Abstract

A novel security-enhanced scheme combining improved deoxyribonucleic acid (DNA) encoding encryption at the bit-level with matrix scrambling at the symbol-level is proposed in OFDM-PON for the first time in this paper. In our proposed scheme, firstly each subcarrier is encrypted by improved DNA encoding encryption, which includes the functioning of key base series and the cross interchange. And the selected encoding rules, decoding rules, key base series, operating principles and the positions of cross interchange are dynamically changing, which enhances the robustness against malicious attacks by illegal attackers. Then during the matrix scrambling process, the non-equal-length quadrature amplitude modulation (QAM) matrix is divided into several squares of equal length according to an optimum method. At the same time, the times of matrix scrambling can be determined randomly. With the multi-fold encryption of the proposed scheme, the achieved key space can reach up to 10154, which can sufficiently ensure the physical layer security. Experimental verification of the proposed security-enhanced strategy was demonstrated in an 8 Gb/s 16QAM orthogonal frequency division multiplexing passive optical network (OFDM-PON) system over 25-km standard single-mode fiber (SSMF). The experimental results prove that the two-level coordinated encryption at the bit-level and symbol-level using chaos and encryption can effectively protect data from violent attacks, differential attacks, etc.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The ever-growing demand for personal communications and the continuous commercialization of broadband terminal services have promoted the development of the next generation passive optical network (NG-PON). Due to its large capacity, low power consumption and easy maintenance, PON has become the mainstream solution to break the “last mile” bottleneck and been widely used in fiber-to-the-home deployments [13]. The upstream transmission in the PON system operates in burst mode, which gives room for a non-uniform distribution of information and bit errors may occur-caused by the induced transient effects. On the other hand, orthogonal frequency division multiplexing (OFDM) technique, thanks to its strong anti-interference ability, high spectrum utilization, potent anti-dispersion ability and significant system flexibility, has been extensively adopted in the PON [4]. However, the security issues of PON is still daunting and challenging as constant eavesdropping and multiple attacking methods in optical networks are making information vulnerable in data transmission.

In order to improve network security, many proposals have been offered by research communities [5,6]. The laser chaos technology can enhance the security of the physical layer by adjusting the injection and feedback strength of the laser in the PON. But in practical applications, some problems do exist such as channel interference and parameter matching, which are urgent to be addressed on priority basis [7]. Quantum key distribution has been proved to be secure theoretically [8]. However, there is not even a single ideal photon source available. Generation, modulation and other processes of signals such as error correction are mainly realized in the digital domain for OFDM-PON. Since the signal processing in the digital domain has high flexibility, it is easier to implement encryption technology, such as digital chaos, to improve the security of the OFDM-PON system. Zhang et al. proposed an OFDM-PON physical enhancement security strategy based on chaos scrambling in frequency domain [9]. Liu et al. has verified that constellation masking and dimension-transformed chaotic permutation could effectively prevent the invasion of illegal optical network units (ONUs) in OFDM-PON [10,11]. Recently, a chaotic Walsh-Hadamard Transform precoding scheme has been proposed and demonstrated to enhance the physical layer security in OFDM transmission [12]. Some scholars have proposed to combine chaotic encryption with polar codes to improve the reliability of the system in optical OFDM transmission systems [13]. In [14], a novel method has been introduced to improve the physical layer security by using chaos and Fractional Fourier transform (FrFT) techniques. The chaotic sequences were used to perform the OFDM subcarriers masking and to control the fractional order of the FrFT operation. A method based on chaotic sequences has been demonstrated in [15] for phase rotation and subcarrier mapping. Additionally, using chaotic sequences to disturb the real and imaginary phases of orthogonal amplitude-modulated symbols is relatively a simple encryption technique at the physical layer [16]. Further, encrypting probability shaping [17,18] parameters is another security enhancement scheme at physical layer [19]. All the above-mentioned physical layer security enhancement technologies are implemented at the symbol-level in the time domain or frequency domain, lacking of flexibility with respect to the bit-level maneuvering. However, bit is a basic form of data in the optical network physical layer, and encryption at the bit-level can better enhance the security of optical communication system. In [20,21], the authors applied an encryption technique in the field of image processing and called it deoxyribonucleic acid (DNA) encryption. An encryption algorithm which combined a DNA addition with a chaotic map to encrypt a gray scale image has been proposed in Ref. [22]. A novel encryption scheme combining hyper chaotic system and DNA technology has been put forward in Ref. [23], but the secret keys in this scheme were fixed, this would reduce the overall safety performance in this condition. Novel encrypted compressive sensing of images based on Fractional order hyper chaotic Chen system and DNA operations has been introduced in Ref. [24]. However, these methods of DNA encryption are used in images and have not been implemented in optical communication systems. Because of the large-scale parallelism of DNA, massive storage space and special base-pairing structure, some articles have taken such advantages to apply chaos and DNA encryption to optical networks in recent year [25,26]. Traditional DNA encryption was applied to optical communication and its performance was demonstrated in Ref. [25], but there weren’t improvements in DNA encryption methods. Four bases were extended to eight bases in Ref. [26], however it was only encrypted at the bit-level. DNA encryption and spiral scrambling were introduced in Ref. [27], but only simulation results were discussed. It is of great necessity to carry out experiments to verify the reliability of the method. DNA encoding encryption can be performed at the bit-level, so it is more difficult for intruders to crack the correct information. However, coding encryption at the bit-level alone or matrix scrambling at the symbol-level alone will still leave the possibility of successful eavesdropping for illegal eavesdroppers. At present, most of the physical layer encryption documents are only encrypted at the symbol-level or bit-level, so the security issue is needed to be resolved urgently. If two levels of encryption can be implemented at the same time, there is stupendous hope for stronger security guarantees.

In this article, a novel security-enhanced scheme with DNA encoding encryption, adjacent base series cross interchange and subcarrier matrix scrambling for OFDM-PON is proposed in order to guard against the eavesdropping of valid information. Traditional DNA encryption includes encoding, operation and decoding, which can achieve certain security performance. On top of this DNA encryption, the article adds cross interchange between adjacent columns and the positions of cross interchange can be dynamically changed. Using Logistic chaos and 4D-hyperchaotic map, two levels of encryption are realized. In the process of improved DNA encoding encryption at the bit-level, the encoding and decoding rules, key base series, the operations between DNA base series and key base series, the positions of odd and even base series cross interchange are determined by different chaotic sequences. In the process of matrix scrambling at the symbol-level, the times of scrambling are also variable. We successfully transmitted 8 Gb/s encrypted optical OFDM signals over 25-km standard single-mode fiber (SSMF) while enhancing the security of the physical layer without adversely affecting peak-to-average power ratio (PAPR) of OFDM signals.

