1 Introduction

Large multimedia companies (such as Facebook, Twitter, Snapchat, etc.,) invest a big amount of money in the market. This market has an increasing demand and a lot of customers and needs to protect and secure its materials. Many applications (military communications, medical imaging, etc.,) need to secure their materials in case data exchange over a channel or in storage media. The cryptosystem is the optimal solution for protection and security of digital multimedia. Image encryption has gained a remarkable attention in research because of its several vital applications such as cable TV, confidential chatting, etc. One of the successful techniques for image encryption is the chaotic maps. Chaotic maps attracted the attention of researchers in the field of image encryption because it has a random performance as well as the high sensitivity to the encryption key. These advantages guarantee to achieve Shannon's requirements of diffusion and confusion [1]. The performance of the encryption techniques based on chaotic maps reveals a satisfactory level in terms of efficiency and security. In literature, researchers propose image encryption techniques based on ergodicity such as [2, 3]. While others propose discrete chaos based on image cryptosystem, but their cryptosystem performance lacks the required level of security [4,5,6,7,8,9,10].

The main two techniques to implement the image chaotic encryption are generating a pseudo-random key for plaintext image masking (stream cipher) [11], and a secret key which is employed to govern the shuffling, rounding times to pass the required level of encryption (block cipher) [6, 12]. Kanso et al. and Zhang et al. [13, 14] proposed approaches that generalize the 2-D chaotic map to 3-D to enhance the security level by symmetric image encryption. Kanso et al. proposed a 3-D Baker map while Zhang et al. proposed a 3-D Cat map.

There are two types of image encryption techniques, the first is based on permutation while the second is based on substitution [15,16,17,18,19,20,21,22,23,24,25]. The first type based on scrambling the pixel position of the plaintext image [26,27,28,29,30,31]. The main advantage of this type is the low execution time. The drawback is the congruent of the histogram of the plaintext and ciphertext images. Cat map and Baker map are examples of the first type of image encryption techniques [20,21,22,23,24]. Substitution cryptosystems are altering the pixels’ values in a way that the cipher image appears fully random. This type introduces a higher level of security and not easy to hack. But in terms of efficiency, they have a larger execution time which makes them not appropriate for live digital multimedia exchange. The Advanced Encryption Standard (AES) and RC6 are examples of such technique [25,26,27]

While chaotic maps are an efficient application field in the design of cryptosystems, many encryption algorithms as the above-mentioned systems fail to achieve the required level of security for communications because the introduced cryptanalysis is not enough. The experimental results of the mentioned systems are performed for a few samples which leads to unrealistic results for security and efficiency obtained from small statistical tests. The experimental results of the mentioned systems are obtained from a low number of statistical tests which leads to unrealistic results for security and efficiency. By considering the drawbacks of the image encryption cryptosystem, we propose a cryptosystem for image encryption characterized by high security and efficiency for image communication. Thus, a new implementation of the 2-D chaotic Baker map for image encryption is presented. Three different modes of operation are employed to implement 2D chaotic Baker map which are the CBC mode, the CFB mode, and the OFB mode. The novelty of the proposed implementation is that it combines the advantage of the speed of chaotic maps with the randomness of the mode of operation which makes the proposed cryptosystem has the feature of both fast and secure. The advantages of the proposed cryptosystem are high robustness, high quality, immunity against channel noise, low execution time and in general it introduces a promising encryption-decryption performance.

The proposed implementation depends on the segmentation of the image into blocks, then the encryption of these blocks with the 2D chaotic Baker map by the tree modes of operation. The initialization vector (IV) in this implementation can be considered the main key. The bits formation of the IV has to be uncorrelated and randomly as possible to obtain an effective encryption scheme. The grayscale Lena image is considered as the original image with size 512 × 512. We use parts of the ciphered grayscale Cameraman image as the IV. There are two benefits from this procedure, low execution time to encrypt scale variant images and a high level of security by involving the permutation and substitution in the proposed cryptosystem. The proposed cryptosystem in this work is applied to standard and traditional analyses to evaluate its performance. Also, a comparison between the proposed image cryptosystem, the traditional 2-D chaotic Baker map (as an example of a permutation cryptosystem) and the RC6 cryptosystems (as an example of substitution cryptosystem) is presented in this paper. Moreover, a comparison with the related recent algorithms is held.

