Double‐image asymmetric cryptosystem using cylindrical diffraction and spectrum fusion and compression

IET OptoelectronicsVolume 14, Issue 4 p. 169-175 Research Article Free Access Double-image asymmetric cryptosystem using cylindrical diffraction and spectrum fusion and compression Changtao He, School of Electronics and Information Engineering, Sichuan University, Chengdu, 610065 People's Republic of China Sichuan Jiuzhou Electric Group Co., Ltd., Mianyang, 621000 People's Republic of ChinaSearch for more papers by this authorZhigang Liu, Sichuan Jiuzhou Electric Group Co., Ltd., Mianyang, 621000 People's Republic of ChinaSearch for more papers by this authorXudong Chen, School of Electronics and Information Engineering, Sichuan University, Chengdu, 610065 People's Republic of ChinaSearch for more papers by this authorJun Wang, Corresponding Author jwang@scu.edu.cn School of Electronics and Information Engineering, Sichuan University, Chengdu, 610065 People's Republic of ChinaSearch for more papers by this author Changtao He, School of Electronics and Information Engineering, Sichuan University, Chengdu, 610065 People's Republic of China Sichuan Jiuzhou Electric Group Co., Ltd., Mianyang, 621000 People's Republic of ChinaSearch for more papers by this authorZhigang Liu, Sichuan Jiuzhou Electric Group Co., Ltd., Mianyang, 621000 People's Republic of ChinaSearch for more papers by this authorXudong Chen, School of Electronics and Information Engineering, Sichuan University, Chengdu, 610065 People's Republic of ChinaSearch for more papers by this authorJun Wang, Corresponding Author jwang@scu.edu.cn School of Electronics and Information Engineering, Sichuan University, Chengdu, 610065 People's Republic of ChinaSearch for more papers by this author First published: 01 August 2020 https://doi.org/10.1049/iet-opt.2019.0159Citations: 1 AboutSectionsPDF 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 onEmailFacebookTwitterLinked InRedditWechat Abstract A double-image asymmetric cryptosystem is proposed by using cylindrical diffraction and spectrum fusion and compression in the zigzag-scanned domain of discrete cosine transform (DCT). First, each plaintext of double image is converted into spectrum coefficients (SCs) by DCT, and the SCs are zigzag scanned. Second, the first 1/4 of SCs is resized to two low-frequency images, the second 1/4 of SCs is resized to two high-frequency images, while the last 1/2 of SCs is discarded. Third, the two low-frequency and two high-frequency images are fused and merged into three rounds of encryption process by using the complex combination, random phase encoding, and phase reserving–truncation in the cylindrical diffraction transform domain. Finally, the plaintexts of the double image are successfully encrypted into a ciphertext and three private keys with each only 1/8 and totally 1/2 of the size of the plaintext, which gains a high compression efficiency. In the proposed cryptosystem, the quality of the reconstructed image is improved due to the compression in the zigzag-scanned DCT domain, and the security is improved owing to the asymmetric cylindrical diffraction and spectrum-fusion algorithm. The effectiveness and flexibility of the proposed cryptosystem have been validated by the numerical simulation results. 1 Introduction With the booming development of the Internet, it has become extremely important to the security of data transmission. Owing to the advantages of parallel processing, multidimensional capabilities etc. [1-3], the techniques of optical image encryption have been widely studied in past decades. Among various optical encryption techniques, the double-random-phase encoding (DRPE) is the most classical method, which can encrypt an image into a stationary noise-like image using double-random-phase masks placed in the input and output planes of Fourier domains [4]. To improve the security and increase the keyspace, other domains, e.g. the fractional Fourier [5], Fresnel [6, 7], and the gyrator transform [8, 9], are involved in several extensions of the DRPE. Unfortunately, the DRPE-based technique is linear and is a kind of symmetric cryptosystem with identical encryption and decryption keys, which is known to be vulnerable to various types of attacks [10-12]. To conquer the security issues inherent in the symmetric system, several asymmetric cryptosystems have been reported [13-15]. Nevertheless, an attack method based on iterative retrieval algorithm (IRA) can successfully extract the original plaintext information [16]. Owing to the interest of further enhancing the encryption efficiency, a technique of double-image encryption (DIE) is becoming a valuable issue. A technique