2. Principles

The proposed OFDM-PON based on improved DNA encoding encryption and subcarrier matrix scrambling is illustrated in Fig. 1.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the proposed method based on improved DNA encoding encryption and matrix scrambling (PRBS: pseudo random binary sequence; S/P: serial-to-parallel; IFFT: inverse fast Fourier transform; CP: cyclic prefix; P/S: parallel-to-serial; FFT: fast Fourier transform).

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A pseudo random binary sequence (PRBS) is used as the original input data on the optical line terminal (OLT) side. After serial-to-parallel (S/P), the $N \times \textrm{4}M$ matrix will be obtained, where N represents the number of symbols carried by one subcarrier of the OFDM signals, and M is the number of subcarriers. Before quadrature amplitude modulation (QAM) mapping, each subcarrier is disturbed using the improved DNA encoding encryption. Deoxynucleotide consists of 4 bases: adenine (A), guanine (G), thymine (T) and cytosine (C). For the molecular structure of DNA, two polydeoxynucleotide chains are coiled around a common central axis to form a double helix structure. The bases on one chain must exist in a corresponding way to the bases on the other chain, that is, adenine corresponds to thymine (A to T or T to A), guanine corresponds to cytosine (G to C or C to G) to form a base pair, this arrangement is called the principle of base complementation. For binary coding, the four bases of “A” “T” “C” “G” need to be represented by 2 binary bits, a pair of 0 and 1. According to the principle of permutation and combination, there are 24 ways to express 4 bases. However, in compliance with the principle of complementary pairing, if “00” represents “A”, then “T” can only be represented by “11”, so only 8 of them satisfy the requirements, which are list in Table 1. As analyzed above, if the transmitted bits are {10000111}, then after encoding according to rule 1, the resulting base series is {GACT}.

Tables Icon

Table 1. DNA Encoding and Decoding Rules

In this paper, we use 16QAM for transmission, and each symbol is represented by four bits. As shown in Fig. 2, each subcarrier can transmit N symbols, 4N bits. For the i-th subcarrier, the symbol transmitted by the initial subcarrier is {1100, 0101, 0011, 0110…0101, 1000}. Each column is DNA encoded, so that 4 groups of base series can be obtained $\{{{A_{i1}},{A_{i2}},{A_{i3}},{A_{i4}}} \}$, and all subcarriers have $\textrm{4}M$ groups. The chaotic sequence ${S^\alpha }$ controls the encoding rules of each column, every element ${S^\alpha }$ is ${S^\alpha } \in \{ 1,2,3 \cdots 8\}$ and presents a DNA encoding rule. The coding rule of the h column corresponds to ${S^\alpha }_h(h \in [1,4M],h \in {N^ + })$.

 figure: Fig. 2.

Fig. 2. DNA encoding process.

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Logistic chaos generates the chaotic sequence U. Logistic chaos is expressed by the following formula:

$${p_{n + 1}} = \mu {p_n}(1 - {p_n}),p \in (0,1)\& \mu \in [\textrm{3}\textrm{.57},4]. $$
Use chaotic sequence U to generate a bit series whose length is N. The series is controlled by ${S^\alpha }$ to generate key base K. That is, the key base series is not fixed, and the key base ${K_h}$ of the h column changes as ${S^\alpha }_h$ changes.

The dynamic key base series are operated with base series per column. There are three operation methods, including addition, subtraction, and XOR, as shown in Table 2, Table 3, and Table 4, respectively.

Tables Icon

Table 2. Addition [ + ] Operation

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Table 3. Subtraction [-] Operation

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Table 4. Exclusive OR [XOR] Operation

${S^\beta }$ is a random number series, and every element ${S^\beta }$ is within $\{{1,2,3} \}$ and presents an operation rule. After the operation, the base series is $\textrm{\{ }{B_{i1}},{B_{i2}},{B_{i3}},{B_{i4}}\textrm{\} }$, as shown in Fig. 3.

 figure: Fig. 3.

Fig. 3. The operation process between the first two columns of the i-th subcarrier and the key base series.

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After that, every two adjacent columns of base series are cross interchange, such as ${B_{i1}}$ and ${B_{i2}}$,${B_{i3}}$ and ${B_{i4}}$,as shown in Fig. 4. The position of cross interchange is controlled by ${S^\gamma }$. After the DNA strands are cross-exchanged, new DNA strands are obtained, then we decode the DNA strands according to Table 1. The decoding rule of each column for each subcarrier is controlled by the chaotic sequence ${S^\chi }$, every element in ${S^\chi }$ is ${S^\chi } \in \{ 1,2,3 \cdots 8\}$ and presents a DNA decoding rule.

The random sequences $X,Y,Z,W$ are generated by the 4D-hyperchaotic mapping, and the 4D-hyperchaotic map is expressed by the following formula

$$\left\{ \begin{array}{l} \mathop x\limits^ \bullet{=} a(y - x) + w, \\ \mathop{\textrm y}\limits^ \bullet{=} \textrm{dx + cy - xz}, \\ \mathop{\textrm z}\limits^ \bullet{=} xy - bz, \\ \mathop w\limits^ \bullet{=} yz + rw, \end{array} \right.$$
where $a,b,c,d$ and $r$ are parameters, $x,y,z$ and $w$ are variables. The key of the 4D-hyperchaotic system can be expressed as ($a,b,c,d,r,x,y,z,w$). After mapping, we can get 4 sets of chaotic sequences $X,Y,Z$ and W.
$$\left\{ \begin{array}{ll} {S^\alpha }_h = \bmod (fix((X(h) + 30) \cdot {10^{14}}),8), &h \in [1,4M],h \in {N^ + }, \\ {S^\beta }_h = \bmod (fix((Y(h) + 30) \cdot {10^{14}}),3),&h \in [1,4M],h \in {N^ + }, \\ {S^\chi }_h = \bmod (fix((Z(h) + 30) \cdot {10^{14}}),8),&h \in [1,4M],h \in {N^ + }, \\ {S^\gamma }_h = Extract(W(h),14),&h \in [1,2M],h \in {N^ + }, \end{array} \right.$$
where the function $Extract(W(h),14)$ returns an integer, which is the 14th digit in the decimal part of $W(h)$.

 figure: Fig. 4.