The rest of this paper is organized as follows. Section 2 demonstrates a brief review of the traditional 2-D chaotic Baker map and the RC6 cryptosystems. Section 3 presents the proposed image cryptosystem implemented in the CBC, the CFB, and the OFB modes of operation. Section 4 gives a discussion of the quality metrics that are used for performance evaluation of the proposed image cryptosystem. Section 5 shows a discussion of the paper results and comparative study with recent existing cryptosystems. Finally, the conclusion of the work is given in Section 6.

2 Review of the traditional cryptosystems

In this selection, a brief review of two of the traditional cryptosystems, the 2-D chaotic Baker map cryptosystem and the RC6 cryptosystem. Each of them is a symmetric block cipher cryptosystem is presented. In both cryptosystems, the key used for encryption and decryption is the same [28].

2.1 The 2-D chaotic baker map cryptosystem

In chaotic image encryption, image pixels are rearranged, arbitrarily. The Baker map, The Line map, and the Cat map are examples of chaotic maps that can be used for image encryption. The Baker map changes the positions of the pixels by repeating of a scrambling process in horizontal and vertical directions. In the Line map, all pixels are rearranged as a one row, and they are bended based on particular rules. This leads to a random distribution of the plaintext image pixels and breaks the correlation between neighboring pixels in the cipher image. Otherwise, a geometric transformation operation is carried out in the Cat map [8, 29].

The chaotic Baker map, B, in a continuous form, is described with the following equation [29]:

$$ B\left(x,y\right)=\Big\{{\displaystyle \begin{array}{c}\left(2x,y/2\right)\kern8.75em 0\le x<1/2\\ {}\\ {}\left(2x-1,y/2+1/2\right)\kern5.25em 1/2<x\le 1\ \end{array}} $$
(1)

where the digital image is represented as a lattice of pixels, hence a discrete representation of Baker map is required. Specifically, the Baker map in a discrete form must transfer the positions of all pixels in a bijective way. The discretized Baker map is mathematically expressed for a matrix of size M × M matrix as follows [14, 30,31,32,33]:

$$ B\left(r,s\right)=\left[\frac{M}{n_i}\left(r-{M}_i\right)+s \operatorname {mod}\left(\frac{M}{n_i}\right),\frac{n_i}{M}\left(s-s \operatorname {mod}\left(\frac{M}{n_i}\right)\right)+{M}_i\right] $$
(2)

where B(r, s) is the new position of the pixel at (r, s), Mi ≤ r < Mi + ni, 0 < s < M and Mi = n1 + n2 + ... + ni.

The discretized form of Baker map must be as close as possible to the continuous map in properties, and it will be congruent when the pixel extended to the infinity [29]. The baker map performs a permutation process by moving the positions of the pixels. So, the encrypted image has the same histogram of the plaintext image which considers as a modest degree of security. On the other hand, Baker map is very fast and simple which is suitable to use in video encryption applications.

2.2 The RC6 cryptosystem

The RC6 cryptosystem is classified as a diffusion cryptosystem. Essentially, the RC6 is employed for data encryption, also it is suitable for image encryption. The RC6 works by four registers with 32 bits for each, so it treats with 128 bits for input-output blocks. For image, each pixel formed from 8 bits, so, 16 pixels compose the 128 bits block. The performance of RC6 depends on the size of the secret key in bytes, the size of the word in bits and how many rounds. The multiplication process in RC6 produces a big diffusion every round which achieves higher security level with larger throughput and leads to a small number of rounds [30]. The RC6 cryptosystem does not depend on a lookup table in the encryption process, while the other encryption techniques use it. This will make the hardware implementation of RC6 easier than other techniques. The RC6 is characterized by simplicity, compact, and achieves a high level of security while the disadvantage is the need for more time for encryption [30].

