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Chaotic RNA and DNA for security OFDM-WDM-PON and dynamic key agreement

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Abstract

A chaotic ribonucleic acid (RNA) and deoxyribonucleic acid (DNA) encryption scheme is firstly proposed for security OFDM-WDM-PON in this paper. We adopt a dynamic key agreement based on the messenger RNA (mRNA) codebook to distribute the key, and the security and randomness of this key are enhanced by a pre-sharing key parameter set instead of transmission of a key directly. Also, the security key can be dynamically updated in real-time according to the needs of the users. The real (I) and imaginary (Q) parts of the QAM symbol matrix after modulation are encrypted by the correspondence between transfer RNA (tRNA) and amino acids and the selection mapping of DNA base complementary rules. Also, we add cubic permutation to ensure all data security encryption. The encrypted signals of 35.29 Gb/s on different wavelength channels are successfully demonstrated over a 25-km standard single-mode fiber (SSMF) and a back-to-back (BTB) system. It is proved that the proposed security OFDM-WDM-PON encryption scheme is compatible with the traditional WDM system, which can make full use of bandwidth resources and enhance the security with a large key space.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

A passive optical network (PON) has become the optimal solution to break the “last 1-km” bottleneck due to its large capacity, low power consumption, and easy maintenance. Orthogonal frequency division multiplexing (OFDM) is widely used in the PON thanks to its high spectrum efficiency and strong anti-dispersion capability [1,2]. Wavelength division multiplexing (WDM) is one of the key technologies to improve the speed and capacity of optical communication [3]. OFDM-PON based on WDM (OFDM-WDM-PON) is compatible with the WDM-PON. The optical line terminal (OLT) uses WDM technology to transmit multiple OFDM-modulated optical signals to different optical network units (ONUs) so that the access network can adapt to a highly dynamic flow pattern, and provide ultra-large capacity transmission. OFDM-WDM-PON has shown great potential in the next-generation access network. However, with the rapid growth of users, a large amount of personal information has become the shared resources of the Internet. The OLT and the ONUs adopt broadcasting over the downlink communication, which makes the transmitted data vulnerable to eavesdropping and attack by illegal attackers [4,5]. Therefore, the security of PON has attracted more and more scholars’ attention.

Chaos is regarded as an effective and secure method for data transmission and encryption at the physical layer due to its characteristics of large bandwidth, high randomness, and sensitivity to initial values. In recent years, the physical layer chaotic communication has become the main solution to the security problems of the optical access network. For the transmitted signal, Bi et al. scrambled the subcarriers in the time and frequency domains separately [6]. Chen et al. proposed a random chaotic pilot interval and permutation scheme that does not require redundant sideband information [7]. Zhao et al. used hyperchaos to generate four masking factors to achieve ultra-high security encryption in four different dimensions. The dimension coordination optimization was adopted to reduce the time cost of the system and improve the encryption efficiency by 3 times [8]. Zhang et al. employed a pseudorandom number sequence generated by a chaotic logistic map to control the frequencies of RF subcarriers, which greatly improves the security of OFDM-PON [9]. Liu et al. verified that the constellation masking and chaotic dimension permutation can effectively resist illegal ONUs in OFDM-PON [10,11]. By randomly mapping the quadrature amplitude modulation (QAM) symbols to new positions on the complex plane, a noise-like constellation was generated to improve the security level of physical layer data transmission [12]. The high security optical access network based on carrier-less amplitude phase modulation (CAP) was proposed [13,14]. Also, multi-layer encryption schemes have been studied, the data was partitioned and encrypted with different encryption algorithms, different encryption sequences, and different security keys [15]. Based on cryptanalysis, the encryption from symbols to units realized a single non-repetitive permutation and plaintext-related diffusion to resist attackers [16]. Two-layer encryption of I/Q was implemented by using 7-D hyperchaos, and Walsh-Hadamard and discrete cosine transform were used to effectively reduce the computational complexity and increase the key space [17]. For the encryption mechanism, Brownian motion was used to carry out hybrid symbol substitution and interleaving to improve the security of coherent optical OFDM-PON system [18]. Wu et al. divided the 3-D symbols into cells and carried out Brownian motion chaotic scrambling [19,20]. The chaotic compressive sensing (CS) algorithm aimed at compressing the transmitted data and enhancing the security of data transmission [21]. The subcarrier rotation based on Turbo coding was proposed to keep robustness and achieve security communication [22]. Deoxyribonucleic acid (DNA) coding has the advantages of large storage capacity, large parallelism, and low power consumption [23], and it has been widely used in image encryption [2427]. The complexity and randomness of encryption sequences in OFDM-PON were enhanced through DNA coding and DNA extension coding [28,29]. The improved DNA coding at the bit-level and chaotic scrambling at the symbol-level were used to improve the security [30,31]. However, these schemes all used DNA coding at the bit-level, and the encoding and decoding rules were selected by chaos. Moreover, they only involved the DNA base coding and lacked the researches on the DNA base complementary, which makes the coding methods relatively simple. Besides, ribonucleic acid (RNA) is also a kind of genetic material that carries out the coding instructions in the organism. If DNA and RNA coding are combined for data encryption, the randomness of data changes and the ability to resist attackers can be improved, and the stronger security guarantee can be realized.

