Ring oscillator as confusion – diffusion agent: a complete TRNG drove image security

IET Image ProcessingVolume 14, Issue 13 p. 2987-2997 Research ArticleFree Access Ring oscillator as confusion – diffusion agent: a complete TRNG drove image security Rethinam Sivaraman, Rethinam Sivaraman Department of ECE, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorSundararaman Rajagopalan, Corresponding Author Sundararaman Rajagopalan raman@ece.sastra.edu orcid.org/0000-0003-3505-3260 Department of ECE, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorJohn Bosco Balaguru Rayappan, John Bosco Balaguru Rayappan Department of ECE, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorRengarajan Amirtharajan, Rengarajan Amirtharajan Department of ECE, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this author Rethinam Sivaraman, Rethinam Sivaraman Department of ECE, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorSundararaman Rajagopalan, Corresponding Author Sundararaman Rajagopalan raman@ece.sastra.edu orcid.org/0000-0003-3505-3260 Department of ECE, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorJohn Bosco Balaguru Rayappan, John Bosco Balaguru Rayappan Department of ECE, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this authorRengarajan Amirtharajan, Rengarajan Amirtharajan Department of ECE, School of EEE, SASTRA Deemed University, Thanjavur, 613401 IndiaSearch for more papers by this author First published: 05 October 2020 https://doi.org/10.1049/iet-ipr.2019.0168Citations: 22AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract The utility of true random number generators (TRNGs) is not only restricted to session key generation, nonce generation, OTP generation etc. in cryptography. In the proposed work, two ring oscillator (RO) based TRNG structures adopting identical and non-identical ring of inverters have alone been employed for confusion (scrambling) and diffusion (intensity variation) processes for encrypting the greyscale and RGB images. Cyclone IVE EP4CE115F29C7 FPGA was utilised to generate a couple of random synthetic images using the two RO architectures which took a maximum of 520 combinational units and 543 logic registers. The suggested scheme of image encryption was tested on 100 test greyscale images of size 256 × 256. This non-chaos influenced image ciphering has resulted in an approximate average entropy of 7.99 and near-zero correlation figures for the greyscale & RGB cipher images. The attack resistance capability was checked by performing various occlusion and noise attacks on encrypted images. 1 Introduction Image encryption plays an important role in safeguarding various image modalities [1]. Chaotic maps have occupied a significant place in encryption for a single round or multi-round confusion and diffusion processes [2–5]. Such maps namely logistic, tent, sine, combine chaotic etc. are being used extensively in the recent research works [6–12]. However, the non-uniform chaotic range provided by the maps needs critical attention. This selective chaotic region restricts the random range width even though the sensitivity to initial conditions forms the basis for time series generation through the chaotic maps or attractors. Chaos-based ciphering techniques are becoming vulnerable to attacks [13]. Recently, cryptanalysis has been performed by Norouzi and Mirzakuchaki [14] on chaos-based greyscale image encryption wherein the algorithm was compromised through the chosen plaintext attack. Dou et al. also performed a cryptanalysis on logistic maps blend DNA-based combined image encryption scheme. Their work was capable of cracking through a novel chosen-plaintext attack [15]. Random image or Synthetic image generated through the hardware seems to be an option for chaotic maps. Any strong alternative must be capable of providing the impact of confusion and diffusion yielded by the chaos influenced maps. Random bits acquired through unique features of hardware can resist the attacks due to the difficulties in arriving a particular mathematical model. In a DNA – Chaotic image encryption work proposed by Zhang et al. [16], a key image was generated using randint command of Matlab 7.1. However, the correlation of this synthetic image was inferred to be low. Noticeably, true