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Abstract
In this paper, we propose a block compressive sensing (BCS) based chaotic embedded encryption scheme for multi-core fiber orthogonal frequency division multiplexing (MCF-OFDM) system. BCS technology is used to recover the entire desired information from the small amounts of data. Meanwhile, a four-dimensional discrete chaotic encryption model generates four masking factors, which are respectively used for coefficient random permutation (CRP), measurement matrix, diffusion and singular value decomposition (SVD) embedding to achieve ultra-high security encryption of four different dimensions. In terms of compressive sensing, CRP can make the discrete cosine transform (DCT) coefficient distribute randomly to improve the sampling efficiency of BCS. Compared with the data without compressive sensing, the data volume is reduced by 75%. In chaotic encryption, SVD technology embeds secret images of noise-like after initial encryption into carrier images to generate encrypted images with visual security. The key space reaches 10120 and it realizes the dual protection of source image data and external representation. The proposed scheme using a 2km 7-core optical fiber achieves a 78.75 Gb/s transmission of encrypted OFDM signals. The received optical power is greater than -14 dBm, and the bit error rate (BER) of core1-core7 is lower than 10−3. When the compression ratio sets to 0.25 and the attack range of encrypted data is up to 30%, the image can still recover the outline and general information. The experimental results show that this scheme can improve the security performance and reduce the complexity of information transmission system. Furthermore, the scheme combines The BCS chaotic embedded encryption technology with MCF-OFDM system, which has a good application prospect in the future optical networks.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of Internet technology, multimedia information such as image, voice and video has become the main media for information exchange. Multimedia information has the characteristics of carrying large amount of information, image and intuition, and is widely used in various fields such as economy, medicine, national defense and people's livelihood [1,2]. However, as more and more devices connect to the global Internet, channel bandwidth and information storage space are under enormous pressure [3]. In addition, due to the increasing openness of optical networks, network attacks have become diversified and complicated, which poses a great threat to the protection of information privacy [4,5]. Faced with the problems of limited information storage space and hidden danger of information security, how to effectively guarantee the security of information while meeting users’ demand for large-capacity and high-speed information has broad application prospects for the development of optical network in the future [6].
In recent years, image is an important carrier of information transmission, and its larger size and higher definition requirements for efficient transmission and storage of information put forward a great challenge. Therefore, it is very necessary to compress image data to save bandwidth, transmission time and storage space [7,8]. Compressed sensing (CS) is proposed as a new information acquisition and processing technology, which can compress the data according to the characteristics of the image. It can effectively reduce the cost of signal sampling, transmission and storage, and can recover the original image at the receiving end. CS technology has been widely used in military security, medical image processing and network transmission [9–11]. However, a single CS framework is executed column by column. With the increase of image dimension, the consumption of computing time and storage space is also increasing. In order to obtain better compression and reconstruction performance, block compressive sensing (BCS) is proposed as an effective scheme [12,13].
In addition, in the face of massive information and user interaction data, the processing speed of traditional upper layer protocol encryption algorithm is limited and the computational complexity is also increasing. Therefore, this algorithm cannot meet the requirements of secure transmission of high-rate and large-capacity optical signals [14]. Chaotic encryption has highly sensitive to the initial state, complex dynamic behavior, and does not conform to probability statistics principle in distribution. It is widely study by researchers [15–17]. Reference [18] improves the security performance of digital filter multiple access passive optical network (DFMA-PON) by using phase masking and frequency obfuscation method. Reference [19] improves the complexity and randomness of chaotic encrypted sequences through DNA encoding method to achieve security performance in orthogonal frequency-division multiple access (OFDMA) network. Reference [20] realizes high security in orthogonal frequency division multiplexing (OFDM) data transmission through chaotic drift of quadrature amplitude modulation (QAM) constellation. However, as the technology to crack encrypted information is also constantly updated, noise-like or texture-like cryptographic images are easy to attract the attention of hackers and be attacked [21]. Therefore, it is worthy of further study to propose a visually meaningful encryption scheme to enhance the level of information security.
In this paper, a high security scheme based on BCS chaotic embedded encryption is proposed for multi-core fiber orthogonal frequency division multiplexing (MCF-OFDM) systems. In this scheme, original images are segmented and sparsely represented in the discrete cosine transform (DCT) domain, and its coefficients are confused by the coefficient random permutation (CRP) strategy, which is encrypted by BCS to obtain the secret image (SI). Then, using singular value decomposition (SVD) embedding technology, the secret image is embedded into the carrier image to generate the final cipher image, which realizes the dual protection of the source image data and external representation. Finally, OFDM is selected as the transmission format, which can well match other communication technologies such as mobile front-end. The proposed scheme is verified experimentally in a 2 km 7-core fiber transmission system at a rate of 78.75 Gb/s, and the performance of the system is analyzed. The received optical power is greater than −14 dBm, and the bit error rate (BER) of core1-core7 is lower than 10−3. When the compression ratio is set to 0.25, the attack range of cipher image data is up to 30%, the image can still recover the outline and general information. Compared with the encryption scheme without BCS technology, the amount of transmitted data is reduced by 75%. The results show that the proposed scheme achieves a key space of 10120, and can effectively resist illegal attacks with better robustness and efficiency.