for DIE based on random phase encoding in the fractional Fourier transform domain is first proposed [17, 18]. Subsequently, the gyrator transform is introduced to enhance the DIE technique cooperated with iterative random binary encoding [19], pixel scrambling [20, 21], and iterative phase retrieval algorithm [22]. Meanwhile, discrete fractional random transform (DFrRT) is also proved to be an effective approach to DIE [23, 24]. Besides, the asymmetric strategy with phase truncation (PT) has been employed in DIE [25-27]. More recently, novel DIE methods are reported, which are based on compressive ghost imaging [28] and incoherent illuminated cryptosystem with rotating random phase mask [29]. Above-mentioned DIE schemes can achieve effective encryption, while encryption with compression is scarce. To obtain an efficient DIE-compression (DIEC), a novel DIEC scheme is proposed by combining compressive sensing with the DFrRT [30]. Furthermore, an improved DIEC scheme is proposed by combining co-sparse representation with random pixel exchanging and the DFrRT [31]. However, these DIEC schemes are symmetric systems, which might be a threat by various types of symmetric attacks. Although some asymmetric DIEs such as [25-27] have good security performance, their encryption are not efficient in view of data storage of transmittance. In this view, there is a clear motivation to develop an efficient asymmetric DIEC with high security. In this paper, we propose a double-image asymmetric cryptosystem by using cylindrical diffraction and spectrum fusion and compression in the zigzag-scanned domain of discrete cosine transform (DCT). In the proposed encryption process, each plaintext of double images is first converted into spectrum coefficients (SCs) by DCT, and the SCs are zigzag scanned. Second, the first 1/4 of SCs is resized to two low-frequency images, the second 1/4 of SCs is resized to two high-frequency images, while the last 1/2 of SCs is discarded. Third, the two low-frequency and two high-frequency images are fused and merged into three rounds of encryption process by using the complex combination, random phase encoding, and phase reserving and truncation (PRT) in the cylindrical diffraction transform (CDT) domain. Finally, a ciphertext and three private keys are obtained, and each is only 1/8 of the size of the plaintext, which is 1/2 of the size of plaintext totally. The decryption process is the inverse one of the proposed encryption. The proposed cryptosystem achieves a high quality of the reconstructed image due to the compression in the zigzag-scanned DCT domain. Meanwhile, because of the asymmetric cylindrical diffraction and spectrum fusion, the proposed cryptosystem gains improved security in aspects of information disclosure and IRA special attack, respectively. The numerical simulation results have verified the effectiveness and flexibility of the proposed cryptosystem. 2 Proposed asymmetric cryptosystem 2.1 PRT in CDT domain According to the cylindrical diffraction theory in [32, 33], the object and the observation surfaces are concentric cylindrical surfaces. Figs. 1a and b show the two, inside-out propagation (IOP) and outside-in propagation (OIP) models when the objects are placed on the inside and outside surfaces, respectively. Figure 1Open in figure viewerPowerPoint Principle of cylindrical diffraction theory (a) IOP model, (b) OIP model In both cases of IOP and OIP models, U1(θ1, z1) and U2(θ2, z2) are the input and output of CDT, respectively, CDT{•} denotes a CDT, and the point pulse function of CDT [33] can be expressed as ((1)) ((2)) where λ is the wavelength of the incident light and r1, r2 denote the radii of the input and output cylindrical surfaces, respectively. Since the diffraction processes of OIP and IOP are asymmetric, the cryptosystem based on cylindrical diffraction is naturally asymmetric and can resist the special attack of iteration retrieval algorithm (IRA). To further improve the security, the method of PRT is used to generate decryption keys, which is different from the encryption keys, in the CDT domain, and it can be expressed by ((3)) where PRT[•] is the PRT operation. E and P are amplitude and phase results of PT and reserving operations, which are ciphertext and private key, respectively. 