random number generators (TRNGs) have been incorporated in earlier works for the diffusion of images [17]. Rajagopalan et al. [18] suggested an ring oscillator (RO) based synthetic image captured using IC 7404 inverter rings. This near-uniform histogram yielding random image had an entropy of 7.954 close to 8. In another work, Sundararaman et al. [19] utilised a synthetic image generated through PLLs driven by beat frequency detection. They implemented this TRNG on Cyclone II FPGA which took 480 LEs for the formation of a synthetic image with an entropy of 7.99. A five-layer DICOM medical image encryption proposed by Ravichandran et al. [20] incorporated a PLL-based synthetic image which consumed 98 hardware units for a generation. In all these works, chaotic maps/attractors played a significant role along with TRNG-based random images. Noticeably, the proposed method has utilised only the FPGA-based RO TRNG structures for both the confusion and diffusion operations without any chaotic schemes. The absence of floating-point units which will be required for hardware-based chaotic maps reduces the hardware consumption. Moreover, the entropy source adopted in this work does not need an initial seed or condition to trigger the generation of a random synthetic image. 2 Methodology 2.1 Synthetic image generation In this image encryption scheme, clock jitters from ROs were utilised as a source of randomness to create the synthetic images which act as primary keys. The two different RO-based TRNG structures (Identical ROs and Non-identical ROs) adopted are shown in Figs. 1a and b, respectively. ROs are the promising agents for producing jittery clocks from which the jitters can be extracted using a harvesting mechanism to generate true random bits. Fig. 1Open in figure viewerPowerPoint Entropy source (a) Identical RO TRNG, (b) Non-identical RO TRNG Fig. 1a illustrates the identical RO TRNG where it has 8 rings of 24 inverters. Jittery clock from each ring has been XORed to acquire the sequence of true random bits. Fig. 1b depicts the non-identical RO TRNG in which 64 inverters were used to form the TRNG structure and the bits from each ring were XORed to produce true random sequence [21]. Further, the generated true random bits from TRNGs need to be packed as 65,536 numbers of 8-bit width to form 256 × 256 synthetic images for the proposed application. Both the TRNGs have been designed using HDL and implemented on Altera Cyclone IV EP4CE115F29C7 FPGA using Altera Quartus 13.0 Electronic Design Automation tool. Hardware analyses shown in Table 1 present the performance evaluation of TRNGs on Cyclone IV FPGA. Synthetic image of identical RO TRNG (Fig. 2a) achieves an entropy of 7.9368 with correlation figures of 0.0038, −0.0017 and 0.0106 whereas non-identical RO TRNG-based synthetic image (Fig. 2b) yields an entropy of 7.9701 and correlation metrics of −0.00047, −0.00081 and 0.0051. As per the timing analysis performed using the Logic analyser, 42.6 ms was required to generate the synthetic image at a throughput of 12.307 Mbps. Fig. 2Open in figure viewerPowerPoint Synthetic image (a) Identical RO, (b) Non-identical RO Table 1. Hardware analysis: RO TRNGs Target device Cyclone IV E EP4CE115F29C7 FPGA TRNG structures identical Rings TRNG non-identical Rings TRNG logic elements combinational functions 518/1,14,480 520/1,14,480 logic registers 543/1,14,480 543/1,14,480 memory bits 83,88,608 83,88,608 power dissipation, mW static power 98.68 98.68 dynamic power 16.58 16.61 IO power 32.31 32.31 Bold font is used for representing the headings. 2.2 Encryption procedure In general, image encryption should have two unique operations, namely pixel scrambling and diffusion. Scrambling process breaks the correlation between pixels wherein the diffusion performs intensity modification. The proposed encryption of images can be performed through the following steps for greyscale as well as RGB images (see Fig. 3 and 4). Encryption process can be explained with a 4 × 4 matrix as follows: Fig. 3Open in figure viewerPowerPoint Greyscale image encryption Fig. 4Open in figure viewerPowerPoint RGB image encryption Let the input 4×4 image matrix I(i,j), generated Identical RO synthetic 4×4 image matrix §1 (i,j) and generated Non-identical