new symmetric image encryption algorithm based on the Henon chaotic system and Arnold Cat map. The algorithm uses Henon map to generate pseudo-random key values for pixel encryption and Arnold Cat map for pixel shuffling. Encryption involves XORing pixel values with keys and shuffling pixels, while decryption reverses these processes to recover the original image using the same keys.
The document proposes and evaluates a new digital image security scheme that uses Residue Number System (RNS) encoding/decoding and a modified Arnold transform algorithm. Key points:
- The encryption process encodes the plain image into residual images using RNS, then encrypts them by applying the modified Arnold transform multiple times.
- The decryption process decrypts the cipher image by applying the inverse Arnold transform, then decodes the residual images back into the plain image using RNS and the Chinese Remainder Theorem.
- Experimental results on images of different sizes show the scheme can encrypt/decrypt without information loss. Security analysis indicates resistance to statistical attacks like histograms and strong sensitivity to encryption keys.
The document proposes and evaluates a new digital image security scheme that uses Residue Number System (RNS) encoding/decoding and a modified Arnold transform algorithm. Key points:
- The encryption process encodes the plain image into residual images using RNS, then encrypts them using the modified Arnold transform.
- The decryption process decrypts the cipher image using the inverse Arnold transform, then decodes the residual images back into the plain image using RNS and the Chinese Remainder Theorem.
- Experimental results on test images of different sizes and formats show the scheme can effectively encrypt and decrypt without information loss. Security analysis also indicates resistance to statistical attacks like histograms and strong sensitivity to encryption keys.
Color Image Encryption and Decryption Using Multiple Chaotic MapsIJTET Journal
Owing to advances in communication technology, a bulk of visual digital data is being stored and transmitted over the internet now-a-days. Particularly millions and millions of images transfer through the network per day as per the statistics and a result, the security of image data is an important requirement. Image encryption algorithm is used to provide this security. In this paper, an image encryption algorithm based on confusion diffusion architecture that uses dynamic key space is proposed. An internal key generator is used to generate the initial seeds for the overall encryption scheme is proposed. With these initial seeds logistic map generates pseudo random numbers then these numbers are converted into permutation order for permutation. The diffusion bits are generated in parallel using the logistic map and manipulated with pixels confused. The image pixels are iteratively confused and diffused using permutation order and diffusion bits respectively to produce cipher image in minimum number of rounds. This paper proposes a new kind of initial seed generation that utilizes the combo of logistic and tent maps. Even all external seeds are same. The internal seeds will be totally different. This ensures the key sensitivity. The simulation results and analysis confirm that the satisfactory level of security is achieved in three rounds and overall encryption time is saved.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Encryption-Decryption RGB Color Image Using Matrix Multiplicationijcsit
An enhanced technique of color image encryption based on random matrix key encoding is proposed. To
encrypt the color image a separation into Red Green and Blue (R, G, B) channels will applied. Each
channel is encrypted using a technique called double random matrix key encoding then three new coding
image matrices are constructed. To obtain the reconstructed image that is the same as the original image
in the receipted side; simple extracted and decryption operations can be maintained. The results shown
that the proposed technique is powerful for color image encryption and decryption and a MATLAB and
simulations were used to get the results.
The proposed technique has high security features because each color component is separately treated
using its own double random matrix key which is generated randomly and make the process of hacking the
three keys very difficult.
HYBRIDIZATION OF DCT BASED STEGANOGRAPHY AND RANDOM GRIDSIJNSA Journal
With the increasing popularity of information technology in communication network, security has become an inseparable but vital issue for providing for confidentiality, data security, entity authentication and data origin authentication. Steganography is the scheme of hiding data into a cover media to provide confidentiality and secrecy without risking suspicion of an intruder. Visual cryptography is a new technique which provides information security using simple algorithm unlike the complex, computationally intensive algorithms used in other techniques like traditional cryptography. This technique allows visual information to be encrypted in such a way that their decryption can be performed by the Human Visual System (HVS), without any complex cryptographic algorithms. To provide a better secured system that ensures high data capacity and information security, a multilevel security system can be thought for which can be built by incorporating the principles of steganography and visual cryptography.
Hybrid chaos-based image encryption algorithm using Chebyshev chaotic map wit...IJECEIAES
The media content shared on the internet has increased tremendously nowadays. The streaming service has major role in contributing to internet traffic all over the world. As the major content shared are in the form of images and rapid increase in computing power a better and complex encryption standard is needed to protect this data from being leaked to unauthorized person. Our proposed system makes use of chaotic maps, deoxyribonucleic acid (DNA) coding and ribonucleic acid (RNA) coding technique to encrypt the image. As videos are nothing but collection of images played at the rate of minimum 30 frames/images per second, this methodology can also be used to encrypt videos. The complexity and dynamic nature of chaotic systems makes decryption of content by unauthorized personal difficult. The hybrid usage of chaotic systems along with DNA and RNA sequencing improves the encryption efficiency of the algorithm and also makes it possible to decrypt the images at the same time without consuming too much of computation power.
The key is the important part at any security system because it determines whether the system is strength or weakness. This paper aimed to proposed new way to generate keystream based on a combination between 3D Henoun map and 3D Cat map. The principle of the method consists in generating random numbers by using 3D Henon map and these numbers will transform to binary sequence. These sequence positions is permuted and Xoredusing 3D Cat map. The new key stream generator has successfully passed theNIST statistical test suite. The security analysisshows that it has large key space and its very sensitive initial conditions.