2. Principles
The principle of BCS chaotic embedded encryption scheme is shown in Fig. 1. Firstly, the original image is segmented, compressed and encrypted under BCS and CRP architecture. The data compression block is reconstructed and re-encrypted using diffusion algorithm to generate a like-noise secret image. Then the secret image is embedded into the carrier image by SVD technology to generate the final cipher image. Cover-up factors generated by the 4D discrete chaos model system are used for CRP, measurement matrix, diffusion and SVD embedding. Finally, the encrypted signals modulated by OFDM are sent to multi-core fiber channel for transmission. The receiver with the correct key can decrypt the information in the encrypted signal and obtain the original data using the opposite method of computation from the encrypted end.
2.1 Chaotic sequence generation
In this scheme, pseudo-random sequence generated by 4D discrete chaos model is used as masking factor to compress and encrypt information data. A four-dimensional discrete chaotic system generates four chaotic sequences simultaneously. The system can be expressed as:
2.2 Original image is encrypted based on CRP strategy
The CRP strategy is used to encrypt the original image blocks, that is, the source image is divided into blocks, DCT, Z-shaped scanning, CRP and other operations. For a more intuitive understanding, an image with a size of 4×4 is taken as an example, as shown in Fig. 3. Firstly, the image with a size of 4×4 is equally divided into 4 plates. Two-dimensional DCT was performed on each plate to obtain the DCT coefficient matrix, and then Z-shaped scanning was performed to obtain four coefficient vectors Xi (i = 1,2,3,4), where Xi was the coefficient vector of the ith block. Then the DCT coefficient matrix is separately stretched into an array Xij (ij = 11,12,13,14,21…), where Xij represents the jth component of the ith array. The CRP strategy was used to confuse the vector Xi, and the vector was reordered according to the pseudo-random sequence to obtain the confusion vector Yi (i = 1, 2, 3, …), The permutation process can be expressed as:
where $Y_i^j$ and $X_i^j$ represent the jth frequency component of Yi and Xi respectively. Sj is the order of the jth coefficient. The scheme uses pseudo-random sequence generated by 4D discrete chaotic system as the sort order.2.3 Principle of block compressive sensing and diffusion
The data is sampled and compressed simultaneously by CS technology. Its schematic diagram is shown in Fig. 4. Assuming that signal x∈RN has sparsity, x can be expressed as:
where ψ is a matrix of orthogonal sparse bases, α is the sparse coefficient vector. y∈RM that is the compressed observation of x can be expressed as: where $\phi \in {R^{M \times N}}$ is the measurement matrix. According to Eqs. (3) and (4), the compressive sensing equation is: where D is the product of $\phi$ and ψ, known as the perception matrix.BCS is to divide an image of size N×N into equal and non-overlapping chunks of size B×B. These blocks are sparsely represented in a domain and then reconstructed into vectors of length B2. Then, the measurement matrix is used to compress the coefficient vector to obtain the corresponding measurement vector. The sampling process is denoted as:
where i represents the ith vectorized signal scanned by Z-shaped scanning, yi is the measurement vector, ${\phi _{Bi}}$ is the measurement matrix of size nB×B2, and nB is the compression ratio. xi is the coefficient vector. In this scheme, ${\phi _{Bi}}$ uses Hadamard matrix to improve the compression efficiency which is generated by chaotic sequence and updated according to certain blocks. The stored measurement matrix is nB×B2 in size, not a full (CR×N2)×N2. Therefore, BCS technology can save storage space.The initial encryption of the source image is completed by diffusion operation. First, the corresponding measurement matrix is used to measure the vector to obtain the output vector Zi, whose size is CR×B2, where CR represents the compression ratio. The output vector is transformed into a matrix of (n/4)×n, and then recombined into a matrix of (N/4)×N, named P1. The elements of P1 are quantized to the range of (0,255) image data to obtain the matrix P2. Chaotic sequences are used to perform forward and reverse diffusion to obtain secret images. The process can be expressed as follows:
where P3(i) and P4(i) represent the value of the matrix, D(i) represents chaotic sequence, P4 represents the secret image.2.4 Principle of SVD embedding
SVD technology can embed watermarks in overwritten images by modifying subband singular values in transform domain. Figure 5 shows the flow diagram of embedding secret images into carrier images by SVD technology. Firstly, the carrier image of size N×N is divided into equal and non-overlapping blocks of size m×m, while the secret image of size (N/4)×N is divided into blocks of size (m/4)×m. The carrier image is decomposed by IWT, and four coefficient matrices Q1, Q2, Q3 and Q4 are obtained. Singular value decomposition of coefficient matrix Q1 can be expressed as follows:
where ${U_{{Q_1}}}$ and ${V_{{Q_1}}}$ are two unitary matrices, ${S_{{Q_1}}}$ is a diagonal matrix containing all singular values.Then, the elements of diagonal matrix ${S_{{Q_1}}}$ are operated according to Eq. (10), and the SI is embedded into the carrier image. That is, the secret image block is embedded into the carrier image block at the same coordinate position.
where a represents the gain factor.Finally, the improved integer coefficient matrix MQ1 is calculated:
A visually secure encrypted image is obtained by applying inverse IWT to a combination of the four coefficient matrices MQ1, Q2, Q3 and Q4. SVD is executed in block mode, which can improve the ability to resist illegal attacks.
3. Experiment setup
The experimental setup of the proposed MCF-OFDM encryption scheme is shown in Fig. 6. The encrypted OFDM signal is generated on the optical line terminal (OLT) by offline digital signal processing (DSP). The receiver sets up a normal receiving optical network unit (ONU) with secure key, while the illegal ONU without secure key can only obtain information through brute force. At the transmitter, the original image is compressed and encrypted by block compressive sensing and SVD technology, and then the encrypted data is output by OFDM modulation. The encrypted data is converted to analog radio frequency (RF) signals using an arbitrary waveform generator (AWG, TekAWG70002A) with a sampling rate of 10 GSa/s. After passing through an electrical amplifier (EA), the RF signal is then loaded via the Mach-Zehnder modulator (MZM) onto a continuous optical carrier generated by a tunable light source with a wavelength of 1550 nm. Then the optical signal pass through 1:8 the beam splitter is sent to the 2km 7-core optical fiber for transmission. The weakly coupled 7-core single-mode fiber was used in this experiment. The cross section is shown in Fig. 6(a). After testing, the isolation degree between the cores is shown in Table 1. The minimum isolation degree between cores can reach 34.9dB and it has good isolation performance. Erbium doped fiber amplifier (EDFA) is used to amplify optical signals.
Fig. 6. Experimental setup (DSP: digital signal process; OLT: optical line terminal; AWG: arbitrary waveform generator; MZM: Mach-Zehnder modulator; EDFA: erbium-doped fiber amplifier; PS: power splitter; VOA: variable optical attenuator; PD: photodiode; MSO: mixed signal oscilloscope).
Table 1. seven core fiber isolation degree (unit: dBm)
At the receiver, a variable optical attenuator (VOA) is used to adjust the received optical power and then the PD is used for the photoelectric conversion of the received signal. The analog-to-digital conversion is completed by a mixed signal oscilloscope (MSO, TekMSO73304DX) with a sampling rate of 50 GSa/s. Finally, after OFDM demodulation, extracted the secret image, decrypted and reconstructed, the original image is restored.
4. Results and discussion
To verify the sensitivity of the security system, we analyze the influence of tiny change in initial value on the BER of the system. Fixed the received optical power at −10 dBm, BER curves of various ONUs with a tiny change in initial value are shown in Fig. 7. The abscissa represents the disturbance precision of changing in initial value. The ordinate is the corresponding BER. When a parameter of the key changes to more than E-14, the BER rises sharply, the constellation diagram is in a state of confusion and cannot be normally decrypted. That is the tiny change of the initial value will cause the change of the whole chaotic system, so the four-dimensional discrete chaotic system has high sensitivity. Assuming that the parameters of 4D discrete chaotic mapping and the integer bits of the initial value are set to typical values, our key-space can be conservatively estimated as ${({{{10}^{15}}} )^8} = {10^{120}}$. The key space is large enough to effectively resist illegal eavesdropping.
Under normal receiving conditions, ONUs can use the same key as the sender to properly decrypt the encrypted information. Figure 8 shows the BER performance curves, constellation diagram and decrypted image in the seven-core optical fiber transmission system. In general, the BER in core1- core7 decreases with the increase of received power. When the received optical power is greater than −15dBm, the BER of core7 is less than 10−3. When the optical power is greater than −14 dBm, the BER of core1 is less than 10−3. Compared with core7, the power loss of core1 is about 1dB. In addition, as illustrated in illustrations (b) and (c), when the optical power is −13 dBm, the BER is low, the constellation points converge and the decrypted image is clearly visible.