RO synthetic 4×4 image matrix §2 (i,j) be (1) Sorting the values of §2 (i,j) in ascending order, we get The location indices of sorted pixels of the matrix §1(sorted) in §1(i,j) are given by Scrambling the pixel positions of input image I(i,j) using §1(sorted_loc), we get Now, performing diffusion by bitwise XORing of Iconfused (i,j) and §2 (i,j) to get final encrypted matrix 3 Results and discussion The proposed image encryption scheme was implemented using LabVIEW 2013 tool with FPGA generated synthetic images as primary keys. The significance of this work is that the TRNG assisted synthetic images cannot be reproduced, which also possesses high randomness and keyspace to yield good encryption. The algorithm was tested on 100 greyscale images and 5 RGB images. Figs. 5a–d and 6a–d show four test greyscale images among the pool of images considered and their corresponding encrypted images. Figs. 7a–d and 8a–d present the four test colour images and their corresponding encrypted images. The sternness of the proposed encryption technique was evaluated through the statistical and chosen-plaintext attack analyses. Fig. 5Open in figure viewerPowerPoint Original greyscale images (a) Boat, (b) Cameraman, (c) Hydrangeas, (d) Peppers Fig. 6Open in figure viewerPowerPoint Encrypted greyscale images (a) Boat, (b) Cameraman, (c) Hydrangeas, (d) Peppers Fig. 7Open in figure viewerPowerPoint Original colour images (a) Airplane, (b) Lena, (c) Peppers, (d) Splash Fig. 8Open in figure viewerPowerPoint Encrypted colour images (a) Airplane, (b) Lena, (c) Peppers, (d) Splash 3.1 Statistical attack analyses 3.1.1 Entropy analysis Entropy is defined as a measure of uncertainty which represents the degree of randomness in the encrypted image. For a good encrypted greyscale image, entropy must be close to 8. This work achieves an average entropy of 7.99654 close to the ideal value. Entropy can be calculated as [12] (2)where N is the number of intensity levels and P(Li) is the probability of each greyscale intensities in the whole image. Fig. 9 portrays the computed entropy of 100 greyscale images and an average value of 7.993518, which is close to the required entropy value 8, was inferred through this analysis. Fig. 9Open in figure viewerPowerPoint Entropy analysis for 100 greyscale test images 3.1.2 Correlation analysis Correlation between the adjacent pixels of an encrypted image must be close to zero. In this work, the synthetic image has been employed for the confusion which has resulted in near-zero correlation. The correlation coefficients have been computed in three different directions namely horizontal, vertical and diagonal. For the computation of correlation among the adjacent pixels, parameters namely mean, variance and covariance are estimated for the chosen pixels of the image considered. The computation of correlation is expressed through (3)–(6) [13]. Tables 2 and 3 present the entropy and correlation results of greyscale and RGB images, respectively. Table 4 compares the entropy and correlation coefficients of original and encrypted images with respect to the earlier works. Also, Fig. 10 expresses the correlation analyses of 100 encrypted images. It can be inferred that the proposed algorithm achieves an average correlation value close to zero (see Figs. 11 and 12) (3) (4) (5) (6)where E(x) and D(x) are the mean and variance of the selected number of pixels, respectively. E(y) and D(y) are the mean and variance of the adjacent pixels. Cov (x, y) is the co-variance computed with the variance values of x and y. Using the covariance and individual variances of x and y, the correlation in a specific direction can be computed. For this analysis, entire pixels of the images were considered. From the results, it can be inferred that the near-zero correlation has been obtained for encrypted images. Fig. 10Open in figure viewerPowerPoint Correlation analysis for 100 greyscale test images Fig. 11Open in figure viewerPowerPoint Correlation analysis: original greyscale Pepper image (a) Horizontal, (b) Vertical, (c) Diagonal Fig. 12Open in figure viewerPowerPoint Correlation analysis: encrypted greyscale Pepper image (a) Horizontal, (b) Vertical, (c) Diagonal Table 2. Statistical analysis – Greyscale images Images Entropy H V