A new four-dimensional hyper-chaotic system for image encryption IJECEIAES
Currently, images are very important with the rapid growth of communication networks. Therefore, image encryption is a process to provide security for private information and prevent unwanted access to sensitive data by unauthorized individuals. Chaos systems provide an important role for key generation, with high randomization properties and accurate performance. In this study, a new four-dimensional hyper-chaotic system has been suggested that is used in the keys generation, which are utilized in the image encryption process to achieve permutation and substitution operations. Firstly, color bands are permuted using the index of the chaotic sequences to remove the high correlation among neighboring pixels. Secondly, dynamic S-boxes achieve the principle of substitution, which are utilized to diffuse the pixel values of the color image. The efficiency of the proposed method is tested by the key space, histogram, and so on. Security analysis shows that the proposed method for encrypting images is secure and resistant to different attacks. It contains a big key space of (2627) and a high sensitivity to a slight change in the secret key, a fairly uniform histogram, and entropy values nearby to the best value of 8. Moreover, it consumes a very short time for encryption and decryption.
A ROBUST CHAOTIC AND FAST WALSH TRANSFORM ENCRYPTION FOR GRAY SCALE BIOMEDICA...sipij
In this work, a new scheme of image encryption based on chaos and Fast Walsh Transform (FWT) has been proposed.
We used two chaotic logistic maps and combined chaotic encryption methods to the two-dimensional FWT of images.
The encryption process involves two steps: firstly, chaotic sequences generated by the chaotic logistic maps are used to
permute and mask the intermediate results or array of FWT, the next step consist in changing the chaotic sequences or
the initial conditions of chaotic logistic maps among two intermediate results of the same row or column. Changing the
encryption key several times on the same row or column makes the cipher more robust against any attack. We tested
our algorithms on many biomedical images. We also used images from data bases to compare our algorithm to those
in literature. It comes out from statistical analysis and key sensitivity tests that our proposed image encryption schemeprovides an efficient and secure way for real-time encryption and transmission biomedical images.
Comparative Performance of Image Scrambling in Transform Domain using Sinusoi...CSCJournals
With the rapid development of technology, and the popularization of internet, communication is been greatly promoted. The communication is not limited only to information but also includes multimedia information like digital Images. Therefore, the security of digital images has become a very important and practical issue, and appropriate security technology is used for those digital images containing confidential or private information especially. In this paper a novel approach of Image scrambling has been proposed which includes both spatial as well as Transform domain. Experimental results prove that correlation obtained in scrambled images is much lesser then the one obtained in transformed images.
The Quality of the New Generator Sequence Improvent to Spread the Color Syste...TELKOMNIKA JOURNAL
This paper shows a new technic applicable for the digital devices that are the result of the finite’s
effect precision in the chaotic dynamics used in the coupled technic and the chaotic map’s perturbation
technics used for the generation of a Pseudo-Random Number Generator (PRNGs).The use of the
pseudo- chaotic sequences coupled to the orbit perturbation method in the chaotic logistic map and the
NewPiece-Wise Linear Chaotic Map (NPWLCM). The pseudo random number generator’s originality
proposed from the perturbation of the chaotic recurrence. Furthermore the outputs of the binary sequences
with NPWLCM are reconstructed conventionally with the Bernoulli’s sequences shifts map to change the
shapes with the bitwise permetation then the results in simulation are shown in progress.After being
perturbed, the chaotic system can generate the chaotic binary sequences in uniform distribution and the
statistical properties invulnerable analysis. This generator also has many advantages in the possible useful
applications of spread spectrum digitalimages, such as sensitive secret keys, random uniform distribution
of pixels in Crypto system in secure and synchronize communication.
SLIC Superpixel Based Self Organizing Maps Algorithm for Segmentation of Micr...IJAAS Team
We can find the simultaneous monitoring of thousands of genes in parallel Microarray technology. As per these measurements, microarray technology have proven powerful in gene expression profiling for discovering new types of diseases and for predicting the type of a disease. Gridding, Intensity extraction, Enhancement and Segmentation are important steps in microarray image analysis. This paper gives simple linear iterative clustering (SLIC) based self organizing maps (SOM) algorithm for segmentation of microarray image. The clusters of pixels which share similar features are called Superpixels, thus they can be used as mid-level units to decrease the computational cost in many vision applications. The proposed algorithm utilizes superpixels as clustering objects instead of pixels. The qualitative and quantitative analysis shows that the proposed method produces better segmentation quality than k-means, fuzzy cmeans and self organizing maps clustering methods.
Hybrid chaotic map with L-shaped fractal Tromino for image encryption and dec...IJECEIAES
Insecure communication in digital image security and image storing are considered as important challenges. Moreover, the existing approaches face problems related to improper security at the time of image encryption and decryption. In this research work, a wavelet environment is obtained by transforming the cover image utilizing integer wavelet transform (IWT) and hybrid discrete cosine transform (DCT) to completely prevent false errors. Then the proposed hybrid chaotic map with L-shaped fractal Tromino offers better security to maintain image secrecy by means of encryption and decryption. The proposed work uses fractal encryption with the combination of L-shaped Tromino theorem for enhancement of information hiding. The regions of L-shaped fractal Tromino are sensitive to variations, thus are embedded in the watermark based on a visual watermarking technique known as reversible watermarking. The experimental results showed that the proposed method obtained peak signal-to-noise ratio (PSNR) value of 56.82dB which is comparatively higher than the existing methods that are, Beddington, Free, and Lawton (BFL) map with PSNR value of 8.10 dB, permutation substitution, and Boolean operation with PSNR value of 21.19 dB and deoxyribonucleic acid (DNA) level permutation-based logistic map with PSNR value of 21.27 dB.