3 The proposed image cryptosystem

This section gives an explanation of the proposed image cryptosystem. The main objective of this cryptosystem is to implement a high-security level in low execution time as much as possible. To achieve this objective, chaotic encryption can be implemented using one of three possible modes of operation: the CBC, the CFB, or the OFB modes [, ]. We will examine the three modes and compare them to determine which of them has the largest security level.

The proposed encryption algorithm of the proposed image cryptosystem can be simply summarized in the following three steps as shown in Fig. 1:

  1. 1.

    Scan the image row-by-row as shown in Fig. (1a).

  2. 2.

    The rows are arranged as w blocks of the plaintext with a size of n × n pixels for each as shown in Fig. (1-b).

  3. 3.

    The 2D Baker map is used to encrypt the blocks in the three modes (CBC, CFB, and OFB) as shown in Fig. 2 and explained in the following subsections.

Fig. 1
figure 1

The proposed image cryptosystem algorithm

Full size image
Fig. 2
figure 2

The proposed image cryptosystem implemented in a The CBC mode, b The CFB mode, and c The OFB mode

Full size image

The proposed image cryptosystem can be implemented in the CBC mode, The CFB mode, and OFB mode. The algorithm depends on the 2D Baker map which performs the encryption process. The scrambling result produced by Baker map successes to create an excellent random distribution [22]. The proposed image cryptosystem uses an IV which can be considered the main key. The IV determines the immunity of the algorithm against attacks, so it must be fully random to withstand the attacks such as brute force. The data blocks are XORed with the bits of the IV. This operation will alter the pixels value, that equivalent to extend the Baker map to be a 3D map. Furthermore, there is a second key that is responsible to perform the permutation process of the Baker map.

The proposed image cryptosystem segments the plaintext image into blocks. One of the most important parameters is the block size which affects the quality of the encryption operation. Detailed analyses about the effect of block size are deferred to section 5. Since the size of the IV is the same size as the plaintext block, the security level increase by increasing the block size. Moreover, the proposed cryptosystem has the advantage of handling a plaintext image with several sizes by dividing it into small blocks.

3.1 Chaotic encryption in the CBC mode

One of the modes of operation is the CBC which is used for block cipher encryption as shown in Fig. (2-a). This mode is adapted in this paper for application with the 2-D chaotic Baker map in the proposed image cryptosystem. In the proposed CBC mode, the size of the IV is similar to the size of the block of pixels. Firstly, the bits of each pixel in the IV are XORed with the bits of the corresponding pixel in the first block, and then the resulting pixels are chaotic encrypted. The bits of the encrypted pixels of the first block are used instead of the IV to encrypt the second block. This process continues until the last block. This can be represented with the following equation:

$$ {C}_j={E}_k\ \left({C}_{j- 1}\oplus \kern0.37em {P}_j\right),j=1,2,3,w $$
(3)

where, C0 = IV, Cj is the encrypted version of the block Pj, ⊕ refers to the XOR process, and Ek refers to the chaotic encryption.

This implementation uses a chaining mechanism that causes the dependence of each block cipher of the ciphertext on all the preceding ciphertext blocks. So, all past blocks' results are located at the next ciphertext block [18]. There is a drawback with the use of CBC that is if an error/attack occurred in one ciphertext block it will affect the decryption of the next two plaintext blocks []. The decryption algorithm is given by:

$$ {P}_j={D}_k\ \left({C}_j\right)\oplus {C}_{j-1},j=1,2,3,\dots .,w $$
(4)

where Dk refers to the decryption process.