D Boat original 7.2644 0.8460 0.8972 0.7984 encrypted 7.9958 0.0073 0.0032 −0.0048 Cameraman original 7.1289 0.9303 0.9590 0.9048 encrypted 7.9962 0.0013 0.0013 0.0006 Hydrangeas original 7.2123 0.9596 0.9660 0.9476 encrypted 7.9966 0.0070 0.0062 −0.0036 Peppers original 7.5768 0.9756 0.9760 0.9538 encrypted 7.9969 0.0030 −0.0039 −0.0055 Lena original 7.4582 0.9234 0.9724 0.9055 encrypted 7.9972 0.0020 −0.0068 0.0036 E – Entropy, H – Horizontal, V – Vertical and D – Diagonal correlation coefficients. Table 3. Statistical analysis – RGB images Images Entropy H V D Airplane original (R) 6.7780 0.9055 0.8869 0.8252 original (G) 6.8795 0.8923 0.8961 0.8309 original (B) 6.2680 0.9088 0.8574 0.8215 encrypted (R) 7.9927 −0.0033 −0.0006 −0.0010 encrypted (G) 7.9914 0.0038 0.0020 −0.0001 encrypted (B) 7.9931 −0.0016 0.0015 −0.0057 Lena original (R) 7.2796 0.93338 0.9641 0.9074 original (G) 7.6315 0.9049 0.9467 0.8802 original (B) 6.9891 0.8597 0.9061 0.8383 encrypted (R) 7.9959 −0.0137 0.0038 0.0036 encrypted (G) 7.9961 −0.0049 −0.0008 −0.0012 encrypted (B) 7.9959 0.0038 0.0017 0.0008 Peppers original (R) 7.3319 0.9424 0.9464 0.9094 original (G) 7.5242 0.9559 0.9617 0.9285 original (B) 7.0793 0.9319 0.9406 0.8981 encrypted (R) 7.9954 0.0019 0.0043 0.0029 encrypted (G) 7.9944 0.0010 0.0052 −0.0018 encrypted (B) 7.9939 0.0001 −0.0006 −0.0064 Splash original (R) 6.9786 0.9824 0.9931 0.9775 original (G) 6.8963 0.9550 0.9681 0.9350 original (B) 6.1340 0.9572 0.9525 0.9224 encrypted (R) 7.9941 0.0033 0.0026 0.0017 encrypted (G) 7.9883 0.0018 −0.0034 −0.0003 encrypted (B) 7.9944 0.0028 0.0032 0.0017 Tree original (R) 7.2104 0.9590 0.9361 0.9159 original (G) 7.4136 0.9687 0.9457 0.9318 original (B) 6.9207 0.9612 0.9406 0.9265 encrypted (R) 7.9955 −0.0038 −0.0044 0.0002 encrypted (G) 7.9964 −0.0012 0.0060 −0.0040 encrypted (B) 7.9952 −0.0083 0.0007 −0.0046 Table 4. Statistical analysis comparison – Greyscale images Image Entropy H V D Lena encrypted 7.9972 0.0020 −0.0068 0.0036 [6] encrypted 7.9912 0.0001 0.0089 0.0091 [11] encrypted 7.9988 −0.0083 0.0040 −0.0463 [12] encrypted 7.9030 0.0018 0.0011 0.0012 [9] encrypted 7.9963 0.0094 0.0048 0.0112 [7] encrypted 7.9971 0.0051 0.0038 0.0092 [1] encrypted 7.9973 0.0010 0.0017 0.125 [3] encrypted 7.9979 0.0010 0.0042 0.0063 [4] encrypted 7.9969 0.0079 −0.0203 0.0049 [8] encrypted 7.9971 0.0097 0.0178 0.0112 [5] encrypted 7.9973 −0.0226 0.0041 0.0368 [2] encrypted 7.9974 −0.0230 0.0019 −00034 Bold values indicate the obtained result of the proposed work. 3.1.3 Histogram analysis The histogram is the graphical representation of the probability distribution of pixel intensities in an image. For an encrypted image, the histogram plot indicates the degree of uniform distribution of intensity values. Figs. 13a and b show the histogram analyses of original and encrypted images of a test greyscale image and Figs. 14a–c and 15a–c present the histogram findings of an RGB image. Fig. 13Open in figure viewerPowerPoint Histogram analysis on greyscale image – Peppers (a) Original, (b) Encrypted Fig. 14Open in figure viewerPowerPoint Histogram analysis of original RGB pepper image (a) Red plane, (b) Green plane, (c) Blue plane Fig. 15Open in figure viewerPowerPoint Histogram analysis on RGB image – Peppers (a), (b), (c) Encrypted Figs. 11a–c portray the horizontal, vertical and diagonal correlation images of greyscale Pepper image, respectively, wherein Figs. 12a–c display their corresponding encrypted versions. 3.2 Keyspace analysis It is a primary analysis to evaluate the key strength in terms of a number of possible random keys to resist the brute force attack. The keyspace of this proposed algorithm for the greyscale image has been calculated as follows: Keyspace for confusion: 28×65536 Keyspace for diffusion: 28×65536 For a 256 × 256 greyscale image, the total keyspace has been calculated as 2(8×65536+1).which is greater than 2128 and also other earlier works [5–9, 11, 12] to resist the brute force attack. 