2.2 Spectrum compression in zigzag-scanned DCT domain DCT is a popular technology in image processing, especially in pattern recognition, compression, and encryption [34] due to its strong 'energy concentration' characteristic. It is a special form of discrete Fourier transform (DFT) in the real number domain since the Fourier transform of the real even function only contains the real cosine term according to the properties of the discrete Fourier transform. Therefore, supposing input function x having n × n pixels, the 1D mathematical definition of DCT can be expressed as ((4)) where Xm is the output function and m denotes the serial number of the output function. In the proposed cryptosystem, the DCT is employed to separate low and high frequencies for spectra fusion in further processing. The process of compression in the zigzag-scanned DCT domain is described as follows. First, the original image is converted into SCs by DCT, and the SCs are zigzag scanned. Second, the first 1/4 of SCs is resized to low-frequency images, the second 1/4 of SCs is resized to high-frequency images, while the last 1/2 of SCs is discarded. The framework of compression using zigzag-scan-then discard is shown in Fig. 2. Figure 2Open in figure viewerPowerPoint Framework of compression using zigzag-scan-then discard 2.3 Processes of encryption and decryption The proposed cryptosystem consists of encryption and decryption processes. Fig. 3 shows the framework for the proposed encryption process which consists of four steps: Step 1: DCT is first applied to two images I1 and I2, which are ciphertexts to be encrypted; then, the compression is performed on the zigzag-scanned DCT SCs by discarding the last half of SCs, which is called scan-then-discard (STD). As a result, two low-frequency images and two high-frequency images are obtained, which are denoted as I1L, I2L, I1H, and I2H, and each of their pixel size is a quarter of the original image. Figure 3Open in figure viewerPowerPoint Framework of encryption Step 2: I1L and I2L are combined into a complex amplitude U1 as real and imaginary parts, respectively, which is represented as ((5)) where i is an imaginary unit. The complex amplitude U1 is modulated by a random phase mask R1, and the result is a new complex amplitude U2, which is represented as ((6)) where R1 is a random distribution at [0, 2π]. Then, a complex amplitude U3 is obtained through the inverse cylindrical diffraction transformation (ICDT) with the input of complex amplitude U2, which is expressed as ((7)) where ICDT represents the inverse cylindrical diffraction transformation. Finally, the phase reservation and truncation (PRT) operation is carried out on the complex amplitude U3, and the phase P1 and amplitude A1 are obtained, which are expressed as ((8)) where PR and PT represent the phase reservation and phase truncation operations, respectively. Step 3: A1, I1H, and R2 are used to replace I1L, I2L, and R1 as inputs, respectively. Step 2 is repeated to obtain phase P2 and amplitude A2, where R2 has a uniform probability distribution on the interval [0, 2π]. Step 4: A2, I2H, and R3 are used to replace I1L, I2L, and R1 as inputs, respectively. Step 2 is repeated to obtain phase P3 and amplitude E, where R3 has a uniform probability distribution on the interval [0, 2π]. The phases P1, P2, and P3 obtained in the above steps (2)–(4) are taken as the private keys, and E is taken as the final ciphertext. Then, the encryption process is done. Fig. 4 shows the framework for the proposed decryption process, which also consists of four steps. These steps are an exactly inverse process of encryption, whose details are omitted for simplicity. Here, the PTS means pad-then-scan, which is the inverse process of STD. Figure 4Open in figure viewerPowerPoint Framework of decryption From the above descriptions and Figs. 3 and 4, the decryption keys of P1–P3 are differed with the encryption keys R1–R3. Therefore, the proposed cryptosystem is asymmetric and expects to resist normal attacks such as known-plaintext, chosen-plaintext, and chosen-ciphertext attacks. Besides, the encryption keys of random phase masks can be generated by three-dimensional (3D)-hyper chaos algorithms [35]. The total data amount to save or transmission including phase keys P1–P3 and ciphertext E are only half of the original input images. Since the operations of DCT, inverse DCT (IDCT), STD, PTS, and PRT cannot be implemented in optical means, the proposed encryption is not easy to implement in optical means. However, the decryption process could be implemented in optical–electronic means, which is popular in recent research because of its high security, since the main processing of CDT operation could be implemented in optical means and other parts could be implemented in electronic means. 