Fig. 4. A schematic diagram of cross interchange of DNA.

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The $N \times \textrm{4M}$ matrix after DNA decoding is converted into a symbol matrix, and the value of each symbol is within $\{{0,1,2 \cdots 15} \}$. The subcarrier symbol matrix is mapped to obtain a complex matrix P. The matrix P is encrypted by changing the position of each element through a non-equal row and column Arnold transformation. We divide a square matrix from the beginning of the short side and use Arnold transform to scramble the square matrix. In order to make the scrambling of matrix P non-regional, starting from the second part, each part is divided in such a way as to have a certain overlapping area, as shown in Fig. 5. The Arnold transform is used to scramble the square matrix in turn until the non-equal matrix $N \times M$ is completely scrambled.

 figure: Fig. 5.

Fig. 5. The non-equal length matrix division rule.

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The formula for Arnold transformation is

$$\left( {\begin{array}{c} u\\ v \end{array}} \right) = \left( {\begin{array}{cc} 1&1\\ 1&2 \end{array}} \right)\left( {\begin{array}{c} {u^{\prime}}\\ {v^{\prime}} \end{array}} \right)\bmod (N),$$
where $(u,v)$ and $(u^{\prime},v^{\prime})$ represent the position coordinates before and after matrix transformation, respectively. N is the width of the square. If the matrix is transformed f times, then
$$\left( {\begin{array}{c} u\\ v \end{array}} \right) = {\left( {\begin{array}{cc} 1&1\\ 1&2 \end{array}} \right)^f}\left( {\begin{array}{c} {u^{\prime}}\\ {v^{\prime}} \end{array}} \right)\bmod (N). $$

Using the above method to divide the matrix, there are many cases of overlapping regions, that is, the original matrix can be divided into different numbers of square matrix. The smaller the number of divided squares, the less time it takes to scramble the matrix. Dividing the complex matrix into as few squares as possible can greatly reduce the time required for matrix scrambling. When the non-equal length matrix is divided into $[{{M / N}} ]+ 1$ square matrices, the time required for scrambling is the least.

Taking the short side N as the side length, the matrix P can be divided into $[{{M / N}} ]+ 1$ $N \times N$ square matrices. Supposing the coincidence length between each square matrix is X, then the equation can be expressed as:

$$M = ({[{{M / N}} ]+ 1} )\times N - [{{M / N}} ]\times X,$$
where $[{{M / N}} ]$ represents the largest integer but not exceeding $[{{M / N}} ]$. $({[{{M / N}} ]+ 1} )\times N$ represents the total length required for $[{{M / N}} ]+ 1$ square transformations. $[{{M / N}} ]\times X$ means the total length of coincidence.

The results of the encryption and decryption of non-equal-length matrix scrambling in the image $(\textrm{450} \times \textrm{600})$ are shown in Fig. 6. We can see from the figure that after 7 times of scrambling, the image has been completely chaotic. By the same times of inverse transforming, we can get the correct image. The same is true for the subcarrier complex matrix.

 figure: Fig. 6.

Fig. 6. (a) Image before encryption; (b) Scrambling once; (c) Scrambling twice; (d) Scrambling seven times; (e) Inverse transformation for single time; (f) Inverse transformation for five times; (g) Inverse transformation for six times; (h) Inverse transformation for seven times.

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3. Experimental setup and results

Figure 7 shows the experimental setup of the chaotic OFDM-PON, based on DNA encoding encryption, adjacent base series cross interchange and subcarrier matrix scrambling. On the OLT side, encrypted OFDM electrical signals were generated offline in a MATLAB program. In this work, the number of subcarriers was 128, the number of symbols on each subcarrier was 120, the size of FFT transformation points was 512, and the length of the CP was 1/16 of FFT transformation points. We used an arbitrary waveform generator (AWG, TekAWG70002A) with 25 GSa/s to convert the digital symbol sequences to analog radio frequency (RF) signals. A tunable light source with less than 100 kHz linewidth and 15 dBm output power was used to generate the continuous optical wave. The light source at 1550 nm was then modulated by the intensity modulator (IM) whose operating voltage is 1.7 V and half-wave voltage is 3 V to achieve electrical/optical conversion. The transmission link was 25-km SSMF. On the ONU side, the modulated optical signal was amplified by an EDFA with 5.5 dB noise figure. After that, a VOA (variable optical attenuator) was applied to adjust the launched signal power into the fiber link. The following photodiode (PD) with 3dB bandwidth of 40 GHz was used to convert optical signals into electrical signals. The converted electrical signals were passed through a mixed-signal oscilloscope (MSO, TeKMSO73304DX) with a sampling rate of 50 GSa/s. The obtained electrical signals were subjected to matrix inverse scrambling, QAM demapping, base series inverse cross, DNA decoding in MATLAB, and then the transmitted signals were recovered. The key of the chaotic system was only shared between the OLT and the legal ONU.

 figure: Fig. 7.

Fig. 7. Experimental setup of physical-enhanced secure OFDM-PON based on improved DNA encoding encryption and non-equal-length matrix scrambling in OFDM-PON (AWG: arbitrary waveform generator; IM: intensity modulator; EDFA: erbium-doped fiber amplifier; VOA: variable optical attenuator; PD: photodiode; MSO: mixed signal oscilloscope; DSP: digital signal processing).

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Logistic chaos is used to generate the key base series. Figure 8 shows a slight change in the initial key from (0.60000000000001, 3.70000000000001) to (0.60000000000002, 3.70000000000002), the two sets of sequences obtained are have nothing in common, it proves the system is extraordinary sensitive to even a slight change in the initial value.

 figure: Fig. 8.

Fig. 8. The difference of the chaotic sequences generated by slightly different keys.

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As can be seen from Fig. 9, the dynamic characteristics of the hyperchaotic system under this condition are extremely complicated and irregular, which greatly increases the randomness of the system, therefore, it is hard for an attacker to obtain the correct key sequences. As a result, using the 4D-hyperchaotic map in the improved DNA encryption algorithm is secure and effective.

 figure: Fig. 9.

Fig. 9. Phase diagram of the 4D-hyperchaotic map.