3.3 Differential attack analysis Number of Pixel Change Ratio (NPCR) and Unified Average Change in Intensity (UACI) are considered as two metrics to evaluate the sensitivity of any image encryption algorithm through differential attack analysis [16]. This analysis is operated on two cipher images (C1, C2) where C1 is the cipher image for the original image and C2 is the cipher image for the modified original image with one pixel change. The algorithm should produce different results for even a small change in the original image. Table 5 depicts the outcomes of differential analysis which satisfies the requirement of image encryption verified through the critical values [16]. From Table 5, the proposed method has yielded acceptable results which are compared with other works. Table 5. Differential analysis Images NPCR UACI Boat 99.5758 32.2809 Cameraman 99.6094 28.7078 Hydrangeas 99.6460 31.3390 Peppers 99.5773 37.8632 Lena 99.6231 30.9135 [7] 99.59 33.48 [8] 98.9182 32.7865 [9] 99.6228 33.7041 [11] 99.6087 33.4584 [12] 99.6166 33.4365 3.4 Encryption quality analysis To verify the effective encryption between the original and cipher images, three standard quality metrics have been considered. The degree of deviation of cipher image from its original image has been estimated through maximum deviation, irregular deviation and deviation from uniform histogram analyses. They can be expressed as Maximum deviation [18]: (7)Irregular deviation [18]: (8)Deviation from uniform Histogram [18]: (9)From Tables 6 and 7, it can be observed that the deviation between original and encrypted images was high which confirms the efficiency of the proposed algorithm to produce a high degree of variation in the intensity levels. Further, this algorithm was tested on 100 greyscale images and the results are shown in Figs. 16a and b, which indicate maximum variations. Fig. 16Open in figure viewerPowerPoint Encryption quality analysis (a) Encryption quality analysis: Maximum deviation and irregular deviation analysis, (b) Encryption quality analysis: Deviation from uniform histogram analysis Table 6. Encryption quality analysis – Greyscale images Images MD ID DH Boat 5.4113 × 104 33,185 0.8207 Cameraman 61,193 30,902 0.9232 Hydrangeas 55,653 15,834 0.8535 Lena 46,254 21,261 0.7049 Peppers 3.7651 × 104 27,168 0.5764 Table 7. Encryption quality analysis – Colour images Images MD ID DH Airplane red 68,589 46,019 1.0349 green 6.7243 × 104 45,327 1.0510 blue 7.9205 × 104 4919 1.2042 Lena red 5.0069 × 104 45,906 0.7734 green 36,473 25,140 0.5492 blue 65,826 2750 0.9882 Peppers red 52,294 39,102 0.8169 green 3.7113 × 104 29,411 0.5934 blue 59,754 16,950 0.9148 Splash red 59,076 45,225 0.8987 green 6.4346 × 104 17,634 1.0265 blue 81,426 20,937 1.2462 Tree red 47,634 34,116 0.7274 green 4.6113 × 104 32,247 0.7087 blue 63,673 37,040 0.9582 3.5 Error metric analyses Mean square error (MSE) and Peak-signal-to-noise ratio (PSNR) are the two significant measures used for differentiating the original and cipher images [22]. Lower PSNR indicates the more degree of variation between original and encrypted images. Figs. 17 and 18a and b illustrate the error metric analyses where the MSE and PSNR values are in the expected range ensuring the quality of encryption. In addition, Figs. 19a and b present the error metric analyses for 100 greyscale images which yielded an average MSE of 10914.3 and PSNR of 17.896 dB thereby indicating the effectiveness of the proposed encryption scheme. Fig. 17Open in figure viewerPowerPoint Error metric analysis – Greyscale images Fig. 18Open in figure viewerPowerPoint Error metric analysis – Colour images (a) MSE, (b) PSNR Fig. 19Open in figure viewerPowerPoint Error metric analysis for 100 greyscale images – (a) MSE, (b) PSNR 3.6 Occlusion & noise attack analyses Attacks during the transmission of encrypted images result in the removal of certain sections or at the worst severe quality degradation of original images. Hence, it is necessary to evaluate the attack resistant capability of any cryptographic algorithm by applying various attacks such as occlusion (cropping) and noise with a threshold level [19]. To prove the attack resistant capability of the proposed work, occlusion and noise attacks have been performed on encrypted images. Figs. 20a–d, Fig. 21a–c and 22a–c depict the impact of cropping attack analysis with intentional removal of two different pixel sections on the greyscale and RGB encrypted images. Fig. 20Open in figure viewerPowerPoint Cropping attack – Greyscale image (a) Level 1 cropping, (b) Decrypted