2.4 Algorithm of spectrum fusion in encryption To improve the performance of the information disclosure of the proposed cryptosystem, the algorithm of spectrum fusion in encryption is proposed. For comparison and analysis, the without spectrum-fusion method is first analysed, which is presented by ((9)) In the without spectrum-fusion case, the attacker can fully get the second image I2 by decompressing the I2L and I2H if the private keys of P2 and P3 are disclosures, which is the worst case of information disclosure combinations of the three private keys. To avoid this worst case, an algorithm of spectrum fusion is proposed by exchanging the position of I1H and I2L in the encryption process, which is presented by ((10)) Therefore, the attacker cannot accomplish decompressing the second image I2 because the I2L is wrong even if the private keys of P2 and P3 are disclosures, which means the only private key of P1 is non-disclosure. Besides, this spectrum-fusion algorithm will not affect the decryption process. The security will be improved significantly with a small cost of changing the combination order. The algorithms of with and without spectrum fusion are shown in Figs. 5a and b, respectively. The difference of with and without spectrum fusion is shown in red lines in Fig. 5a. Figure 5Open in figure viewerPowerPoint Algorithms of (a) With spectrum fusion, (b) Without spectrum fusion 3 Results The simulations are performed on MATLAB R2017a platform to analyse the performance of the proposed cryptosystem with processor Intel CoreTM i7@2.4 GHz, memory 8.0 GB RAM, and 64 bit OS Win10. In the CDT, the inner cylinder r, outer cylinder R, and heights H are set to 10, 200, and 32 mm, respectively. The wavelength λ is 24 µm. The parameters of 3D-hyper chaos are set as [x0, y0, z0] = [0.258, 0.368, 0.568] and [a, b, c] = [35, 3, 28]. Here, [x0, y0, z0] and [a, b, c] are initial values and control parameters, respectively. To evaluate the similarity and quality between the plaintext I and the decrypted image I′, correlation coefficient (CC) and peak signal-to-noise ratio (PSNR) are employed, respectively. CC and PSNR values are calculated by ((11)) ((12)) where cov denotes cross-covariance and σ denotes standard deviation. Moreover, M × N denotes the size of an image. Here, the coordinates are omitted. 3.1 Validation of the cryptosystem The original images and corresponding decrypted images with 512 × 512 px2 as shown in Figs. 6a and b, respectively, which are two pairs of double images. The PSNRs of the decrypted images are all above 35 dB, which means a very high quality of a decompressed image. In the encryption process, there are two sets of three private keys of P1, P2, and P3, which are shown in Figs. 7a and b. The two sets of ciphertexts of the DIE are shown in Figs. 7c and d. Neither the private key nor the ciphertext shows any information about the original double image. Figure 6Open in figure viewerPowerPoint Results of encryption and decryption (a) Plaintexts: Aeroplane, Peppers, House, Hill, (b) Decrypted images of (a), respectively Figure 7Open in figure viewerPowerPoint Private keys and ciphertexts (a) Three private keys of P1, P2, and P3 of double-image Aeroplane and Peppers, (b) Three private keys of P1, P2, and P3 of double image House and Hill, (c) Ciphertext of double-image Aeroplane and Peppers, (d) Ciphertext of double-image House and Hill 3.2 Comparison of compression efficiency During the encryption process, the double image is compressed into half by discarding half of frequency coefficients in zigzag-scanned DCT domain, and other parts of the encryption process are a lossless process in numerical computing. Therefore, the compression efficiency of the cryptosystem, which includes compression ratio (CR) and decompressed quality, can be compared with other methods by setting the CR to 2. For comparison, the discrete wavelet transforms (DWTs) and DCT-based compression schemes are selected. The first compared method is based on DWT and to discard the high–low and high–high frequencies in the first-order decomposition, which remains the low–low (LL) and low–high (LH) frequencies and denotes by DWT-LL-LH [36]. The second compared method is based on DCT and is similar to the proposed method but without zigzag-scan, which denotes by DCT-non-scan. While the compression algorithm used in the proposed method denotes by DCT-scan. The comparison of the decompressed quality of these three methods is shown in Table 1. Table 1. Comparison of the decompressed quality of three methods in the CR of 2 Compression methods Decompressed quality in PSNR, dB for test images Aeroplane Peppers House Hill Average DWT-LL-LH [36] 33.46 34.30 31.76 32.78 33.08 DCT-non-scan 38.93 38.19 36.77 35.41 37.33 DCT-scan (proposed) 43.95 40.10 40.90 37.71 40.67 From Table 1, the simulation results show that the decompressed quality in PSNR of DCT-scan is 40.67 dB in average for four different test images and is 6.59 and 3.34 