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Figures 10(a) and (c) show the auto-correlation functions of X and Y in the 4D hyperchaotic system respectively. Similarly, Figs. 10(b) and (d) show the cross-correlation function of the X sequence that is obtained using the initial value and the X sequence, which is obtained after modifying the initial value. The auto-correlation function is a unit pulse function, and cross-correlation function is close to 0. These characteristics of the 4D hyperchaotic system also indicate that the proposed physical layer encryption scheme has high security.

 figure: Fig. 10.

Fig. 10. Auto-correlation and cross-correlation of X and Y.

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The key space of the entire encryption system can be denoted in a mathematic expression as $(a,\textrm{ }b,\textrm{ }c,\textrm{ }d, r, x,\textrm{ }y,\textrm{ }z,\textrm{ }w,p,\mu )$, and the initial value of each key can be changed. Assuming that the initial integer bits of the Logistic chaos and 4D hyperchaotic map are fixed, we only change the decimal. In this case, the key space can be conservatively estimated as ${\textrm{(1}{\textrm{0}^{\textrm{14}}})^{11}} = {10^{154}}$. This provides a sufficiently large key space to prevent illegal decryption.

Figures 11 and 12 show the relationship between received optical power and measured bit error rate (BER) under five different conditions before and after 25-km SSMF transmission. These schemes include the proposed scheme with improved DNA encoding encryption and subcarrier matrix scrambling, the conventional scheme, improved DNA encoding encryption, subcarrier matrix scrambling and the illegal. It can be seen from Figs. 11 and 12 that for ONUs with correct keys, when the received optical power is greater than -12 dB, the BER is less than $\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 3}}}$. For ONUs that do not have correct key, the BERs are around 0.5, which greatly exceed the forward error correction threshold. Therefore, the encryption scheme proposed in this paper can effectively resist attacks from intruders, and the intruders cannot extract any useful information in the physical layer. At the same time, using the improved DNA encoding and subcarrier matrix scrambling to encrypt at the physical layer has almost no impact on the transmission performance of the OFDM signals. The constellation diagrams of the encrypted OFDM when the received optical power is -12 dB are also shown as inset in Figs. 11 and 12. The measured BER without 25-km SSMF transmission is a little better than 25-km SSMF transmission.

 figure: Fig. 11.

Fig. 11. Measured BER curves for different OFDM signals of b2b (b2b: back to back).

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 figure: Fig. 12.

Fig. 12. Measured BER curves for different OFDM signals after 25km SSMF transmission.

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In OFDM systems, the PAPR is a factor that must be considered. Figure 13 shows the PAPR and complementary cumulative distribution function (CCDF) curves of the two OFDM signals. The OFDM signals after improved DNA encryption and subcarrier matrix scrambling have a similar curve to that of the OFDM signals before encryption, which proves that the PAPR of the two OFDM signals don't differ much. This verifies that our proposed encryption scheme doesn’t reduce the performance of the OFDM system.

 figure: Fig. 13.

Fig. 13. Comparison of the CCDFs for the OFDM signals.

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4. Conclusion

A novel physical layer encryption scheme has been proposed in OFDM-PON. The two-level encryption strategy which is based on improved DNA encoding encryption at the bit-level and subcarrier matrix scrambling at the symbol-level is first proposed. Comparing the proposed scheme with traditional DNA encryption, we have added cross interchange between adjacent columns, and the positions of cross interchange change dynamically. At the same time, the non-equilateral Arnold transformation is applied to symbol-level encryption to further consolidate the security of the system. Chaotic sequences required for two-dimensional encryption are generated by Logistic chaos and 4D-hyperchaotic map, the key space can reach up to 10154. The intruders cannot extract any useful information without knowing the key and matrix scrambling times. Experimental verification of the proposed two-level coordinated encryption scheme was demonstrated in an 8Gb/s 16QAM OFDM-PON system. The proposed scheme can effectively enhance the security performance of the system and resist brute force cracking, obtaining high sensitivity and security. We believe that our novel scheme has broad application prospects in enhancing the security of optical networks in the future.

Funding

National Key Research and Development Program of China (2018YFB1800901); National Natural Science Foundation of China (61675004, 61705107, 61720106015, 61727817, 61775098, 61822507, 61835005, 61875248, 61935005, 61935011, 61975084); BUPT Excellent Ph.D. Students Foundation (CX2020301); Open Fund of IPOC (BUPT); Jiangsu talent of innovation and entrepreneurship; Jiangsu team of innovation and entrepreneurship.

Disclosures

The authors declare no conflicts of interest.