This document proposes a medical image encryption technique that uses multiple chaotic maps. It utilizes the logistic map, Arnold cat map, and Baker's map within a triple data encryption standard (3DES) scheme. The technique encrypts and decrypts medical images efficiently and securely, making it suitable for transmission over insecure networks. It was tested using the transmission control protocol (TCP)/internet protocol (IP) to transfer encrypted images between a server and client. Experimental results found the method resistant to attacks while maintaining encryption performance.
With the development of information security, the traditional image encryption methods have become
outdated. Because of amply using images in the transmission process, it is important to protect the confidential image
data from unauthorized access. This paper presents a new chaos based image encryption algorithm, which can improve
the security during transmission more effectively utilizes the chaotic systems properties, such as pseudo-random
appearance and sensitivity to initial conditions. Based on chaotic theory and decomposition and recombination of pixel
values, this new image scrambling algorithm is able to change the position of pixel, simultaneously scrambling both
position and pixel values. Experimental results show that the new algorithm improves the image security effectively to
avoid unscramble, and it also can restore the image as same as the original one, which reaches to the purposes of image
safe and reliable transmission.
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COLOR IMAGE ENCRYPTION BASED ON MULTIPLE CHAOTIC SYSTEMS
1. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
DOI: 10.5121/ijnsa.2016.8503 39
COLOR IMAGE ENCRYPTION BASED ON MULTIPLE
CHAOTIC SYSTEMS
Yuting Xi, Xing Zhang and Ruisong Ye
Department of Mathematics, Shantou University
Shantou, Guangdong, 515063, P. R. China
ABSTRACT
This paper proposed a novel color image encryption scheme based on multiple chaotic systems. The
ergodicity property of chaotic system is utilized to perform the permutation process; a substitution
operation is applied to achieve the diffusion effect. In permutation stage, the 3D color plain-image matrix
is converted to a 2D image matrix, then two generalized Arnold maps are employed to generate hybrid
chaotic sequences which are dependent on the plain-image’s content. The generated chaotic sequences are
then applied to perform the permutation process. The encryption’s key streams not only depend on the
cipher keys but also depend on plain-image and therefore can resist chosen-plaintext attack as well as
known-plaintext attack. In the diffusion stage, four pseudo-random gray value sequences are generated by
another generalized Arnold map. The gray value sequences are applied to perform the diffusion process by
bitxoring operation with the permuted image row-by-row or column-by-column to improve the encryption
rate. The security and performance analysis have been performed, including key space analysis, histogram
analysis, correlation analysis, information entropy analysis, key sensitivity analysis, differential analysis
etc. The experimental results show that the proposed image encryption scheme is highly secure thanks to its
large key space and efficient permutation-substitution operation, and therefore it is suitable for practical
image and video encryption.
KEYWORDS
Generalized Arnold Map, Permutation, Substitution, Chaotic System, Image Encryption
1. INTRODUCTION
Nowadays more and more images and videos are transmitted through network due to the dramatic
developments of IT era. Cryptographic approaches are therefore critical for secure image storage
and distribution over public networks. As an effective technique to protect contents from being
intercepted, tampered and destroyed illegally, encryption has attracted much attention recently.
Chaos has been extensively adopted in encryption due to its ergodicity, pseudo-randomness and
sensitivity to initial conditions and control parameters, which are in line with the fundamental
requirements like confusion and diffusion in cryptography [1]. These properties make chaotic
systems a potential candidate for construction cryptosystems and many chaos-based image
encryption algorithms are proposed [2,3,4,5,6,7,8,9,10]. Ye proposed an image encryption
scheme with an efficient permutation-diffusion mechanism, which shows good performance,
including huge key space, efficient resistance against statistical attack, differential attack, known-
plaintext attack as well as chosen-plaintext attack [6]. In both the permutation and diffusion
stages, generalized Arnold maps with real number control parameters are applied to generate
pseudo-random sequences and therefore enlarge the key space greatly. Meanwhile, a two-way
diffusion operation is executed to improve the security of the diffusion function. Wang et al. [11]
employed Logistic map in the permutation process and Gravity Model in the diffusion process to
achieve good security and performance. Wen et al. constructed a new improved chaotic system by
2. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
40
a nonlinear combination of 1D Logistic map and sine map. Wang et al. [13] pointed out that
Arnold map has short periodic and is easy to be cracked by chosen-plaintext attack, so they used
this map in a different way to overcome the short periodic issue and enhance the security. In
[14,15], Chebyshev maps and ordinary differential equations were used to generate key stream
respectively to enhance the security and performance of the proposed image encryption. In [16],
Chen et al. presented a novel image encryption scheme using Gray code based permutation
approach. The new permutation strategy takes full advantage of Gray-code achievements, and is
performed with high efficiency. A plain pixel-related image diffusion scheme is introduced to
compose a complete cryptosystem.