3.2 Chaotic encryption in the CFB mode

The CFB mode starts with encrypting the IV in the pixel format with the chaotic Baker map, thereafter he bits of the encrypted IV is XORed with the first plaintext block as shown in Fig. (2-b). This mechanism produces the first encrypted block. To encrypt the subsequent plaintext blocks, the former ciphertext block is chaotic encrypted in the pixel format and the output in the bit format is XORed with the bits of the current plaintext block. The XOR operation conceals the plaintext patterns. The encryption is performed as follows:

$$ {C}_j={P}_j\oplus {E}_k\ \left({C}_{j-1}\right),\kern0.5em j=1,2,3,\dots ..,w $$
(5)

and the decryption is performed as follows:

$$ {P}_j={C}_j\oplus {E}_k\ {\left({C}_{j-1}\right)}_{,}\ j=1,2,3,\dots ..,w $$
(6)

A security issue is noticed in the CFB mode. If the adversary successfully guesses the secondary key (it’s easy to be guessed if the cipher is week), given Cj-1 and Cj, the adversary is able to calculate Pj as follows:

$$ {P}_j={C}_j\oplus {E}_k\ \left({C}_{j-1}\right),j=1,2,3,\dots ..,w $$
(7)

So, the encryption algorithm must be strong enough to resist any attempt to break it.

3.3 Chaotic encryption in the OFB mode

This mode starts with encrypting the IV in the pixel format with the chaotic Baker map as shown in Fig. (2-c). An XOR operation is conducted between the bits of the first plaintext block and the output of the chaotic map to obtain the encrypted block. And so on, the chaotic map output is considered as the input to the next chaotic map as an IV. This will continue until all plaintext blocks are encrypted in the same manner. The encryption algorithm is performed as follows:

$$ {C}_j={P}_j\oplus {I}_j,j=1,2,3,\dots ..,w $$
(8)

and the algorithm of decryption is performed as follows:

$$ {P}_j={C}_j\oplus {I}_{\mathrm{j}},j=1,2,3,\dots ..,w $$
(9)

where Ij = Ek (Ij-1), j = 1, 2, 3…w, and I0 = IV.

Like the CFB mode, the encryption algorithm must be strong enough to resist any attempt to break it.

4 Encryption quality metrices

Any encryption system should be evaluated to judge its strength. Also, the visual inspection of the encrypted image is not sufficient for evaluation. So, numerical metrics are required for evaluation. This work will take into account three metrics to measure the quality of the proposed cryptosystem. Moreover, a comparison is held with traditional image encryption systems to evaluate the performance of the proposed system. The numerical metrics are the histogram deviation, the irregular deviation, and the correlation coefficient. In addition, three other factors are also considered for the evaluation of the encryption quality; the noise immunity, the histogram uniformity, and the processing time [21, 23].

4.1 The histogram deviation

The quality of an encryption system can be measured by the histogram deviation. The value of the histogram deviation should be as maximum as possible between the encrypted and plaintext images [23]. The histogram deviation can be computed as follows:

  1. 1.

    The plaintext image histogram and the encrypted image histogram are computed.

  2. 2.

    The absolute difference between the histograms in step 1 is computed.

  3. 3.

    The area under the absolute difference of step 2 divided by the size of the image is computed as follows:

$$ {D}_H=\frac{\left(\frac{d_0+{d}_{255}}{2}+{\sum}_{i=1}^{254}{d}_i\right)}{M\times N} $$
(10)

where M×N is the size of the plaintext image, di is the amplitude of the absolute difference at any pixel color value. For better performance of an encryption system, the DH should be kept high [23].

4.2 The irregular deviation

The quality of an encryption system can be measured by irregular deviation. The value of the irregular deviation should be as minimum as possible to be very close to the optimum value of the encryption state [21]. The irregular deviation can be computed as follows:

  1. 1.

    The absolute difference is computed between the original image and the corresponding ciphered image.

  2. 2.

    The Histogram H is computed for the absolute difference in step 1.

  3. 3.

    The mean value MH is computed for the histogram in step 2.

  4. 4.

    The absolute of the histogram deviations is computed as follows:

$$ {H}_D(i)=\mid H(i)-{M}_H\mid $$
(11)
  1. 5.

    Finally, the irregular deviation DI is computed as follows:

$$ {D}_I=\frac{\sum_{i=0}^{255}{H}_D(i)}{M\times N} $$
(12)

For better performance of the image encryption system, the DI should be kept small.

4.3 The correlation coefficient

One of the most famous metrics to evaluate the quality of an encryption system is the correlation coefficient. The correlation coefficient is measured between the pixels of the plaintext and encrypted images [24]. The correlation coefficient is computed as follows:

$$ \operatorname{cov}\left(x,y\right)=E\left(x-E(x)\right)E\left(y-E(y)\right), $$
(13)
$$ {r}_{xye}=\frac{\operatorname{cov}\left(x,y\right)}{\sqrt{D(x)}\sqrt{D(y)}}, $$
(14)

where the pixels values of the original and encrypted images at the same coordinates are x and y respectively. The mathematical expressions for E(x),D(x) and cov(x,y) are defined as follows:

$$ E(x)=\frac{1}{L}\sum \limits_{l=1}^L{x}_l $$
(15)
$$ D(x)=\frac{1}{L}\sum \limits_{l=1}^L{\left({x}_l-E(x)\right)}^2, $$
(16)
$$ \operatorname{cov}\left(x,y\right)=\frac{1}{L}\sum \limits_{l=1}^L\left({x}_l-E(x)\right)\left({y}_l-E(y)\right), $$
(17)

where L represents the total number of pixels. The value of rxye is between 1 and -1.

Another correlation coefficient can be computed between the decrypted and original images. It will be referred to as rxyd. and the its expected value is approximately 1 which means there is a fully match between the two images. Hence, the cryptosystem successes to restore the original image with high quality.

4.4 The noise immunity

A common attack measures the strength of the cryptosystem which is the resistance of the cryptosystem to noise attack [25]. The proposed cryptosystem is tested against the noise attack by adding several amounts of noise to encrypted image, then decrypt the image. Now, we need to measure the closeness between the original and the decrypted images. The closeness between the two images reveal to the strength of the cryptosystem and can be measured by the Peak Signal to Noise Ratio (PSNR) which is computed as follows:

$$ PSNR\kern0.48em =\kern0.36em 10\times {\log}_{10}\left(\frac{M\times N\times {255}^2}{\sum \limits_{m=1}^M\sum \limits_{n=1}^N{\left|\left(f\left(m,n\right)-{f}_d\right(m,n\left)\right)\right|}^2}\right) $$
(18)

where f(m, n) is the plaintext image and fd(m, n) is the recovered image.

4.5 Histogram uniformity

The histogram of the encrypted image can be used to assess the image encryption quality. With increasing the uniformity of the histogram, the cryptosystem achieves a higher level of security.

4.6 Processing time

The time needed to encrypt and decrypt the digital image is the processing time. Off course, a good encryption system has a low processing time. In the following section, the relation between the processing time and the changing of the block size will be studied for the proposed cryptosystem in the CBC mode, the CFB mode, and the OFB mode normalized by the processing time of the chaotic Baker map cryptosystem.

5 Results and discussion

In this section, simulation experiments are conducted to encrypt the Lena image by the proposed image cryptosystem using the CBC mode, the CFB mode, and OFB mode. Also, a comparison is held with the traditional Baker map and CR6 cryptosystems. For the proposed image cryptosystem, the IV is taken as a part of the encrypted Cameraman image, which is the same size of the determined block size. The proposed cryptosystem performance will be investigated with different block size as follows:

  1. 1.

    S1 = 128 × 128. The IV is a 128 × 128 section of the encrypted Cameraman image.