image, (c) Level 2 cropping, (d) Decrypted image Fig. 21Open in figure viewerPowerPoint Cropping attack – Color image (a) Level 2 cropping on red plane, (b) Level 2 cropping on green plane, (c) Level 2 cropping on blue plane Fig. 22Open in figure viewerPowerPoint Cropping attack – Colour image (a) Decrypted red plane, (b) Decrypted green plane, (c) Decrypted blue plane Noise attacks have been performed with three different noises namely Gaussian, Salt & Pepper and Speckle with various mean and variance values. Figs. 23a–c, Fig. 24a–c, 25a–c and 26a–c expresse the noise attack analysis on Lena image for the variance of 0.05. Though the attacks happened on encrypted images, the proposed algorithm can retrieve the original images with lesser amount of pixel degradation. From the results, it is verified that the proposed encryption scheme withstands against cropping and noise attacks. Fig. 23Open in figure viewerPowerPoint Noise attack on a test Grayscale image (a) Gaussian noise, (b) Salt & Pepper noise, (c) Speckle noise Fig. 24Open in figure viewerPowerPoint Noise attack on a test Color image (a) Gaussian noise on red plane, (b) Salt & Pepper noise on red plane, (c) Speckle noise on red plane Fig. 25Open in figure viewerPowerPoint Noise attack on Color image (a) Gaussian noise on green plane, (b) Salt & Pepper noise on green plane, (c) Speckle noise on green plane Fig. 26Open in figure viewerPowerPoint Noise attack on Color image (a) Gaussian noise on blue plane, (b) Salt & Pepper noise on blue plane, (c) Speckle noise on blue plane 3.7 NIST SP 800–22 batteries of test National Institute of Standards and Technology (NIST) has released a test suite for evaluating the randomness of any RNG [23]. The ultimate goal of this evaluation is to determine the amount of randomness that can be generated from the source. It analyses the uncertainty of generated random sequences. This test methodology can be used for analysing the cipher images wherein the amount of randomness among the pixels has been investigated. NIST has a few parameter settings to conduct the test which are given as follows: Block frequency Test – Block length (M) = 128 Non-overlapping Template – Block length (m) = 9 Overlapping Template – Block length (m) = 9 Approximate Entropy Test – Block length (m) = 8 Serial Test – Block length (m) = 10 Linear Complexity Test – Block length (M) = 500 'To conduct this test, 65,536 × 8 bits and 65,536 × 3 × 8 bits were taken for greyscale and RGB colour images, respectively. NIST SP 800-22 confirms the randomness when the P (Probability) value is greater than 0.01. Table 8 presents the test results of greyscale in which P value is in the acceptable range. Fig. 27 shows the range of P – values for each plane of RGB images with respect to list of available tests in NIST SP 800–22. From the results, it can be understood that the proposed encryption scheme achieves good encryption. Fig. 27Open in figure viewerPowerPoint NIST SP 800–22 results for RGB images Table 8. NIST SP 800-22 results for greyscale images Test parameters P – values for 5 Test Greyscale images Boat Cameraman Hydrangeas Lena Peppers frequency 0.73991 0.350485 0.739918 0.35048 0.91141 block frequency 0.12232 0.739918 0.350485 0.35048 0.35048 cumulative sums – I 0.03517 0.350485 0.534146 0.73991 0.91413 cumulative sums – II 0.53414 0.534146 0.534146 0.21330 0.73991 runs 0.73991 0.739918 0.534146 0.53414 0.35048 longest run 0.12232 0.73991 0.12232 0.35048 0.35048 rank 0.01143 0.12232 0.35048 0.73991 0.91141 FFT 0.12232 0.73991 0.12232 0.73991 0.53414 non-overlapping template 0.91141 0.91141 0.91141 0.73991 0.91413 overlapping template 0.00204 0.06688 0.73991 0.21330 0.53414 approximate entropy 0.53414 0.53414 0.21330 0.35048 0.73991 serial – I 0.35048 0.73991 0.35048 0.73991 0.12232 serial – II 0.91141 0.35048 0.35048 0.91141 0.35048 linear complexity 0.53414 0.73991 0.53414 0.91141 0.35048 3.8 Chosen-plaintext attack analysis Since the XOR operation has been incorporated in the diffusion process, the effect of XOR operation on original and encrypted images requires to be analysed. From the perspective of cryptanalysts, chosen-plaintext attack can break the algorithm with the original image alone. Hence, that analysis has been conducted in which the