In this paper, we use multiple chaotic systems to generate pseudo-random sequences for color
image encryption with permutation-substitution mechanism. In the permutation stage, we use two
chaotic systems to disorder the pixels’ positions of the plain-image based on the ergodicity of
generalized Arnold maps. Firstly, the 3D color plain-image matrix is converted to 2D image
matrix, then the sum of the pixel values of the 2D image matrix will be used to be the initial gray
value seed. The key streams applied to perform the permutation are yielded by randomly
choosing one of two generalized Arnold maps according to the yielded seed and each pixel’ gray
value of the plain-image. As a result, the permutation process strongly depends on the plain-
image and therefore the image encryption scheme can resist efficiently known-plaintext attack
and chosen-plaintext attack. In the diffusion stage, four vectors are generated by another
generalized Arnold map, then the gray values of row and column pixels of 2D image matrix are
mixed with the pseudo-random number sequences via bitxoring operation. The security and
performance of the proposed image encryption scheme has been analyzed thoroughly, including
statistical analysis (histograms, correlation coefficients, information entropy), key sensitivity
analysis, key space analysis, differential analysis, encryption rate analysis, etc. All the experiment
results show that the proposed image encryption scheme is highly secure and demonstrates
excellent performance.
The remainder of this paper is organized as follow. The proposed image encryption scheme is
presented in Section 2. Section 3 shows the experimental results and performance analysis.
Finally, conclusions are drawn in the last section.
2. THE PROPOSED IMAGE ENCRYPTION SCHEME
2.1. ARNOLD MAP
There are two stages in the proposed color image encryption scheme, permutation and diffusion.
Arnold map, a kind of two-dimensional area-persevering chaotic map, will be adopted in both
processes to shuffle the positions of the plain image pixels and weaken the relationship between
adjacent pixels. The mathematical formula of classical Arnold map is given by
1
1
1 1
mod1
1 2
n n
n n
x x
y y
+
+
= ,
(1)
where " x mod 1" represents the fractional part of a real number x . The map is area preserving
since the determinant of its linear transformation matrix is 1. The unit square is first stretched by
the linear transform matrix and then folded back to the unit square by the modulo operation,
which can be shown in Fig. 1. The 2D classical Arnold map can be generalized by introducing
two real parameters to Eq. (1):
3. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
41
1
1
1
mod1
1
n n
n n
x xp
y yq pq
+
+
= , +
(2)
where p q, are the real system control parameters. The generalized Arnold map (2) has one Lyapunov
characteristic exponent
2 2
1
1+ + +4
=1+ >1
2
ab a b ab
σ ,
so the generalized Arnold map is always chaotic for >0a , 0b > . The extension of ,a b from positive
integer numbers to positive real numbers is an essential generalization of the control parameters, enlarging
the key space significantly if it is used to design cryptosystem. Fig. 2 (a) shows an orbit of
( ) ( )0 0, = 0.5231,0.7412x y with length 1500 generated by the generalized Arnold map (2) with
=5.324, =18.2a b , the x-coordinate and the y-coordinate sequences of the orbit are plotted in Fig. 2 (b) and
Fig. 2(c) respectively. Some other good dynamical features in the generalized Arnold map, such as
desirable auto-correlation and cross-correlation features are demonstrated in Figs. 2(d)-(f). The good
chaotic nature makes it can provide excellent random sequence, which is suitable for designing
cryptosystem.
Fig.1. The Arnold map
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200 250 300 350 400 450 500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
k
x(k)
(a) The orbit of (0.5231, 0.7412) (b) Sequence { , 0, ,1500}kx k = L
0 50 100 150 200 250 300 350 400 450 500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
k
x(k)
(c) Sequence { 0, ,1500}ky k = L, (d) Auto-correlation of { , 0, ,1500}kx k = L
4. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
42
(e) Auto-correlation of { , 0, ,1500}ky k = L (f) Cross-correlation of kx and ky sequences
Fig.2. Orbit derived from the generalized Arnold map with a=5.324, b=18.2.
2.2. PERMUTATION PROCESS
In the permutation process, the 3D color plain-image matrix A with size 3M N× × is converted
to a 2D image matrix B with size 3M N× firstly. Then we will create a zero vector C with
length 3M N× × . Now what we need to do is just put the 3M N× × pixels in B into C randomly.
In this image encryption scheme, we realize it by using two generalized Arnold maps, the detail
operation procedures are described as follows.
Step 1. Set the appropriate parameters 1 1a b, , 2 2a b, for two generalized Arnold maps and
their common initial values x y, . Another sufficiently large integer 1M is also set to be the iterate
times, 1M is usually set to be one integer number close to 3M N× × . In this paper, we set 1M to
be 3M N× × .
Step 2. Modulate x y, by iterating two generalized Arnold maps for 1N times respectively to
avoid the harmful effect of transitional procedure of the chaotic orbits. 1N can be set as a secret
key. For example, we set 1 200N = in the experiments.
Step 3. Calculate
3
1 1
( ) ( 256)
M N
i j
sum B i j p mod sum
= =
= , , = , .∑∑ (3)
We initialize the index matrix index to be zero matrix with size 3M N× and set the initial ergodic
counting number 0K = . For 1 1i M= : , we execute Steps 4-6.
Step 4. Calculate ( 2)q mod p= , , q is equal to 0 or 1, so we can use q to dynamically assign
one generalized Arnold map to generate hybrid chaotic sequences. If 0q = , we iterate the first
generalized Arnold map once to generate new x y, , otherwise, the second generalized Arnold
map will be iterated.
Step 5. The position coordinates ( )s t, can be calculated by
( ) 1 ( 3 ) 1,s floor x M t floor y N= × + , = × + (4)
where ( )floor x returns the nearest integer less than or equal to x .
5. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
43
Step 6. If ( ) 0index s t, = , then set 1K K= + , ( ) ( )C k B s t= , , ( )p B s t= , and ( ) 1index s t, = ;
otherwise, skip this step.
Step 7. Generally speaking, the traversing counting number K is often less than 3M N× ×
after the loop Steps 4-6 is finished. So we need to put the pixels which are not traversed orderly
from left to right and top to bottom into the remainder part of vector C . We finally converted the
vector C into one 2D matrix C with height M and width 3N .
2.3. SUBSTITUTION PROCESS
In the diffusion stage, four vectors are generated by another generalized Arnold map, then the
gray values of row and column pixels of 2D image matrix C are masked with the four pseudo-
random number sequences via bitwise XOR operation. The detail operation procedures are
described as follows.
Step 1. For an given generalized Arnold map with parameter a b, and initial value 1 1x y, , we
modulate 1 1x y, by iterating this generalized Arnold map for 100 times to avoid the harmful effect
of transitional process.
Step 2. Generate two chaotic sequences ( ) ( ) 1x i y i i M, , = : by the generalized Arnold map,
then two row sequence SVR and IVC with length M will be generated by
( ) ( ( ) 256)
( ) ( ( ) 256) 1, ,
SVR i floor x i
IVC i floor y i i M
= × ,
= × , = .L
(5)
Step 3. Generate two chaotic sequences 1( ) 1( ) 1 3x i y i i N, , = : by the generalized Arnold map
with initial values ( ) ( )x M y M, , then two row sequences SVC and IVR with length 3N will be
generated by
( ) ( ( ) 256)
( ) ( ( ) 256) 1, ,3
IVR i floor x i
SVC i floor y i i N
= × ,
= × , = .L
(6)
Step 4. Get the cipher image CC by masking C with the four pseudo-random number
sequences via bitwise XOR operation.
(1 ) (1 ) (1)CC C IVR SVR,: = ,: ⊕ ⊕ , ( ) ( ) ( 1 ) ( ) 2, , ,CC i C i CC i SVR i i M,: = ,: ⊕ − ,: ⊕ , = L
( 1) ( 1) (1)CC CC IVC SVC′:, = :, ⊕ ⊕ , ( ) ( ) ( 1) ( ) 2, ,3CC j CC j CC j SVC j j N:, = :, ⊕ :, − ⊕ , = .L
3. SECURITY AND PERFORMANCE ANALYSIS
According to the basic principle of cryptology [17], an ideal encryption scheme should have large
key space to make brute-force attack infeasible, it should also well resist various kinds of attacks
like statistical attack, differential attack, chosen-plaintext attack, etc. In this section, the security
analysis has been performed on this proposed encryption scheme, such as, key space analysis,
statistical analysis, correlation between plain and cipher images, key sensitivity analysis,
differential analysis, encryption rate analysis, etc. Experimental simulations and extensive
performance analysis for the proposed scheme and the comparable scheme proposed in [18] have
been carried out. The cipher keys for the comparable algorithm are the same as those in [18]. All
the simulations are performed on a computer equipped with an Intel Xeon 2.13 GHz CPU 2GB
6. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
44
memory and 300GB hard disk space running Windows 7 Professional. The compilation platform
is Matlab 7.1. The experimental results prove the superior security and high efficiency of this
scheme.
3.1. KEY SPACE ANALYSIS
Key space is composed of all the possible cipher keys in the proposed image encryption scheme.
An ideal image encryption scheme should contain sufficiently large key space for compensating
the degradation dynamics in PC and should be large enough to effectively resist brute-force attack
and prevent invaders decrypting original data even after they invest large amounts of time and
resources. It was pointed out that the key space should beat at least 100
2 in order to resist all kinds
of common attacks [9]. Regarding our proposed image encryption scheme, the key space consists
of the initial values x y, and parameters 1 1a b, , 2 2a b, of the two chaotic systems in permutation
process and the initial values 1 1x y, , parameters a b, in diffusion process. All the initial values
1 1x y x y, , , and the control parameters 1 1 2 2a b a b a b, , , , , are floating point numbers. If they are
represented as floating number with precision 14
10−
as we have used in the key sensitivity test, the
total number of cipher keys is 14 10 140
10 10×
= , which is approximately equal to 465 bits. The key
space is large enough to resist the brute-force attack.
3.2. STATISTICAL ANALYSIS
Shannon pointed out the possibility to solve many kinds of ciphers by statistical analysis [17].
Therefore, passing the statistical analysis on cipher-image is crucial for a cryptosystem. Indeed,
an ideal cryptosystem should be robust against any statistical attack. To prove the security of the
proposed encryption scheme, we perform the following statistical tests.
(i) Histogram analysis. A histogram shows the distribution of pixel values in an image by plotting
the number of pixels at each grey level. An ideal histogram of an effectively ciphered image
should be uniform and much different from that of the plain image. For an 8-bit gray image, there
are 256 different possible intensities, the histogram shows the distribution of pixels among those
256 intensity values. For a 24-bit color image, we can draw the histogram for red, green, blue
channels respectively. Encrypt the color image Lena one round with cipher keys
(0 3201 0 6317 0 4807 0 7815 100 33 4 8 62 48). , . , . , . , , , , , , . Then we plot the histograms for red, green, blue
channels of Lena and the cipher-image in Fig. 3. It is obvious that the histograms of the cipher
image are uniform and quite different from that of the plain image, which implies that the
redundancy of the plain image is successfully hidden after the encryption, so it does not provide
any useful information for statistical attacks.
(a) plain-image Lena (b) cipher-image of Lena
7. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
45
0 50 100 150 200 250
0
100
200
300
400
500
600
700
800
0 50 100 150 200 250
0
100
200
300
400
500
600
0 50 100 150 200 250
0
100
200
300
400
500
600
700
(c) (d) (e)
0 50 100 150 200 250
0
100
200
300
400
500
600
0 50 100 150 200 250
0
100
200
300
400
500
600
700
800
900
0 50 100 150 200 250
0
100
200
300
400
500
600
(f) (g) (h)
Fig. 3. The histogram analysis result. (c)-(e) Red, green, blue channel component of plain-image; (f)-(h)
Red, green, blue channel component of cipher-image.
(ii) Correlation analysis of adjacent pixels. It is of common sense that in a meaningful image
each pixel is highly correlated with its adjacent pixels either in horizontal, vertical or diagonal
direction. For an ideal encryption technique, the cipher image should get rid of the drawback of
high correlation between pixels. In order to quantify and compare the correlation between plain-
image and cipher-image, we calculate the correlation coefficients for all the pairs of horizontally,
vertically and diagonally adjacent pixels of them respectively. The correlation coefficients of the
selected pairs in horizontal, vertical and diagonal direction are calculated according to Eq. (7),
where ix and iy are the ith selected pair pixels. T is the total pixel pairs’ number of the sample.
The correlation coefficients in horizontal, vertical or diagonal direction of the selected pairs for
plain-image Lena and the cipher-image are given in Table 1. From the data in Table 1, we can see
that even though there is high correlation in plain-image, the correlation in cipher-image is
negligible. The proposed image encryption technique significantly reduces the correlation
between the adjacent pixels of the plain-image.
( )
( ) ( )
cov ,
,
x y
Cr
D x D y
= ( ) ( )( ) ( )( )
1
1
cov ,
T
i i
i
x y x E x y E y
T =
= − −∑ ,
( ) ( ) ( )( )
2
1 1
1 1
,
T T
i i
i i
E x x D x x E x
T T= =
= = −∑ ∑ . (7)
(iii) Information entropy analysis. Information entropy is one of the criteria to evaluate the
randomness and the unpredictability of an information source. The entropy ( )H m of a message
source m is defined by
2 1
2
0
( ) ( )log ( )( )
L
i i
i
H m P m P m bits
−
=
= −∑ , (8)
8. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
46
where m is the source, L is the number of bits to represent the symbol im , and ( )iP m is the
probability of the symbol im . For a truly random source consist of 2L
symbols, the entropy is L.
So for an effective encryption algorithm, the entropy of the cipher image with 256 gray levels
should be close to 8. Otherwise, the information source is not random enough and there exists a
certain degree of predictability, which makes the encryption algorithm insecure.
For a 24-bit color image, the information entropy for each color channel( Red, Green and Blue)
is given by
8
2 1
2
0
1
( ) ( ( )log
( )
R G B R G B
i R G B
i i
H m P R I
P RI
−
/ / / /
/ /
=
= −∑ .
We have calculated the information entropy for plain-image Lena and its cipher-image by the
proposed encryption scheme. The value of information entropy for the cipher-image produced by
the proposed image encryption scheme is very close to the expected value of truly random image,
i.e., 8bits. Therefore the proposed encryption scheme shows extremely robustness against entropy
attacks. For comparison, we also calculate the information entropy of cipher image of Lena by
algorithm in [18]. The results are shown in Table 2. We can see the information leakage in this
proposed encryption procedure is negligible and when faced with entropy analysis attack, this
proposed encryption show good performance.
Table 1. Correlation between adjacent pixels of plain-image and cipher-image.
Image color channel horizontal vertical diagonal
Plain-image Lena R 0.9446 0.9720 0.9212
Cipher-image of Lena R -0.0020 0.0030 0.0035
Plain-image Lena G 0.9465 0.9729 0.9360
Cipher-image of Lena G -0.0036 0.0007 0.0041
Plain-image Lena B 0.9046 0.9465 0.8677
Cipher-image of Lena B 0.0040 0.0043 0.0031
(iv) Correlation between plain-images and cipher-images. For an efficient encryption scheme, the
cipher image should be much different from plain image and has low correction with plain image.
We have already analyzed the correction between plain-image and cipher-image by computing
the two-dimensional correlation coefficients between various color channels of plain-image and
cipher-image. The two-dimensional correlation coefficients are calculated by
1
1 1
2 21 1
1 1 1 1
( )( )
( ( ) )( ( ) )
H W
i j i jH W
i j
AB
H W H W
i j i jH W H W
i j i j
A A B B
C
A A B B
, ,×
= =
, ,× ×
= = = =
− −
=
− −
∑∑
∑∑ ∑∑
,
1 1 1 1
1 1H W H W
i j i j
i j i j
A A B B
H W H W
, ,
= = = =
= , = ,
× ×
∑∑ ∑∑
where A represents one of the three channels of plain-image, B represents one of the three
channels of cipher-image. A and B are the mean value of the two-dimension matrix A and B
9. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
47
respectively. H and W are the height and width of image A or B. So we can get nine different
correlation coefficients for a pair of plain-image and cipher-image ( RR RG RB GR GG GBC C C C C C, , , , , ,BRC
BGC and )BBC . For example, RRC means the correlation between red channel of plain-image and
red channel of cipher-image. The results of correction between Lena and its cipher image are
shown in Table.3. We can see that the correlation between various channels of plain image and
cipher image are very small, hence the cipher-image owns the characteristic of a random image.