  2. 2.

    S2 = 64 × 64. The IV is a 64 × 64 section of the encrypted Cameraman image.

  3. 3.

    S3 = 32 × 32. The IV is a 32 × 32 section of the encrypted Cameraman image.

  4. 4.

    S4 = 16 × 16. The IV is a 16 × 16 section of the encrypted Cameraman image.

  5. 5.

    S5 = 8 × 8. The IV is an 8 × 8 section of the encrypted Cameraman image.

Note that all the IVs are taken as a part of an encrypted version of Cameraman digital image with the same sizes as the block. Fig. 3 shows the encrypted Lena image by the chaotic Baker map encryption system and the RC6 encryption system. Fig. 4 shows the encrypted Lena image by the proposed cryptosystem using the CBC mode, the CFB mode, and OFB mode with the aforementioned block sizes for each. The results depicted in Fig. 4 shows excellent performance of the proposed cryptosystem. But at large block size of OFB mode the results show pattern which indicates excluding the results at large block size of OFB mode. The immunity of the proposed cryptosystem against the noise is examined. The additive white Gaussian noise with SNR = 5 dB is mixed with the encrypted image, then performs the decryption process. Fig. 5 shows the decryption processes of the chaotic Baker map system and the RC6 system in the presence of noise. Fig. 6 shows the results of the decryption process of the proposed cryptosystem in the presence of noise. By visually comparing the Figs. 5 and 6, it is clear that the highest system that resists the noise is the chaotic Baker map. Also, the figures depict that the proposed cryptosystem has a higher resistance to noise from the RC6 system.

Fig. 3
figure 3

Encrypted images using the traditional cryptosystems

Full size image
Fig. 4
figure 4

Encrypted images using the proposed image cryptosystem with different modes of operation and different block sizes

Full size image
Fig. 5
figure 5

Decrypted images using the traditional cryptosystems at an SNR = 5 dB

Full size image
Fig. 6
figure 6

Results of the proposed image cryptosystem: Decryption of Lena Image by CBC, CFB and OFB modes and several sizes of block at SNR = 5 dB

Full size image

The numerical values of the metrics are shown in Table 1 (a, b, c, and d). The values of these metrics are calculated in the presence of AWGN with an SNR = 5 dB. The results in Table 1 reveal the chaotic Baker map cryptosystem is the highest resistant system to noise. This is clearly shown from the DI value of baker map (0.98). Also, the results indicate that the chaotic Baker map has a lower security level from the proposed cryptosystem ad the RC6 system. This is clearly shown in the values of rxye and rxyd. For instance, the rxye value (4.7 × 10−6) in field S2 in the CBC mode indicates a good encryption quality compared to the rxye value of the baker map (10−4).

Table 1 Numerical evaluation metrics for all cryptosystems
Full size table

In addition, the results reveal that the RC6 system is greatly affected by the presence of noise. So, the comparison shows that the proposed cryptosystem has a balance between the resistant of noise and the security level. Fig. 7 shows the performance of the proposed cryptosystem in CBC mode, the CFB mode, and OFB mode with several sizes of the block. The figure illustrates the computed value of the PSNR of the restored Lena image with different amounts of additive noise to the encrypted Lena image. From the results in Fig. 7, we can conclude that all modes of operation have similar behavior when noise is present, and the results get better with increasing the value of SNR. Moreover, it can be seen from the results that the proposed cryptosystem resistance to noise is not affected by changing the block size in the CBC mode, the CFB mode, and OFB mode.