A complete optical access network physical layer security technology should not only include an encryption scheme but also have an effective key distribution method. Most of the above chaotic encryption schemes used the chaotic initial values as the pre-shared security keys. When the key is intercepted by an illegal attacker, the transmitted data is highly likely to be cracked. There are also some researches on key management and distribution. Rapid random polarization state fluctuations were used as the key in the fibers [32]. Li et al. used the redundancy of the training symbols to embed the security key. The receiver extracts the key by comparing the local chaotic sequences with the received chaotic sequences [33]. Zhang et al. proposed a pilot-aided key agreement scheme, which can increase the difficulty of eavesdropping by illegal attackers, but the number of ONUs supported by the system was also limited [34]. Lin et al. proposed a key distribution method controlled by dynamic parameters, but the receiver needs to calculate the correlation coefficient several times to determine whether it has achieved chaotic synchronization [35].

In this paper, we propose an encryption scheme combining chaos with RNA and DNA coding for security enhancement of OFDM-WDM-PON. The dynamic key agreement based on mRNA codebook is used to distribute the security key between OLT and ONU. The plaintext-related hash ruled numbers (HRNS) are defined to select the start codon on the messenger RNA (mRNA) codebook stored locally, and the key generation rules are confidential to illegal ONUs. The security of the key is increased by pre-sharing the key parameter set instead of transmitting the key directly. And the security key can be changed according to the needs of the users in real-time to achieve dynamic key update. The signal is encrypted at two levels: the IQ transfer RNA (tRNA)-DNA encoding and the cubic permutation. The real (I) and imaginary (Q) parts of the QAM matrix are encrypted by the correspondence between tRNA and amino acids, and the selection mapping of DNA base complementary rules. To ensure all data encryption of the physical layer, cubic permutation is carried out. Since the encoding rules are plaintext-related, and the decoding rules are random and nonidentical, the system security and the ability to resist attackers can be improved effectively.

2. Principle

The schematic diagram of the chaotic RNA and DNA encryption in OFDM-WDM-PON is shown in Fig. 1, where the red box represents the dynamic key agreement based on mRNA codebook, and the blue box represents the IQ tRNA-DNA encoding and the cubic permutation encryption. The OLT and the ONU store the same mRNA codebook locally and negotiate the key generation rules in advance. At the OLT, a pseudo-random binary sequence (PRBS) is used as input data. After serial-to-parallel (S/P) and 16-QAM modulation, the bit signal is converted into a plane matrix P = F×N, and F is the number of subcarriers. Each subcarrier carries N QAM symbols, which is equivalent to 4N bits. And then the P is divided into the real matrix I and imaginary matrix Q. Taking any positive integer M (0 < 3M < N), the I and the Q are divided into two sub-matrices of size F×3M and F×(N−3M) respectively, denoted as I1, I2, Q1, Q2. The locally stored mRNA codebook and pre-shared key parameter set are then used to generate the security key. Finally, the encrypted data is transmitted to the ONU through IFFT, inserting cyclic prefix (CP) and parallel-to-serial (P/S) operations.

 figure: Fig. 1.

Fig. 1. The proposed schematic diagram of the chaotic RNA and DNA encryption in OFDM-WDM-PON (OM: optical multiplexer; OS: optical splitter).

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DNA has four bases: adenine (A), guanine (G), thymine (T), and cytosine (C), where A and T are complementary pairs, and C and G are complementary pairs. The DNA sequence determines the sequence of amino acids that make up the protein. The amino acids need to be transcribed by mRNA and translated by tRNA to enter the ribosome. RNA consists of four bases: adenine (A), guanine (G), uracil (U), and cytosine (C), where A and U are complementary pairs, and C and G are complementary pairs. Three consecutive bases of RNA form a codon, and each codon stands for an amino acid, as shown in Table 1. Usually, a base is coded with a two-bit binary composed of “0” and “1”, so 4×3×2×1 = 24 coding rules can be obtained. However, only 8 coding rules can meet the base complementary principle. The encoding and decoding rules of DNA and RNA are shown in Tables 2 and 3.