original images of Cameraman and Peppers (I1, I2) were XORed and their corresponding encrypted images (C1, C2) were XORed. If both XORed images are equal, the algorithm is vulnerable to chosen-plaintext attack. Figs. 28a and b confirm that the XORed results of ciphertext and plain text are not equal which means the algorithm is not vulnerable to the chosen-plaintext attack. Fig. 28Open in figure viewerPowerPoint Chosen plaintext attack (a) I1 XOR I2, (b) C1 XOR C2 When compared to the earlier works of encryption reported in the introduction section, this proposed encryption scheme is well suited for greyscale and RGB images. The results evidence the superiority of the proposed methodology in terms of entropy, correction, differential, error metric and occlusion attack analyses. In addition, NIST SP 800–22 tests have been carried out to ensure the randomness of the encrypted images. The contributions of the proposed work are as follows: Very first work on complete TRNG driven image encryption for greyscale and RGB colour images incorporating both confusion and diffusion whereas some of the earlier works used the TRNG only for diffusion [17–20]. Simple TRNG architecture which consumes only 520 combinational logics and 524 logic registers on Cyclone IV EP4CE115F29C7 FPGA. Identical and Non-identical Ring Oscillator structures have been utilised for yielding better confusion and diffusion. The scheme offers large keyspace of 2(8×65536+1) which promises resistance against brute force attack. This scheme yields a high entropy of 7.99 and near-zero correlation which confirms the resistance towards the statistical attacks when applied on more than 100 test images. The proposed non-chaotic approach improves the efficiency of the encryption and it makes the design free from intensive floating-point conversions. 4 Conclusion A complete TRNG dependent image encryption has been suggested in this work. RO TRNGs using identical and non-identical rings of inverters played a vital role for confusion as well as diffusion operations. TRNGs were implemented on Altera Cyclone IV FPGA for the subsequent generation of synthetic images. Further, the proposed image encryption approach was tested on 100 greyscale and five RGB images to validate the strength through standard metrics. Though the proposed scheme offers good encryption by adopting a chaotic map free approach, it has some limitations due to the irreproducible property of TRNGs. Since the proposed work follows symmetric key encryption, it is necessary to share the keys between encryptor and decryptor securely. The synthetic image is larger almost equal to the size of the original image, and hence a secure key sharing mechanism must be developed. There is also a necessity to identify a proper compression algorithm for random synthetic images as they did not possess more number of redundant pixels which was evident from the entropy computation. The future direction promises the enhancement of proposed work by addressing certain limitations considering the growing hacking attempts on multimedia data. 5 Acknowledgment The authors thank the Department of Science & Technology, New Delhi for the FIST funding (SR/FST/ET-II/2018/221). Also, the authors wish to thank the Intrusion Detection Lab at School of Electrical & Electronics Engineering, SASTRA Deemed University for providing infrastructural support to carry out this research work. The authors also acknowledge Mr. N. S. Srinath, Research Scholar, School of EEE, SASTRA Deemed to be University for his technical support. 6 References 1Hayat U., Azam N.A.: 'A novel image encryption scheme based on an elliptic curve', Signal Process., 2019, 155, pp. 391– 402CrossrefWeb of Science®Google Scholar 2Xu L., Li Z., Li J. et al.: 'A novel bit-level image encryption algorithm based on chaotic maps', Opt. Lasers Eng., 2016, 78, pp. 17– 25CrossrefWeb of Science®Google Scholar 3Li R., Liu Q., Liu L.: 'Novel image encryption algorithm based on improved logistic map', IET Image Process.., 2019, 13, (1), pp. 125– 134Wiley Online LibraryWeb of Science®Google Scholar 4Askar S.S., Karawia A.A., Alammar F.S.: 'Cryptographic algorithm based on pixel shuffling and dynamical chaotic economic map', IET Image Process.., 2018, 12, (1), pp. 158– 167Wiley Online