3.3. KEY SENSITIVITY ANALYSIS
Extreme key sensitivity is an essential feature of an effective cryptosystem, and key sensitivity of
a cryptosystem can be observed in two ways: ( )i completely different cipher-images should be
produced even if we use slightly different keys to encrypt the same plain-image. ( )ii the cipher
image cannot be correctly decrypted even if there is tiny difference between encryption and
decryption keys. For key sensitivity analysis, we will use the following cipher keys to perform the
simulation ( one is master cipher key, the other keys are produced by introducing a sight change
to one of the parameter of master cipher with all other parameters remain the same) . Master
cipher key: MKEY (0 3201 0 6317 0 4807 0 7815 100 33 4 8 62 48). , . , . , . , , , , , , ; Ten slightly different keys:
SKEY1 14
(0 3201 10 0 6317 0 4807 0 7815 100 33 4 8 62 48)−
. − , . , . , . , , , , , , ,
SKEY2 14
(0 3201 0 6317 10 0 4807 0 7815 100 33 4 8 62 48)−
. , . − , . , . , , , , , , ,
SKEY3 14
(0 3201 0 6317 0 4807 10 0 7815 100 33 4 8 62 48)−
. , . , . − , . , , , , , , ,
SKEY4 14
(0 3201 0 6317 0 4807 0 7815 10 100 33 4 8 62 48)−
. , . , . , . − , , , , , , ,
SKEY5 14
(0 3201 0 6317 0 4807 0 7815 100 10 33 4 8 62 48)−
. , . , . , . , − , , , , , ,
SKEY6 14
(0 3201 0 6317 0 4807 0 7815 100 33 10 4 8 62 48)−
. , . , . , . , , − , , , , ,
SKEY7 14
(0 3201 0 6317 0 4807 0 7815 100 33 4 10 8 62 48)−
. , . , . , . , , , − , , , ,
SKEY8 14
(0 3201 0 6317 0 4807 0 7815 100 33 4 8 10 62 48)−
. , . , . , . , , , , − , , ,
SKEY9 14
(0 3201 0 6317 0 4807 0 7815 100 33 4 8 62 10 48)−
. , . , . , . , , , , , − , ,
SKEY10 14
(0 3201 0 6317 0 4807 0 7815 100 33 4 8 62 48 10 )−
. , . , . , . , , , , , , − .
(i)To evaluate the key sensitivity in the first case, we encrypt plain-image Lena with MKEY and
get the first cipher image, then we encrypt Lena with SKEY1-SKEY10 and get other ten cipher
images. We have computed the correlation coefficients between the first cipher image and the
other ten cipher images. The results are given in Table 4. From the table, we can see that all the
correlation coefficients are very small which indicate that even there is only slightly difference
between the cipher keys, the cipher images are greatly different. Hence the proposed encryption
scheme is extremely sensitive to the cipher keys.
(ii)Decryption using keys with slight difference are also performed in order to evaluate the key
sensitivity of the second case. Firstly, we decrypt the cipher image using MKEY and we get the
plain-image Lena. Secondly, ten decrypted images are generated when we decrypt the cipher-
image using SKEY1-SKEY10. We have computed the correlation coefficients between Lena and
this ten decrypted images, the results have been given in Table 5. From the data, we can see even
there is only a slightly difference between the decipher keys, the deciphered images have low
correlation coefficients with the plain-image Lena. So for the second case, the proposed
encryption scheme is of highly sensitive to the cipher keys too.
10. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
48
Table 2. Information entropy analysis.
Image R G B
Plain-image Lena 7.2763 7.5834 7.0160
Cipher-image 7.9972 7.9971 7.9977
Cipher-image [18] 0.9973 7.9973 7.9967
Table 3. Correlation between plain-image Lena and its cipher-image.
Cipher-image R G B
Plain-image Lena R -0.0037 -0.0049 0.0001
G 0.0044 -0.0052 0.0014
B 0.0045 -0.0020 0.0024
3.4. DIFFERENTIAL ATTACK ANALYSIS
For an efficient encryption scheme, a slightly difference in the plain image should cause amount
of difference in the cipher image. Two indicators, which are number of pixels change rate
(NPCR) and unified average changing intensity (UACI), are used to measure the influence of one
pixel change in the plain image on the cipher image. In order to calculate NPCR and UACI,
suppose two plain images 1I and 2I with difference in only one pixel, and their cipher images are
denoted as 1C and 2C . Then we create a matrix D, when 1 2( ) ( )C i j C i j, = , , ( ) 0D i j, = ; otherwise,
( ) 1D i j, = . NPCR and UACI are calculated by
( )
100
i j
D i j
NPCR %
W H
,
,
= × ,
×
∑ 1 2( ) ( )1
( ) 100
255i j
C i j C i j
UACI %
W H ,
| , − , |
= ×
×
∑ ,
where W, H are the width and height of the images. We have performed the differential attack
analysis in two cases: ( )i Encrypt the plain-image Lena using the proposed encryption scheme
and get a cipher image. Add 1 to the last pixel value of Lena, then we get a new plain image.
Encrypt the new plain-image, then the new cipher image is compared with the old cipher image to
calculate NPCR and UACI. The results are given in Table 6. ( )ii Randomly choosing 10
pixels( one at a time ) from Lena and add their values by one unit. The average NPCR and UACI
are given in Table 7. From the two tables, we can see even though the algorithm in [18] have
better performance on NPCR in Table 6, but on the whole, the proposed encryption scheme is
more stable and has better performance on differential analysis.