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Table 1. The Correspondence between Amino Acid and Codon

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Table 2. DNA Encoding and Decoding Rules

In the proposed scheme, the specific steps of the dynamic key agreement based on mRNA codebook are as follows:

Step 1: The OLT selects the s-th base from the mRNA codebook as the start index of the first codon. The value of s is determined by the hash values of the I1, I2, Q1, Q2.

$$\left\{ \begin{array}{l} {I_{1H}} = mod (bin2dec\textrm{(}Extract10\textrm{(}SHA256\textrm{(}{I_1}\textrm{))),8) + 1}\\ {I_{2H}} = mod \textrm{(}bin2dec\textrm{(}Extract10\textrm{(}SHA256\textrm{(}{I_2}\textrm{))),8) + 1}\\ {Q_{1H}} = mod \textrm{(}bin2dec\textrm{(}Extract10\textrm{(}SHA256\textrm{(}{Q_1}\textrm{))),8) + 1}\\ {Q_{2H}} = mod \textrm{(}bin2dec\textrm{(}Extract10\textrm{(}SHA256\textrm{(}{Q_2}\textrm{))),8) + 1} \end{array} \right.$$
where SHA256 is a hash value with a size of 256 bits, Extract10(·) returns the first ten digits, The function of bin2dec(·) is to convert a binary number to a decimal number, mod(r, t) returns the remainder of r divided by t. We define I1H, I2H, Q1H, Q2H as the HRNS, which are positive integers in the range [1,8].
$$s = {\kappa _1} \times {I_{1H}} + {\kappa _2} \times {I_{2H}} + {\kappa _3} \times {Q_{1H}} + {\kappa _4} \times {Q_{2H}}$$
where κi (i = 1,2,3,4)∈ [1,10] is an integer. It is used to determine the position of the start index s as the reference coefficient, denoted as the vector = [κ1, κ2, κ3, κ4].

Step 2: Four codons are selected from s and translated into anti-codons according to the base complementation principle. Each anti-codon can be converted to 6 binary numbers according to Table 3, and then converted to a decimal number. The decimal numbers of the four anti-codons are denoted as m1, m2, m3, and m4.

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Table 3. RNA Encoding and Decoding Rules

Step 3: The process of generating the security key is shown in Fig. 2(a), which is written as

$$x = \textrm{(}\frac{{{m_1}}}{{64}} \times {\eta _1} \times \textrm{0}\textrm{.9 + }\frac{{{m_2}}}{{64}} \times {\eta _2} \times \textrm{0}\textrm{.99 + }\frac{{{m_3}}}{{64}} \times {\eta _3} \times \textrm{0}\textrm{.9 + }\frac{{{m_4}}}{{64}} \times {\eta _4} \times \textrm{0}\textrm{.99)/4}$$
where x is a chaotic initial value as the security key, ηi (i = 1,2,3,4)∈(0,1) is the processing coefficient, which is denoted as the vector η =[η1, η2, η3, η4]. If the encryption process requires several chaotic initial values, the above steps are repeated. Then the start index is denoted as the index vector S, and the reference coefficient and the processing coefficient are denoted as the coefficient matrices K and H, respectively.
$$S = {\left[ {\begin{array}{{cccc}} {{s_1}}&{{s_2}}&{\ldots }&{{s_n}} \end{array}} \right]^T}$$
$${\rm K}\textrm{ = }\left[ {\begin{array}{{cccc}} {{\kappa_{11}}}&{{\kappa_{12}}}&{{\kappa_{13}}}&{{\kappa_{14}}}\\ {{\kappa_{21}}}&{{\kappa_{22}}}&{{\kappa_{23}}}&{{\kappa_{24}}}\\ \vdots & \vdots & \vdots & \vdots \\ {{\kappa_{n1}}}&{{\kappa_{n2}}}&{{\kappa_{n3}}}&{{\kappa_{n4}}} \end{array}} \right]$$
$${\rm H}\textrm{ = }\left[ {\begin{array}{{cccc}} {{\eta_{11}}}&{{\eta_{12}}}&{{\eta_{13}}}&{{\eta_{14}}}\\ {{\eta_{21}}}&{{\eta_{22}}}&{{\eta_{23}}}&{{\eta_{24}}}\\ \vdots & \vdots & \vdots & \vdots \\ {{\eta_{n1}}}&{{\eta_{n2}}}&{{\eta_{n3}}}&{{\eta_{n4}}} \end{array}} \right]$$

 figure: Fig. 2.

Fig. 2. The dynamic key agreement based on mRNA codebook. (a) The security key is generated; (b) The key parameter set is pre-shared.

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Step 4: The HRNS I1H, I2H, Q1H, Q2H, coefficient matrices K and H are pre-shared between the OLT and ONU. The security key is generated by the pre-agreed rules for encryption. The pre-sharing process is briefly described in Fig. 2(b).

In the end, the specific steps of the dynamic key agreement based on mRNA codebook are completed.

Next, we perform the IQ tRNA-DNA encoding on the transmitted signal. The specific steps are as follows:

Step 1: The real (I) and imaginary (Q) parts of each QAM symbol are respectively represented by 2 bits. The sizes of I1, I2, