Digital Image Cryptography using Index Keys

Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 Available Online at www.ijcsmc.com International Journal of Computer Science and Mobile Computing A Monthly Journal of Computer Science and Information Technology ISSN 2320–088X IMPACT FACTOR: 7.056 IJCSMC, Vol. 12, Issue. 2, February 2023, pg.26 – 37 Digital Image Cryptography using Index Keys Prof. Ziad Alqadi; Prof. Qazem Jabber Albalqa Applied University Faculty of Engineering Technology Jordan Amman DOI: https://doi.org/10.47760/ijcsmc.2023.v12i02.003 Abstract: A simple and easy to implement method of data cryptography will be introduced. This method can be easily used to encrypt-decrypt digital images with any type and size, it can be used to treat gray images, color images and secret messages. The simplified encryption and decryption function will minimize the required time for cryptography and they will use a simple operation of pixels’ values rearrangement to apply encryption and decryption. The values rearrangement is to be applied using a generated index key. The index key is generated using the chaotic logistic key formed by running a chaotic logistic map model using a selected values of chaotic parameters. The proposed method will increase the level of image protection by using a private key which is capable to increase the key space to resist hacking attacks. The proposed method will be tested and implemented using various images, the obtained results will be analyzed to prove the quality, efficiency and sensitivity of the proposed method. Keywords: Cryptography, PK, index key, CLK, CLMM, quality, speed, sensitivity. Introduction Digital images [48-54] are represented by a 2D matrix (gray image) or a 3D matrix (color image: one 2D matrix for each color: red, green and blue) (see figure 1) [1-10], each element in the matrix represents the color value and it falls within the range 0 to 255. Color histogram is a vector of 256 elements, and each element value points to the repetition of this value in the image, histogram can be easily used to test the image quality [40-47]. Digital images are very popular data types and they are used in various computer applications. Digital image may be secret or private or holding secret data, thus it requires protection from being hacked by unauthorized persons. One of the most popular methods used to protect digital images is data cryptography method. Cryptography means image encryption before sending and image decryption after image receiving [30-35]. The crypto system as shown in figure 2 contains: Source image (plain image), encrypted image (cipher image), decrypted image (plain image), private key (PK), encryption function and decryption function [35-39]. © 2023, IJCSMC All Rights Reserved 26 Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 The objectives of this paper research is to introduce a method of image cryptography which must satisfy the following requirements [15-20]: - Multipurpose using: the method will be used to encrypt-decrypt color images, gray images and secret messages. - Image protection: Providing a high level of security by using a complicated secret private key. - High speed of processing: Simplifying the encryption and decryption functions and minimizing the encryption-decryption time, thus maximizing the throughput of data cryptography process. Figure 1: Color image and representations Figure 2: Crypto system © 2023, IJCSMC All Rights Reserved 27 Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 - Image quality: the encrypted image must have a low quality, it must be damaged image and the quality parameters measured between the source image and encrypted image must satisfy the requirements listed in table 1 [26-30] (High mean squ8are error (MSE), low peak signal to noise ratio (PSNR), low correlation coefficient (CC), and high number of values change ratio (NVCR)). While the quality of the decrypted image must be very high and the decrypted image must be identical to the source image) [20-25]. Table 1: Quality requirements Quality parameters Measured between source and encrypted images Measured between source and decrypted images MSE PSNR NVCR(%) Low CCred, CCgreen, CCblue Low High 0 Infinite 1 0 High Many methods were introduced and used to encrypt-decrypt digital data, many of these methods were based on the standards of data cryptography (DES and AES) [8-12], these methods are suitable to deal with small data sizes, and they use a fixed data blocks and the efficiency of these methods is low. In [1] the authors provided a performance comparisons of standard methods and it was shown that DES method provided a throughput of 7988 bytes per second, 