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References

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  1. H. Rahbari and M. Krunz, “Exploiting frame preamble waveforms to support new physical-layer functions in OFDM-Based 802.11 systems,” IEEE Trans. Wireless Commun. 16(6), 3775–3786 (2017).
    [Crossref]
  2. D. Nesset, “PON roadmap [Invited],” J. Opt. Commun. Netw. 9(1), A71–A76 (2017).
    [Crossref]
  3. C. DeSanti, L. Du, J. Guarin, J. Bone, and C. Lam, “Super-PON: an evolution for access networks [Invited],” J. Opt. Commun. Netw. 12(10), D66–D77 (2020).
    [Crossref]
  4. W. Shieh, “OFDM for flexible high-speed optical networks,” J. Lightwave Technol. 29(10), 1560–1577 (2011).
    [Crossref]
  5. X. Wang, F. Liu, D. Fan, H. Tang, and P. C. Mason, “Continuous physical layer authentication using a novel adaptive OFDM system,” in 2011 IEEE International Conference on Communications (ICC), (2011), 1–5.
  6. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
    [Crossref]
  7. S. Xiang, A. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. Guo, and J. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
    [Crossref]
  8. P. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85(2), 441–444 (2000).
    [Crossref]
  9. L. Zhang, X. Xin, B. Liu, and J. Yu, “Physical-enhanced secure strategy in an OFDM-PON,” Opt. Express 20(3), 2255–2265 (2012).
    [Crossref]
  10. B. Liu, L. Zhang, X. Xin, and J. Yu, “Constellation-masked secure communication technique for OFDM-PON,” Opt. Express 20(22), 25161–25168 (2012).
    [Crossref]
  11. B. Liu, L. Zhang, X. Xin, and Y. Wang, “Physical layer security in OFDM-PON based on dimension-transformed chaotic permutation,” IEEE Photonics Technol. Lett. 26(2), 127–130 (2014).
    [Crossref]
  12. A. Hajomer, X. Yang, and W. Hu, “Chaotic Walsh–Hadamard transform for physical layer security in OFDM-PON,” IEEE Photonics Technol. Lett. 29(6), 527–530 (2017).
    [Crossref]
  13. Y. Xiao, J. Cao, Z. Wang, C. Long, Y. Liu, and J. He, “Polar coded optical OFDM system with chaotic encryption for physical-layer security,” Opt. Commun. 433, 231–235 (2019).
    [Crossref]
  14. L. Deng, M. Cheng, X. Wang, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Secure OFDM-PON system based on chaos and Fractional Fourier transform techniques,” J. Lightwave Technol. 32(15), 2629–2635 (2014).
    [Crossref]
  15. X. Zhang, Y. Wang, J. Zeng, and Y. Wang, “A secure OFDM transmission scheme based on chaos mapping,” in 2015 IEEE International Performance Computing & Communications Conference (IPCCC), (2015), 1–6.
  16. W. Zhang, C. Zhang, C. Chen, W. Jin, and K. Qiu, “Joint PAPR reduction and physical layer security enhancement in OFDMA-PON,” IEEE Photonics Technol. Lett. 28(9), 1 (2016).
    [Crossref]
  17. J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
    [Crossref]
  18. X. Wang, Q. Zhang, X. Xin, R. Gao, Q. Tian, F. Tian, C. Wang, X. Pan, Y. Wang, and L. Yang, “Robust weighted K-means clustering algorithm for a probabilistic-shaped 64QAM coherent optical communication system,” Opt. Express 27(26), 37601–37613 (2019).
    [Crossref]
  19. J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
    [Crossref]
  20. H. Liu, X. Wang, and A. kadir, “Image encryption using DNA complementary rule and chaotic maps,” Appl. Soft Comput. 12(5), 1457–1466 (2012).
    [Crossref]
  21. M. Babaei, “A novel text and image encryption method based on chaos theory and DNA computing,” Nat. Comput. 12(1), 101–107 (2013).
    [Crossref]
  22. H. Hermassi, A. Belazi, R. Rhouma, and S. Belghith, “Security analysis of an image encryption algorithm based on a DNA addition combining with chaotic maps,” Multimed. Tools Appl. 72(3), 2211–2224 (2014).
    [Crossref]
  23. L. Liu, D. Wang, and Y. Lei, “An image encryption scheme based on hyper chaotic system and DNA with fixed secret keys,” IEEE Access 8, 46400–46416 (2020).
    [Crossref]
  24. S. Kayalvizhi and S. Malarvizhi, “A novel encrypted compressive sensing of images based on fractional order hyper chaotic Chen system and DNA operations,” Multimed. Tools. Appl. 79(5-6), 3957–3974 (2020).
    [Crossref]
  25. C. Zhang, W. Zhang, C. Chen, X. He, and K. Qiu, “Physical-enhanced secure strategy for OFDMA-PON using chaos and deoxyribonucleic acid encoding,” J. Lightwave Technol. 36(9), 1706–1712 (2018).
    [Crossref]
  26. T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
    [Crossref]
  27. Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020).
    [Crossref]

2020 (6)

C. DeSanti, L. Du, J. Guarin, J. Bone, and C. Lam, “Super-PON: an evolution for access networks [Invited],” J. Opt. Commun. Netw. 12(10), D66–D77 (2020).
[Crossref]

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

L. Liu, D. Wang, and Y. Lei, “An image encryption scheme based on hyper chaotic system and DNA with fixed secret keys,” IEEE Access 8, 46400–46416 (2020).
[Crossref]

S. Kayalvizhi and S. Malarvizhi, “A novel encrypted compressive sensing of images based on fractional order hyper chaotic Chen system and DNA operations,” Multimed. Tools. Appl. 79(5-6), 3957–3974 (2020).
[Crossref]

T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
[Crossref]

Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020).
[Crossref]

2019 (3)

2018 (1)

2017 (3)

A. Hajomer, X. Yang, and W. Hu, “Chaotic Walsh–Hadamard transform for physical layer security in OFDM-PON,” IEEE Photonics Technol. Lett. 29(6), 527–530 (2017).
[Crossref]

H. Rahbari and M. Krunz, “Exploiting frame preamble waveforms to support new physical-layer functions in OFDM-Based 802.11 systems,” IEEE Trans. Wireless Commun. 16(6), 3775–3786 (2017).
[Crossref]

D. Nesset, “PON roadmap [Invited],” J. Opt. Commun. Netw. 9(1), A71–A76 (2017).
[Crossref]

2016 (2)

2014 (3)

H. Hermassi, A. Belazi, R. Rhouma, and S. Belghith, “Security analysis of an image encryption algorithm based on a DNA addition combining with chaotic maps,” Multimed. Tools Appl. 72(3), 2211–2224 (2014).
[Crossref]

B. Liu, L. Zhang, X. Xin, and Y. Wang, “Physical layer security in OFDM-PON based on dimension-transformed chaotic permutation,” IEEE Photonics Technol. Lett. 26(2), 127–130 (2014).
[Crossref]

L. Deng, M. Cheng, X. Wang, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Secure OFDM-PON system based on chaos and Fractional Fourier transform techniques,” J. Lightwave Technol. 32(15), 2629–2635 (2014).
[Crossref]

2013 (1)

M. Babaei, “A novel text and image encryption method based on chaos theory and DNA computing,” Nat. Comput. 12(1), 101–107 (2013).
[Crossref]

2012 (3)

2011 (1)

2005 (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

2000 (1)

P. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85(2), 441–444 (2000).
[Crossref]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Babaei, M.

M. Babaei, “A novel text and image encryption method based on chaos theory and DNA computing,” Nat. Comput. 12(1), 101–107 (2013).
[Crossref]

Belazi, A.

H. Hermassi, A. Belazi, R. Rhouma, and S. Belghith, “Security analysis of an image encryption algorithm based on a DNA addition combining with chaotic maps,” Multimed. Tools Appl. 72(3), 2211–2224 (2014).
[Crossref]

Belghith, S.

H. Hermassi, A. Belazi, R. Rhouma, and S. Belghith, “Security analysis of an image encryption algorithm based on a DNA addition combining with chaotic maps,” Multimed. Tools Appl. 72(3), 2211–2224 (2014).
[Crossref]

Bone, J.

Cao, J.

Y. Xiao, J. Cao, Z. Wang, C. Long, Y. Liu, and J. He, “Polar coded optical OFDM system with chaotic encryption for physical-layer security,” Opt. Commun. 433, 231–235 (2019).
[Crossref]

Chen, C.

C. Zhang, W. Zhang, C. Chen, X. He, and K. Qiu, “Physical-enhanced secure strategy for OFDMA-PON using chaos and deoxyribonucleic acid encoding,” J. Lightwave Technol. 36(9), 1706–1712 (2018).
[Crossref]

W. Zhang, C. Zhang, C. Chen, W. Jin, and K. Qiu, “Joint PAPR reduction and physical layer security enhancement in OFDMA-PON,” IEEE Photonics Technol. Lett. 28(9), 1 (2016).
[Crossref]

Chen, Y.

Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020).
[Crossref]

Cheng, M.

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Deng, L.

DeSanti, C.

Du, L.

Fan, D.

X. Wang, F. Liu, D. Fan, H. Tang, and P. C. Mason, “Continuous physical layer authentication using a novel adaptive OFDM system,” in 2011 IEEE International Conference on Communications (ICC), (2011), 1–5.

Fischer, I.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Fu, S.

Gao, R.

Garcia-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Guarin, J.

Guo, X.

Hajomer, A.

A. Hajomer, X. Yang, and W. Hu, “Chaotic Walsh–Hadamard transform for physical layer security in OFDM-PON,” IEEE Photonics Technol. Lett. 29(6), 527–530 (2017).
[Crossref]

Han, S.

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

He, J.

Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020).
[Crossref]

Y. Xiao, J. Cao, Z. Wang, C. Long, Y. Liu, and J. He, “Polar coded optical OFDM system with chaotic encryption for physical-layer security,” Opt. Commun. 433, 231–235 (2019).
[Crossref]

He, X.

Hermassi, H.

H. Hermassi, A. Belazi, R. Rhouma, and S. Belghith, “Security analysis of an image encryption algorithm based on a DNA addition combining with chaotic maps,” Multimed. Tools Appl. 72(3), 2211–2224 (2014).
[Crossref]

Hu, W.

A. Hajomer, X. Yang, and W. Hu, “Chaotic Walsh–Hadamard transform for physical layer security in OFDM-PON,” IEEE Photonics Technol. Lett. 29(6), 527–530 (2017).
[Crossref]

Huang, H.

T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
[Crossref]

Jiang, L.

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

Jin, W.

W. Zhang, C. Zhang, C. Chen, W. Jin, and K. Qiu, “Joint PAPR reduction and physical layer security enhancement in OFDMA-PON,” IEEE Photonics Technol. Lett. 28(9), 1 (2016).
[Crossref]

kadir, A.

H. Liu, X. Wang, and A. kadir, “Image encryption using DNA complementary rule and chaotic maps,” Appl. Soft Comput. 12(5), 1457–1466 (2012).
[Crossref]

Kayalvizhi, S.

S. Kayalvizhi and S. Malarvizhi, “A novel encrypted compressive sensing of images based on fractional order hyper chaotic Chen system and DNA operations,” Multimed. Tools. Appl. 79(5-6), 3957–3974 (2020).
[Crossref]

Krunz, M.

H. Rahbari and M. Krunz, “Exploiting frame preamble waveforms to support new physical-layer functions in OFDM-Based 802.11 systems,” IEEE Trans. Wireless Commun. 16(6), 3775–3786 (2017).
[Crossref]

Lam, C.

Larger, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Lei, Y.

L. Liu, D. Wang, and Y. Lei, “An image encryption scheme based on hyper chaotic system and DNA with fixed secret keys,” IEEE Access 8, 46400–46416 (2020).
[Crossref]

Li, H.

Li, J.

Lin, L.

Liu, B.

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

B. Liu, L. Zhang, X. Xin, and Y. Wang, “Physical layer security in OFDM-PON based on dimension-transformed chaotic permutation,” IEEE Photonics Technol. Lett. 26(2), 127–130 (2014).
[Crossref]

L. Zhang, X. Xin, B. Liu, and J. Yu, “Physical-enhanced secure strategy in an OFDM-PON,” Opt. Express 20(3), 2255–2265 (2012).
[Crossref]

B. Liu, L. Zhang, X. Xin, and J. Yu, “Constellation-masked secure communication technique for OFDM-PON,” Opt. Express 20(22), 25161–25168 (2012).
[Crossref]

Liu, D.

Liu, F.

X. Wang, F. Liu, D. Fan, H. Tang, and P. C. Mason, “Continuous physical layer authentication using a novel adaptive OFDM system,” in 2011 IEEE International Conference on Communications (ICC), (2011), 1–5.

Liu, H.

H. Liu, X. Wang, and A. kadir, “Image encryption using DNA complementary rule and chaotic maps,” Appl. Soft Comput. 12(5), 1457–1466 (2012).
[Crossref]

Liu, L.

L. Liu, D. Wang, and Y. Lei, “An image encryption scheme based on hyper chaotic system and DNA with fixed secret keys,” IEEE Access 8, 46400–46416 (2020).
[Crossref]

Liu, Y.

Y. Xiao, J. Cao, Z. Wang, C. Long, Y. Liu, and J. He, “Polar coded optical OFDM system with chaotic encryption for physical-layer security,” Opt. Commun. 433, 231–235 (2019).
[Crossref]

Long, C.

Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020).
[Crossref]

Y. Xiao, J. Cao, Z. Wang, C. Long, Y. Liu, and J. He, “Polar coded optical OFDM system with chaotic encryption for physical-layer security,” Opt. Commun. 433, 231–235 (2019).
[Crossref]

Ma, J.

Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020).
[Crossref]

Malarvizhi, S.

S. Kayalvizhi and S. Malarvizhi, “A novel encrypted compressive sensing of images based on fractional order hyper chaotic Chen system and DNA operations,” Multimed. Tools. Appl. 79(5-6), 3957–3974 (2020).
[Crossref]

Mao, Y.

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

Mason, P. C.

X. Wang, F. Liu, D. Fan, H. Tang, and P. C. Mason, “Continuous physical layer authentication using a novel adaptive OFDM system,” in 2011 IEEE International Conference on Communications (ICC), (2011), 1–5.

Mirasso, C.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Nesset, D.

Pan, W.

Pan, X.

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Preskill, J.

P. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85(2), 441–444 (2000).
[Crossref]

Qiu, K.