Table 4. Key sensitivity analysis I.
Correlation coefficients between the encrypted images obtained using MKEY and
SKEY1 SKEY2 SKEY3 SKEY4 SKEY5 SKEY6 SKEY7 SKEY8 SKEY9 SKEY10
Crr 0.0030 -0.0089 -0.0011 -0.0012 0.0021 -0.0030 -0.0000 -0.0021 -0.0080 -0.0027
Crg 0.0027 -0.0039 0.0014 -0.0066 -0.0042 0.0024 0.0024 0.0040 -0.0044 0.0008
Crb 0.0088 -0.0016 -0.0021 0.0084 0.0033 0.0010 0.0047 0.0078 -0.0013 -0.0041
Cgr 0.0001 -0.0038 0.0063 -0.0043 -0.0009 0.0006 -0.0048 -0.0012 0.0020 0.0006
Cgg 0.0009 -0.0005 -0.0010 -0.0025 -0.0042 0.0025 0.0025 -0.0043 0.0039 -0.0018
Cgb 0.0018 0.0004 0.0015 0.0032 0.0048 -0.0003 -0.0029 -0.0036 0.0044 -0.0016
Cbr 0.0064 0.0009 0.0026 0.0009 0.0037 0.0010 0.0025 0.0070 0.0020 -0.0063
Cbg 0.0048 -0.0006 -0.0009 0.0021 0.0005 0.0090 -0.0046 -0.0008 0.0032 -0.0003
Cbb 0.0033 -0.0048 -0.0007 0.0038 0.0033 -0.0032 -0.0054 -0.0006 0.0060 0.0027
11. International Journal of Network Security & Its Applications (IJNSA) Vol.8, No.5, September 2016
49
Table 5. Key sensitivity analysis II.
Correlation coefficients between the decrypted images obtained using MKEY and
SKEY1 SKEY2 SKEY3 SKEY4 SKEY5 SKEY6 SKEY7 SKEY8 SKEY9 SKEY10
Crr 0.0086 0.0038 -0.0065 0.0004 0.0158 0.0015 0.0014 0.0119 0.0097 0.0064
Crg 0.0067 0.0081 -0.0061 0.0044 0.0011 -0.0054 0.0050 0.0046 0.0147 0.0065
Crb 0.0046 0.0014 -0.0005 -0.0051 -0.0023 -0.0078 0.0116 0.0027 0.0090 -0.0044
Cgr 0.0097 0.0054 -0.0044 -0.0014 0.0106 -0.0026 0.0035 0.0091 0.0092 0.0035
Cgg 0.0052 0.0086 -0.0063 0.0015 0.0012 -0.0061 0.0068 0.0090 0.0137 0.0058
Cgb 0.0053 0.0030 -0.0003 -0.0056 -0.0026 -0.0124 0.0103 0.0041 0.0043 -0.0028
Cbr 0.0099 0.0046 -0.0043 -0.0024 0.0099 -0.0029 0.0044 0.0059 0.0088 0.0007
Cbg 0.0050 0.0047 -0.0048 -0.0006 0.0003 -0.0050 0.0057 0.0086 0.0095 0.0046
Cbb 0.0042 0.0027 0.0016 -0.0063 -0.0021 -0.0132 0.0071 0.0021 0.0011 -0.0008
Table 6. Differential analysis I.
NPCR(%) UACI(%)
Red Green Blue Red Green Blue
The proposed scheme 99.61 99.59 99.59 33.55 33.60 33.55
The scheme proposed in [18] 99.57 99.64 99.65 33.42 33.19 33.38
Table 7. Differential analysis II.
Average NPCR(%) Average UACI(%)
Red Green Blue Red Green Blue
The proposed scheme 99.64 99.60 99.60 33.44 33.52 33.53
The scheme proposed in [18] 79.68 87.69 79.66 26.75 29.31 26.69
4. CONCLUSIONS
In this paper, we proposed a color image encryption scheme based on multiple chaotic systems. In
this encryption algorithm, a parameter depending on the plain-image is applied to dynamically
assign two generalized Arnold maps to generate chaotic sequences, so the proposed encryption
scheme can well resist chosen/known plain-image attack and the chaotic sequences show good
chaotic properties. In the diffusion stage, four vectors are generated by another generalized
Arnold map, then the gray values of row and column pixels of 2D image matrix are mixed with
the pseudo-random number sequences via bitxoring operation, which greatly weaken the
correction between plain-image and cipher-image. Simulation results show that the proposed
encryption scheme has good performance to resist all kinds of attacks.
ACKNOWLEDGEMENTS
This research is supported by National Natural Science Foundation of China (No. 11271238).
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AUTHORS
Yuting Xi, master degree candidate at department of mathematics in Shantou University.
Xing Zhang, master degree candidate at department of mathematics in Shantou University.
Ruisong Ye was born in 1968 and received the B.S. degree in Computational Mathematics in 1990 from
Shanghai University of Science and Technology, Shanghai, China and the Ph. D. degree in Computational
Mathematics in 1995 from Shanghai University, Shanghai, China. He is a professor at Department of
Mathematics in Shantou University, Shantou, Guangdong, China since 2003. His research interest includes
bifurcation theory and its numerical computation, fractal geometry and its application in computer science,
chaotic dynamical system and its application in computer science, specifically the applications of fractal
chaotic dynamical systems in information security, such as, digital image encryption, digital image hiding,
digital image watermarking, digital image sharing.