3DES provided 2683 bytes per second, AES provided 5326 bytes per second, while BF provided 10176 bytes per second. These throughputs are too small and it is not convenient to use them to encrypt-decrypt large size data such as digital color image. In [13] the authors introduced a method base on chaotic map model, the throughput was improved and reached 0.1691 M byte per second, while in [14] the introduced method gave a throughput equal 0.71 M byte per second. In [2] the authors made performance comparisons between chaotic and non-chaotic methods of data cryptography, the final results of comparisons are shown in table 2. Table 2: Cryptography methods performance comparisons [2-7] Method Throughput(K bytes per second) Non-chaotic approach[2] 170.3906 Chaotic approach{2] 141.2305 Hyper Chaotic approach[2] 636.3379 In [3] 888.8867 In [4] 638.4082 In [5] 911.0352 In [6] 360.4102 In [7] 384.9609 In [3] the authors provided a robust and fast image encryption scheme based on a mixing technique. In [4] the authors provided cosine-transform-based chaotic system for image encryption, while in [5] the authors introduced a novel image encryption algorithm based on polynomial combination of chaotic maps and dynamic function generation. In [6] the authors introduced Multiple-image Encryption Algorithm Based on DNA Encoding and Chaotic System, while in [7] the authors produced a multiple-image encryption with bit-plane decomposition and chaotic maps, these methods provided good quality a have various speeds as shown in table 2. © 2023, IJCSMC All Rights Reserved 28 Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 The Proposed Method The proposed method uses a PK, which contains the values of the chaotic parameters required to run a chaotic logistic map model (CLMM) to generate a chaotic logistic key (CLK), the generated CLK is to be converted to index key using the mat lab function sort. The length of the index key is equal 256 to cover the color range 0 to 255. The following is a sequence of operation needed to generate the index key: The contents of the index key depend on the selected values of CLMM parameters, making any changes in these values will change the index key, and the key is very sensitive to the selected values of the PK, figure 3 shows how the index key will be changed when changing the CLMM parameters: Figure 3: Changing CLMM parameters changes the index keys The index key will contain the values from 0 to 255, this key will be used to encrypt-decrypt the pixel’s values by applying pixels’ values rearrangement, in the encryption phase the pixel value will be replaced by the contents of the index key pointed by the pixel value, in the decryption phase the pixel value will be replaced by the index of the index key which contains the pixel value. The pixel’s rearrangement operation is a very simple operation and it will simplify the process of encryption and decryption. Suppose that the pixel’s range is 0 to 9, the index key here must contain 10 elements, figures 4 and 5 show an examples of using the generated index keys to apply image encryption and decryption: © 2023, IJCSMC All Rights Reserved 29 Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 Figure 4: Using index key (example 1) Figure 5: Using index key (example 2) The proposed encryption phase can be implemented applying the following steps: Step 1: Image preparation: Get the image, retrieve the image size, this step can be implemented applying the following mat lab sequence of operations: Step 2: Index key generation: Get the PK, run CLMM to generate CLK, convert CLK to index key, this step can be implemented applying the following mat lab sequence of operations: © 2023, IJCSMC All Rights Reserved 30 Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 Step 3: Pixels values rearrangement: for each pixel in the image use the index key to rearrange the values, , this step can be implemented applying the following mat lab sequence of operations: The decryption phase can be implemented using the same steps but the rearrangement must be performed using the following sequence of mat lab operations: Implementation and Results Discussion The proposed method was implemented using various images, figures 6, 7, and 8 show a sample outputs of the process of implementation: Figure 6: Sample of source image © 2023, IJCSMC All Rights Reserved 31 Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 Figure 7: Encrypted image and histograms Red histogram Decrypted image 3000 2000 1000 0 0 Green histogram 200 Blue histogram 3000 3000 2000 2000 1000 1000 0 100 0 0 100 200 0 100 200 Figure 8: Decrypted image and histogram From figures 7 and 8 we can visually prove the quality of