T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
[Crossref]

C. Zhang, W. Zhang, C. Chen, X. He, and K. Qiu, “Physical-enhanced secure strategy for OFDMA-PON using chaos and deoxyribonucleic acid encoding,” J. Lightwave Technol. 36(9), 1706–1712 (2018).
[Crossref]

W. Zhang, C. Zhang, C. Chen, W. Jin, and K. Qiu, “Joint PAPR reduction and physical layer security enhancement in OFDMA-PON,” IEEE Photonics Technol. Lett. 28(9), 1 (2016).
[Crossref]

Rahbari, H.

H. Rahbari and M. Krunz, “Exploiting frame preamble waveforms to support new physical-layer functions in OFDM-Based 802.11 systems,” IEEE Trans. Wireless Commun. 16(6), 3775–3786 (2017).
[Crossref]

Ren, J.

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

Rhouma, R.

H. Hermassi, A. Belazi, R. Rhouma, and S. Belghith, “Security analysis of an image encryption algorithm based on a DNA addition combining with chaotic maps,” Multimed. Tools Appl. 72(3), 2211–2224 (2014).
[Crossref]

Shi, J.

Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020).
[Crossref]

Shieh, W.

Shor, P.

P. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85(2), 441–444 (2000).
[Crossref]

Shore, K.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Shum, P.

Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref]

Tang, H.

X. Wang, F. Liu, D. Fan, H. Tang, and P. C. Mason, “Continuous physical layer authentication using a novel adaptive OFDM system,” in 2011 IEEE International Conference on Communications (ICC), (2011), 1–5.

Tang, M.

Tian, F.

Tian, Q.

Wang, C.

Wang, D.

L. Liu, D. Wang, and Y. Lei, “An image encryption scheme based on hyper chaotic system and DNA with fixed secret keys,” IEEE Access 8, 46400–46416 (2020).
[Crossref]

Wang, X.

X. Wang, Q. Zhang, X. Xin, R. Gao, Q. Tian, F. Tian, C. Wang, X. Pan, Y. Wang, and L. Yang, “Robust weighted K-means clustering algorithm for a probabilistic-shaped 64QAM coherent optical communication system,” Opt. Express 27(26), 37601–37613 (2019).
[Crossref]

L. Deng, M. Cheng, X. Wang, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Secure OFDM-PON system based on chaos and Fractional Fourier transform techniques,” J. Lightwave Technol. 32(15), 2629–2635 (2014).
[Crossref]

H. Liu, X. Wang, and A. kadir, “Image encryption using DNA complementary rule and chaotic maps,” Appl. Soft Comput. 12(5), 1457–1466 (2012).
[Crossref]

X. Wang, F. Liu, D. Fan, H. Tang, and P. C. Mason, “Continuous physical layer authentication using a novel adaptive OFDM system,” in 2011 IEEE International Conference on Communications (ICC), (2011), 1–5.

Wang, Y.

X. Wang, Q. Zhang, X. Xin, R. Gao, Q. Tian, F. Tian, C. Wang, X. Pan, Y. Wang, and L. Yang, “Robust weighted K-means clustering algorithm for a probabilistic-shaped 64QAM coherent optical communication system,” Opt. Express 27(26), 37601–37613 (2019).
[Crossref]

B. Liu, L. Zhang, X. Xin, and Y. Wang, “Physical layer security in OFDM-PON based on dimension-transformed chaotic permutation,” IEEE Photonics Technol. Lett. 26(2), 127–130 (2014).
[Crossref]

X. Zhang, Y. Wang, J. Zeng, and Y. Wang, “A secure OFDM transmission scheme based on chaos mapping,” in 2015 IEEE International Performance Computing & Communications Conference (IPCCC), (2015), 1–6.

X. Zhang, Y. Wang, J. Zeng, and Y. Wang, “A secure OFDM transmission scheme based on chaos mapping,” in 2015 IEEE International Performance Computing & Communications Conference (IPCCC), (2015), 1–6.

Wang, Z.

Y. Xiao, J. Cao, Z. Wang, C. Long, Y. Liu, and J. He, “Polar coded optical OFDM system with chaotic encryption for physical-layer security,” Opt. Commun. 433, 231–235 (2019).
[Crossref]

Wei, H.

T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
[Crossref]

Wen, A.

Wen, H.

T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
[Crossref]

Wu, T.

T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
[Crossref]

Wu, X.

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

Xiang, S.

Xiao, Y.

Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020).
[Crossref]

Y. Xiao, J. Cao, Z. Wang, C. Long, Y. Liu, and J. He, “Polar coded optical OFDM system with chaotic encryption for physical-layer security,” Opt. Commun. 433, 231–235 (2019).
[Crossref]

Xin, X.

Xu, X.

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

Yang, L.

Yang, X.

A. Hajomer, X. Yang, and W. Hu, “Chaotic Walsh–Hadamard transform for physical layer security in OFDM-PON,” IEEE Photonics Technol. Lett. 29(6), 527–530 (2017).
[Crossref]

Yu, J.

Zeng, J.

X. Zhang, Y. Wang, J. Zeng, and Y. Wang, “A secure OFDM transmission scheme based on chaos mapping,” in 2015 IEEE International Performance Computing & Communications Conference (IPCCC), (2015), 1–6.

Zhang, C.

T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
[Crossref]

C. Zhang, W. Zhang, C. Chen, X. He, and K. Qiu, “Physical-enhanced secure strategy for OFDMA-PON using chaos and deoxyribonucleic acid encoding,” J. Lightwave Technol. 36(9), 1706–1712 (2018).
[Crossref]

W. Zhang, C. Zhang, C. Chen, W. Jin, and K. Qiu, “Joint PAPR reduction and physical layer security enhancement in OFDMA-PON,” IEEE Photonics Technol. Lett. 28(9), 1 (2016).
[Crossref]

Zhang, H.

Zhang, J.

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

Zhang, L.

Zhang, Q.

Zhang, W.

C. Zhang, W. Zhang, C. Chen, X. He, and K. Qiu, “Physical-enhanced secure strategy for OFDMA-PON using chaos and deoxyribonucleic acid encoding,” J. Lightwave Technol. 36(9), 1706–1712 (2018).
[Crossref]

W. Zhang, C. Zhang, C. Chen, W. Jin, and K. Qiu, “Joint PAPR reduction and physical layer security enhancement in OFDMA-PON,” IEEE Photonics Technol. Lett. 28(9), 1 (2016).
[Crossref]

Zhang, X.