dB higher than those of the compression algorithms of DWT-LL-LH and DCT-non-scan. Therefore, the proposed cryptosystem has a high quality of the decrypted image. As considering CR, the proposed method is compared with other typical DIE methods [20, 27, 36] as shown in Table 2. The CR is considered for the ratio of plaintext data to the total data for transmission or storage. From Table 2, the CR of the proposed method is 2 and is the highest one compared with other typical DIE methods. Table 2. Comparison of the data amount of the proposed and other methods Encryption methods Data amount (unit: 1 = one image size) and CR Plaintext Ciphertext Private keys Total CR Proposed method 2 1/4 3/4 2 Chen-OE-2014 [20] 2 2 0 1 Wu-OC-2019 [36] 1 1/4 3/4 1 Kumar-OLT-2018 [27] 2 2 1 2/3 3.3 Key sensitive and space The security of a cryptosystem is related to the key sensitivities and keyspace. The double image of House and Hill are employed for the key sensitivities and keyspace. In the proposed scheme, diffraction parameters of λ, r, R, and H are the encryption keys. The key sensitive is that a tiny change to the right key will cause decryption failure. The decryption results in minimum changes, which is a threshold, and just causes the decryption failure to the diffraction parameters as shown in Fig. 8. It shows that none of the plaintext information can be recognised from the decrypted images. The CC values of the decrypted results are ranged from 0.0071 to 0.0973, and they are all below 0.1, which is regarded as no correlation between the decrypted and original images. The threshold changes of diffraction parameters of λ, r, R, and H are 3.0 × 10−10, 1.0 × 10−6, 2.0 × 10−6, and 3.0 × 10−7, respectively. As a result, the keyspace of diffraction parameters is 6.0 × 1027. Figure 8Open in figure viewerPowerPoint Results of decryption with wrong encryption keys (a) Δλ = 3.0 × 10−10, CC = 0.0529, 0.0071, (b) Δr = 1.0 × 10−6, CC = 0.0960, 0.0266, (c) ΔR = 2.0 × 10−6, CC = 0.0973, 0.0085, (d) ΔH = 3.0 × 10−7, CC = 0.0838, 0.0842 The decrypted CC results of threshold changes to the parameters of 3D-hyper chaos are shown in Table 3. It shows that they are ranged from − 0.0058 to 0.0067, which is regarded as no correlation between the decrypted and original images. The threshold changes of chaos parameters of x0, y0, z0, a, b, and c are 10−16, 10−16, 10−16, 10−14, 10−14, and 10−14, respectively. As a result, the keyspace of chaos parameters is 1090. Therefore, the total keyspace should be more than 6 × 10117, which is great enough to resist the brute force attack. Table 3. Key sensitivity of parameters of 3D-hyper chaos Δ Δx0 = 10−16 Δy0 = 10−16 Δz0 = 10−16 Δa = 10−14 Δb = 10−14 Δc = 10−14 CC house 0.0039 0.0067 0.0045 0.0006 −0.0051 −0.0021 hill −0.0058 0.0054 0.0045 −0.0047 0.0032 0.0024 3.4 Noise attacks We investigate the noise attack performance of the proposed cryptosystem by adding Gaussian noise to the ciphertext and evaluating the quality of the decrypted image. Fig. 9 shows the decrypted results of the ciphertext noisy by different strengths of Gaussian noise. The noisy model is represented by ((13)) where G is Gaussian noise with zero mean and different variance. Figs. 9a–d are the results of House and Hill with variances of 0.01, 0.02, 0.05, and 0.1. The corresponding PSNR values of House are 27.99, 25.10, 21.17, and 18.32 dB, respectively. Moreover, the corresponding PSNR values of Hill are 27.81, 25.05, 21.21, and 18.34 dB, respectively. These PSNR results show that the proposed method is robust with the noise attacking. Figure 9Open in figure viewerPowerPoint Decryption results of noise attack by using Gaussian noise with zero mean and different variances (a) 0.01, (b) 0.02, (c) 0.05, (d) 0.1, for House and Hill, respectively 3.5 Test of information disclosure Since there are three private keys of P1, P2, and P3, there is a risk that one or two of the keys is disclosure. More details about the information disclosure can be found in [14, 37]. Therefore, a test of information disclosure is carried out as shown in Fig. 10 for House and Hill. First, one key disclosure is evaluated. Figs. 10a–c are the results of the disclosures of P1, P2, and P3, respectively. Then, two keys disclosure is evaluated. Figs. 11a–c are the results of non-disclosures of P1, P2, and P3, respectively, which means disclosures of [P2, P3], [P1, P3], and [P1, P2], respectively. In all the cases, the information disclosure of [P2, P3] is the worst case, while it is still safe according to the result shown in Fig. 11a. Figure 10Open in figure viewerPowerPoint Results of information disclosure of (a) P1, (b) P2, (c) P3. The test double images are House and Hill