LibraryWeb of Science®Google Scholar 5Xu L., Gou X., Li Z. et al.: 'A novel chaotic image encryption algorithm using block scrambling and dynamic index based di ff usion', Opt. Lasers Eng. J., 2017, 91, (November 2016), pp. 41– 52Google Scholar 6Wu J., Liao X., Yang B.: 'Colour image encryption based on chaotic systems and elliptic curve ElGamal scheme', Signal Process., 2017, 141, pp. 109– 124CrossrefWeb of Science®Google Scholar 7Wang X., Wang S., Wei N. et al.: 'A novel chaotic image encryption scheme based on hash function and cyclic shift', IETE Tech. Rev. (Institution Electron. Telecommun. Eng. India), 2018, 4602, (May), pp. 1– 10Google Scholar 8Ur A., Jan R., Khan S. et al.: ' A new image encryption scheme based on dynamic S-boxes and chaotic maps'. 3D Res., 77, 2016. Available at https://doi.org/10.1007/s13319-016-0084-9Google Scholar 9Belazi A., El-Latif A.A.A., Belghith S.: 'A novel image encryption scheme based on substitution-permutation network and chaos,' Signal Process., 2016, 128, (Supplement C), pp. 155– 170CrossrefWeb of Science®Google Scholar 10Kar M., Mandal M.K., Nandi D. et al.: 'Bit-plane encrypted image cryptosystem using chaotic, quadratic, and cubic maps', IETE Tech. Rev. (Institution Electron. Telecommun. Eng. India), 2016, 33, (6), pp. 651– 661CrossrefWeb of Science®Google Scholar 11Zhang Y.: 'The image encryption algorithm with plaintext-related shuffling', IETE Tech. Rev., 2016, 33, (3), pp. 310– 322CrossrefWeb of Science®Google Scholar 12Zhang Y., Xiao D.: 'An image encryption scheme based on rotation matrix bit-level permutation and block diffusion', Commun. Nonlinear Sci. Numer. Simul., 2014, 19, (1), pp. 74– 82CrossrefWeb of Science®Google Scholar 13Preishuber M., Hütter T., Katzenbeisser S. et al.: 'Depreciating motivation and empirical security analysis of chaos-based image and video encryption', IEEE Trans. Inf. Forensics Secur., 2018, 13, (9), pp. 2137– 2150CrossrefWeb of Science®Google Scholar 14Norouzi B., Mirzakuchaki S.: 'Optik breaking an image encryption algorithm based on the new substitution stage with chaotic functions', Opt. – Int. J. Light Electron Opt., 2016, 127, (14), pp. 5695– 5701CrossrefGoogle Scholar 15Dou Y., Liu X., Fan H. et al.: 'Cryptanalysis of a DNA and chaos based image encryption algorithm', Opt. – Int. J. Light Electron Opt., 2017, 145, pp. 456– 464CrossrefCASGoogle Scholar 16Zhang Q., Guo L., Wei X.: 'A novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system', Opt. – Int. J. Light Electron Opt., 2013, 124, (18), pp. 3596– 3600CrossrefGoogle Scholar 17Liu H., Kadir A., Sun X.: 'Chaos-based fast colour image encryption scheme with true random number keys from environmental noise', IET Image Process.., 2017, 11, (55), pp. 324– 332Wiley Online LibraryWeb of Science®Google Scholar 18Rajagopalan S., Rethinam S., Arumugham S. et al.: 'Networked hardware assisted key image and chaotic attractors for secure RGB image communication', Multimedia Tools Appl., 2018, 77, pp. 23449– 23482CrossrefWeb of Science®Google Scholar 19Sundararaman R., Sivaraman R., Upadhyay H.N. et al.: 'ON-chip peripherals are ON for chaos – an image fused encryption', Microprocess. Microsyst., 2018, 61, pp. 257– 278CrossrefWeb of Science®Google Scholar 20Ravichandran D., Rajagopalan S., Upadhyay H.N. et al.: 'Encrypted biography of biomedical image – a pentalayer cryptosystem on FPGA', J. Signal Process. Syst., 2018, 91, pp. 475– 501CrossrefWeb of Science®Google Scholar 21Sunar B., Martin W.J., Stinson D.R.: 'A provably secure true random number generator with built-in tolerance to active attacks', IEEE Trans. Comput., 2007, 56, (1), pp. 109– 119CrossrefWeb of Science®Google Scholar 22Arumugham S., Rajagopalan S., Amirtharajan R. et al.: 'Tamper-resistant secure medical image carrier: an IWT – SVD – chaos – FPGA combination', Arab. J. Sci. Eng., 2019, 44, (11), pp. 9561– 9580CrossrefWeb of Science®Google Scholar 23Bassham L.E., Rukhin A.L., Soto J. et al.: ' A statistical test suite for random and pseudorandom number generators for cryptographic applications'. Natl. Inst. Stand. Technol., Tech. Rep., Gaithersburg, MD, USA, Gaithersburg, MD, USA, 2010, AprilCrossrefGoogle Scholar Citing Literature Volume14, Issue13November 2020Pages 2987-2997 FiguresReferencesRelatedInformation