Fig. 8. BER curves of normal received ONU in core1-core7. (a) The constellation diagram; (b) Decrypted image; (c) The constellation diagram of (b).
The result of image encryption and decryption is shown in Fig. 9. We obtain the secret image (c) after compression and encryption of the original image, and embed it into the carrier image (b) to obtain the cipher image (d). It can be seen that there is no significant visual difference between the cipher image (d) and the carrier image (b). Hence, the proposed encryption algorithm can effectively ensure the visual security of encrypted image.
Fig. 9. Result graph of encryption and decryption (a) original image; (b) carrier image; (c)secret image; (d)cipher image; (e) decrypted image.
In addition, original image recovery is performed for unattacked cipher image, 5%, 10% and 30% cipher images maliciously attacked, respectively, to verify the robustness of the scheme against attack. The compression ratio is fixed at 0.25. The results graph of encryption and decryption are shown in Fig. 9, Fig. 10, Fig. 11, and Fig. 12, where (a) is the original image, (b) is the carrier image, (c) is the secret image, (d) is the attacked cipher image, and (e) is the decrypted image. Under the condition that the cipher image is not attacked, the scheme can recover the original image well, and its details can be clearly seen. In the case of cipher images being attacked by 5% to 10%, the quality of the image is basically not affected, and the vast majority of information can be clearly displayed. In the case that the attack range of cipher image reaches 30%, although it has a certain impact on the reconstruction quality, it has little impact on the vision, and the outline and general information of the image can still be observed. Therefore, the scheme has good robustness and can effectively resist illegal attacks.
The transmission quality of the scheme is evaluated by peak signal to noise ratio (PSNR) and average structural similarity (MSSIM) values. The compression ratio is set to 0.25, and the PSNR and MSSIM values between the cipher image and the carrier image were calculated, as shown in Fig. 13. The average value of PSNR-cipher is about 30 dB, larger than the common benchmark. The value of PSNR-decrypted increases with the increase of the received optical power. When receiving power is greater than −14 dBm, the PSNR-decrypted value is greater than 30 dB. Hence, image quality and visual perception are good. Furthermore, when the receiving power is greater than −19 dBm, the MSSIM-cipher value is greater than 0.9. When the receiving power is greater than −16 dBm, the MSSIM-decrypted value is greater than 0.7. Therefore, there is a great similarity between the original image and the ciphertext image and between the original image and the decrypted image.
In the experiment, we also analyze sharpen attack and histogram equalization attack. Figure 14(a) and (d) are cipher images, Fig. 14(b) and (e) are cipher images of sharpen attack and histogram equalization attack respectively, Fig. 14(c) and (f) are decrypted images. The experimental results show that the proposed scheme can still recover the image under typical image attack. The PSNR-decrypted value is greater than 16.8 dB, and the MSSIM-decrypted value is greater than 0.31. In conclusion, the scheme proposed in this paper has good recovery performance of original image data in the experiment of 7-core optical fiber transmission system.
5. Conclusion
In this paper, BCS technology and SVD embedding technology are combined to propose a encryption scheme with high robustness and high security, which is applied in MCF-OFDM system. The proposed scheme can effectively reduce the pressure of data transmission, storage and processing by compressing image data. In addition, four masking factors generated by four-dimensional discrete chaotic mapping are used to complete four-dimensional ultra-high security encryption. Finally, the balance performance of data compression security robustness is achieved. The scheme has been validated in a 2km 7-core optical fiber system. The results successfully show that the proposed scheme has high sensitivity and key space up to 10120, which can effectively protect information security against brute force attack. In addition, when the received optical power is greater than −14 dBm, the BER of core1-core7 is lower than 10−3. When receiving power is greater than −14 dBm, the PSNR values are greater than 30dB. When the receiving power is greater than −16 dBm, the MSSIM values are greater than 0.7. The scheme can restore the original image well and its details are clearly visible. When the attack range of encrypted data is up to 30%, the decrypted image has little visual impact, and the outline and general information of the image can still be observed. Compared with the data without compressed sensing, the data volume is reduced by 75%. This scheme ensures the security of cipher image transmission and greatly reduces the bandwidth occupied by cipher image. Our findings have the potential to be applied to future high-capacity and high-security optical transmission system.
Funding
National Key Research and Development Program of China (2018YFB1801004); National Natural Science Foundation of China (61835005, 62171227, 61727817, U2001601, 62035018, 61875248, 61935005, 61935011, 61720106015, 61975084); Jiangsu team of innovation and entrepreneurship; The Startup Foundation for Introducing Talent of NUIST.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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