Figure 11Open in figure viewerPowerPoint Results of information non-disclosure of (a) P1, (b) P2, (c) P3. The test double images are House and Hill For comparison, a test of information disclosure based on the non-spectrum-fusion method is carried out. Figs. 12a–c show the results of information non-disclosures of P1, P2, or P3, respectively, for the non-spectrum-fusion method, which is mentioned in Section 2.4. It shows that the second image I2 is fully decrypted when private keys of P2 and P3 are leakages as shown in Fig. 12a, which means this method cannot resist the attack of the critical path or the worst case. Test for information disclosure with the single private key is not necessary because of leaking less information and being more critical to the attacker than information disclosure with double private keys. Figure 12Open in figure viewerPowerPoint Results of information non-disclosure of (a) P1, (b) P2, (c) P3, for the non-spectrum-fusion method. The test double images are House and Hill The comparison shows that the proposed cryptosystem is still safe due to the spectrum fusion even in the worst case. Therefore, the algorithm of spectrum fusion significantly improves the performance of information disclosure of the proposed cryptosystem. 3.6 Special attack based on IRA Since the proposed cryptosystem is asymmetric based on PT, it might be attacked by a special attack based on IRA [16]. We have discussed that the proposed cryptosystem is still safe even if any two of three private phase keys were disclosures in the previous section. However, there is a risk to be attacked by the special attack of IRA in the worst case that the private keys of P2 and P3 were disclosed. That means the attacker knew A1 and tries to get U2 without P1. The result of the special attack, in this case, is shown in Fig. 13a. For comparison, the result of the special attack in the same condition while only CDT is replaced by Fourier transform [16], which is shown in Fig. 13b. Figure 13Open in figure viewerPowerPoint CC results of IRA attack according to iteration numbers with (a) CDT, (b) Fourier transform In Fig. 13a, the maximum CC value is below 0.05, which means no useful information can be obtained from the attacking. While in Fig. 13b, the CC value is converged to 0.6 after iteration of 30 times, which means the attacking could be successful. The comparison of CC values versus iteration numbers shows that the special attack of IRA is vulnerable even in the worst case that private keys of P2 and P3 were disclosed. Therefore, the security of the proposed cryptosystem on resisting special attack is greatly improved by CDT. 3.7 Test of chosen-plaintext attack Generally, there are four types of traditional attacks, namely cipher-only attack, known-plaintext attack, chosen-cipher attack, and chosen-plaintext attack, among which chosen-plaintext attack is the easiest one. Hence, if a cryptosystem could resist chosen-plaintext attack, it can resist other attacks. Supposing the proposed method is known, the illegal user may use a chosen double image to encrypt and obtain a fake private key, and could try to decrypt the original image with the obtained fake private key. The results of chosen-plaintext attack are shown in Fig. 14. The chosen attacking double images are shown in Fig. 14a, which are House, Hill, Black, and White. The original double image of Flower and Birds are shown in Fig. 14b. The attack results using House and Hill are shown in Fig. 14c. Moreover, the attack results using Black and White are shown in Fig. 14d. We cannot obtain any valid information, which indicates that the proposed scheme has high security and strong robustness to resist chosen-plaintext attack. Figure 14Open in figure viewerPowerPoint Results of chosen-plaintext attack (a) Chosen plaintexts of House, Hill, Black, and White, (b) Fake images of Flower and Birds, (c) Attack results using House and Hill, (d) Attack results using Black and White 4 Conclusions In this paper, we propose a double-image asymmetric cryptosystem by using cylindrical diffraction and spectrum fusion and compression in the zigzag-scanned domain of DCT with high security and compression efficiency. There are three main contributions in this paper. First, the proposed encryption successfully hides the double images into one ciphertext and three private keys, and each is only 1/8 of the size of the plaintext, which is 1/2 of the size of plaintext totally. Second, the proposed cryptosystem achieves an improved quality of the reconstructed image due to the compression in the zigzag-scanned DCT domain, which means a high compression efficiency. 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