Fig. 7
figure 7

The PSNR values of decrypted Lena image with different amounts of SNR of the proposed image cryptosystem for a The CBC mode, b The CFB mode, c The OFB mode

Full size image

Fig. 8 shows the histograms of the plaintext image of Lena, the corresponding encrypted image by the chaotic Baker map system and the corresponding encrypted image by the CR6 system. Fig. 9 shows the histograms of the encrypted Lena image by the proposed cryptosystem with the modes CBC, CFB, and OFB and several sizes of the block. Form Fig. 8, the histogram of encrypted Lena image by the Baker map system is identical to the plaintext Lena image histogram which is considered a defect of the chaotic Baker map system and low-security level. On the other hand, the Histogram of the encrypted Lena image by the RC6 system is uniform which indicates a high-security level. The results depicted in Fig. 9 show that the proposed cryptosystem has uniformity histograms which reveal a high-security level with the exclusion of the results of the OFB mode of operation when the sizes of the block are large. The structure of the RC6 system leads to more time for encryption than the Baker map system, which makes sense to exclude the RC6 system from processing time comparison.

Fig. 8
figure 8

Histograms of Lena image (a) Plaintext image, (b) Encrypted by Baker map, (c) Encrypted by RC6

Full size image
Fig. 9
figure 9

The histograms of the encrypted Lena images using the proposed image cryptosystem with different block sizes of the modes of operation

Full size image

The processing time (encryption and decryption) comparison is depicted in Table 2. The results in Table 2 reveal that all modes with different sizes of block almost have similar normalized processing time. Also, it is noticed that the processing time is low with larger block sizes due to a small number of blocks.

Table 2 The normalized estimated computational time in the proposed cryptosystem for the tested modes at different block sizes
Full size table

To prove the superior performance of the proposed cryptosystem over the other systems, a comparison is held between the proposed cryptosystem and the recent related encryption systems, such as encryption systems in [5, 7,8,9,10, 29, 33,34,35,36]. We have compared the statistical security analysis of the entropy, correlation coefficient, number of changing pixel rate (NPCR), unified averaged changed intensity (UACI), and PSNR between the proposed cryptosystem and recent encryption systems as shown in Table 3.

Table 3 The statistical security analysis results for cipher Lena image for the proposed image cryptosystem and the literature schemes in [5, 7,8,9,10, 29, 33,34,35,36]
Full size table

The results in Table 3 indicate that the proposed cryptosystem achieves the highest entropy value which is very close to the optimum value 8. So, the proposed cryptosystem can successfully resist the entropy attack better than the comparative encryption systems. In addition, the correlation coefficient values of the proposed cryptosystem are the lowest (almost zero, optimum value) between the systems which reveal that the proposed cryptosystem successfully breaks the correlation between the original and encrypted images. Table 3 depicts the values of NPCR and UACI which indicates the ability of the proposed cryptosystem to effectively resist the differential attack. Also, the values of the PSNR indicate the ability of the proposed cryptosystem to successfully decrypt the image in the presence of noise. In general, the comparison presents in Table 3 indicates that the proposed cryptosystem is robust and has a high level of security.

6 Conclusions

This work proposes a new image cryptosystem that segments the plaintext image into blocks and encrypts each block with the 2-D chaotic Baker map encryption system in different modes of operation; the CBC mode, the CFB mode, and the OFB mode. The proposed cryptosystem is characterized by the balancing between the advantages of high noise resistance and high security. The results reveal that the proposed cryptosystem produces a uniform histogram of the encrypted image which the chaotic Baker map system cannot achieve by its encryption process. Also, the results reveal that the proposed cryptosystem has a satisfactory processing time, and lower than that of the traditional chaotic Baker map cryptosystem if the images of large dimensions to be encrypted are divided into a small number of blocks. In addition, the suggested cryptosystem has both the advantage of permutation cryptosystems (speed) as well as the advantage of substitution cryptosystems (security). The experimental studies demonstrated the advantages of the proposed cryptosystem which are: 1) secure against statistical attacks, 2) efficient confusion features and 3) high resistance to noise attack. In future work, it is suggested to extend our work to includes watermarking and steganography in the encryption process for a more robust and more degree of security. Also, we will fuse the proposed cryptosystem with a deep learning algorithm to increase the degree of security.