X. Zhang, Y. Wang, J. Zeng, and Y. Wang, “A secure OFDM transmission scheme based on chaos mapping,” in 2015 IEEE International Performance Computing & Communications Conference (IPCCC), (2015), 1–6.

Zhang, Y.

Zhang, Z.

T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
[Crossref]

Zhao, J.

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
[Crossref]

Appl. Soft Comput. (1)

H. Liu, X. Wang, and A. kadir, “Image encryption using DNA complementary rule and chaotic maps,” Appl. Soft Comput. 12(5), 1457–1466 (2012).
[Crossref]

IEEE Access (2)

L. Liu, D. Wang, and Y. Lei, “An image encryption scheme based on hyper chaotic system and DNA with fixed secret keys,” IEEE Access 8, 46400–46416 (2020).
[Crossref]

T. Wu, C. Zhang, H. Huang, Z. Zhang, H. Wei, H. Wen, and K. Qiu, “Security improvement for OFDM-PON via DNA extension code and chaotic systems,” IEEE Access 8, 75119–75126 (2020).
[Crossref]

IEEE Photonics J. (1)

Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020).
[Crossref]

IEEE Photonics Technol. Lett. (4)

B. Liu, L. Zhang, X. Xin, and Y. Wang, “Physical layer security in OFDM-PON based on dimension-transformed chaotic permutation,” IEEE Photonics Technol. Lett. 26(2), 127–130 (2014).
[Crossref]

A. Hajomer, X. Yang, and W. Hu, “Chaotic Walsh–Hadamard transform for physical layer security in OFDM-PON,” IEEE Photonics Technol. Lett. 29(6), 527–530 (2017).
[Crossref]

W. Zhang, C. Zhang, C. Chen, W. Jin, and K. Qiu, “Joint PAPR reduction and physical layer security enhancement in OFDMA-PON,” IEEE Photonics Technol. Lett. 28(9), 1 (2016).
[Crossref]

J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-security physical layer in CAP-PON system based on floating probability disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020).
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S. Kayalvizhi and S. Malarvizhi, “A novel encrypted compressive sensing of images based on fractional order hyper chaotic Chen system and DNA operations,” Multimed. Tools. Appl. 79(5-6), 3957–3974 (2020).
[Crossref]

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M. Babaei, “A novel text and image encryption method based on chaos theory and DNA computing,” Nat. Comput. 12(1), 101–107 (2013).
[Crossref]

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A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. Mirasso, L. Pesquera, and K. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
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Opt. Commun. (1)

Y. Xiao, J. Cao, Z. Wang, C. Long, Y. Liu, and J. He, “Polar coded optical OFDM system with chaotic encryption for physical-layer security,” Opt. Commun. 433, 231–235 (2019).
[Crossref]

Opt. Express (4)

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Other (2)

X. Wang, F. Liu, D. Fan, H. Tang, and P. C. Mason, “Continuous physical layer authentication using a novel adaptive OFDM system,” in 2011 IEEE International Conference on Communications (ICC), (2011), 1–5.

X. Zhang, Y. Wang, J. Zeng, and Y. Wang, “A secure OFDM transmission scheme based on chaos mapping,” in 2015 IEEE International Performance Computing & Communications Conference (IPCCC), (2015), 1–6.

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Figures (13)

Fig. 1.
Fig. 1. Schematic diagram of the proposed method based on improved DNA encoding encryption and matrix scrambling (PRBS: pseudo random binary sequence; S/P: serial-to-parallel; IFFT: inverse fast Fourier transform; CP: cyclic prefix; P/S: parallel-to-serial; FFT: fast Fourier transform).
Fig. 2.
Fig. 2. DNA encoding process.
Fig. 3.
Fig. 3. The operation process between the first two columns of the i-th subcarrier and the key base series.
Fig. 4.
Fig. 4. A schematic diagram of cross interchange of DNA.
Fig. 5.
Fig. 5. The non-equal length matrix division rule.
Fig. 6.
Fig. 6. (a) Image before encryption; (b) Scrambling once; (c) Scrambling twice; (d) Scrambling seven times; (e) Inverse transformation for single time; (f) Inverse transformation for five times; (g) Inverse transformation for six times; (h) Inverse transformation for seven times.
Fig. 7.
Fig. 7. Experimental setup of physical-enhanced secure OFDM-PON based on improved DNA encoding encryption and non-equal-length matrix scrambling in OFDM-PON (AWG: arbitrary waveform generator; IM: intensity modulator; EDFA: erbium-doped fiber amplifier; VOA: variable optical attenuator; PD: photodiode; MSO: mixed signal oscilloscope; DSP: digital signal processing).
Fig. 8.
Fig. 8. The difference of the chaotic sequences generated by slightly different keys.
Fig. 9.
Fig. 9. Phase diagram of the 4D-hyperchaotic map.
Fig. 10.
Fig. 10. Auto-correlation and cross-correlation of X and Y.
Fig. 11.
Fig. 11. Measured BER curves for different OFDM signals of b2b (b2b: back to back).
Fig. 12.
Fig. 12. Measured BER curves for different OFDM signals after 25km SSMF transmission.
Fig. 13.
Fig. 13. Comparison of the CCDFs for the OFDM signals.

Tables (4)

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Table 1. DNA Encoding and Decoding Rules

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Table 2. Addition [ + ] Operation

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Table 3. Subtraction [-] Operation

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Table 4. Exclusive OR [XOR] Operation

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

p n + 1 = μ p n ( 1 p n ) , p ( 0 , 1 ) & μ [ 3 .57 , 4 ] .
{ x = a ( y x ) + w , y = dx + cy - xz , z = x y b z , w = y z + r w ,
{ S α h = mod ( f i x ( ( X ( h ) + 30 ) 10 14 ) , 8 ) , h [ 1 , 4 M ] , h N + , S β h = mod ( f i x ( ( Y ( h ) + 30 ) 10 14 ) , 3 ) , h [ 1 , 4 M ] , h N + , S χ h = mod ( f i x ( ( Z ( h ) + 30 ) 10 14 ) , 8 ) , h [ 1 , 4 M ] , h N + , S γ h = E x t r a c t ( W ( h ) , 14 ) , h [ 1 , 2 M ] , h N + ,
( u v ) = ( 1 1 1 2 ) ( u v ) mod ( N ) ,
( u v ) = ( 1 1 1 2 ) f ( u v ) mod ( N ) .
M = ( [ M / N ] + 1 ) × N [ M / N ] × X ,

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