the proposed method, the encrypted image is a damaged image, while the decrypted image is identical to the source image. The speed of the proposed method was tested, several images were selected and processed using the proposed method, table 3 shows the obtained speed results (encryption time (ET) and throughput (TP)): Image 1 2 3 4 5 6 Average Size(byte) 150849 518400 1890000 4326210 5140800 6119256 Table 3: speed results ET(second) 0.0400 0.1620 1.0300 3.1250 3.9940 5.1600 TP(K bytes per second) 3682.8 3125.0 1791.9 1351.9 1257.0 1158.1 2061.1 From table 3 we can see that the proposed method gave good speed results for all images (with any size), the results are better than the results of the methods used by other authors (which are listed in the introduction part), the © 2023, IJCSMC All Rights Reserved 32 Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 proposed method speeds up the process of cryptography and it provides a significant speed up comparing with other existing methods of data cryptography as shown in table 4: Method Table 4: Speed comparisons Throughput(K bytes per second) Non-chaotic approach[2] Chaotic approach{2] Hyper Chaotic approach[2] In [3] In [4] In [5] In [6] In [7] Proposed 170.3906 141.2305 636.3379 888.8867 638.4082 911.0352 360.4102 384.9609 2061.1 Speed up method 12.0963 14.5939 3.2390 2.3187 3.2285 2.2624 5.7188 5.3541 1.0000 of the proposed The proposed method was tested for quality, the selected images were processed and the quality parameters were calculated, the obtained values showed that the proposed method satisfied the quality requirements listed in table 1, table 5 shows the quality parameters measured between the source images and the encrypted ones. Image 1 MSE 12535 2 10509 3 10964 4 9317.9 5 9242.9 6 6856.2 Remarks High Table 5: Quality parameters of the encrypted images PSNR CCr, CCg, CCb 16.4622 0.0165, -0.0105, 0.00084836 18.2256 0.0196, 0.0079, 0.0084 17.8011 0.0190, 0.0129, 0.0803 19.4284 0.0020, 0.0515, 0.0125 19.5092 0.0027, 0.0347, 0.0302 22.4961 -0.0393, 0.0318, 0.0020 Low Low NVCR(%) 100 100 100 100 100 100 High The generated decrypted image depends on the selected values of the PK, the encryption and decryption phases must use the same PK, any changes in the PK during the decryption phase will be considered as a hacking attempt by producing a damaged decrypted image. Image 2 was processed and encrypted using PK1, the decrypted image was obtained using each of the following PKs: © 2023, IJCSMC All Rights Reserved 33 Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 Figures 9 and 10 show the encrypted and decrypted images, while table 6 shows the quality parameters between the source image and the decrypted images using various PKs in the decryption phase. Figure 9: Encrypted image using PK1 Figure 10: Decrypted image using other PK Table 6: Quality parameters of the decrypted images using various PKs MSE PSNR CCr, CCg, CCb NVCR Remarks 0 7989.9 Infinite 20.9659 PK3 9842.1 18.8810 PK4 10820 17.9336 Used PK in the decryption phase PK1 PK2 © 2023, IJCSMC All Rights Reserved 1, 1 , 1 0.2928, 0.2615 0.0875, 0.0821 -0.0027, 0.0100 0.2767, 0 100 Correct Damaged 0.0998, 100 Damaged -0.0036, 100 Damaged 34 Prof. Ziad Alqadi et al, International Journal of Computer Science and Mobile Computing, Vol.12 Issue.2, February- 2023, pg. 26-37 From figures 9 and 10 and from table 6 we can see that the obtained decrypted image is very sensitive to the selected values of the PK Conclusion A simplified encryption and decryption functions were proposed, the process of pixels’ values cryptography was performed using values rearrangement based on the indexes and the contents of the generated index key. The proposed method provided a good level of image protection by using a special complicated private key; this key contains the values of the chaotic parameters needed to run a chaotic logistic map model to generate a chaotic logistic key, which was converted to index key. The values and the indexes of the index key were used to apply image encryption and decryption. The proposed method was tested using various color images, and it was shown that the proposed method satisfied the quality requirements. The speed of the proposed method was tested and it was shown that the proposed method provided a significant speed up comparing with other existing methods of data cryptography. The generated decrypted images were very sensitive to the selected values of the private key, any changes in the private key during the decryption phase was considered as a hacking attempt by producing a damaged decrypted image. References [1]. Aamer Nadeem, Dr M. 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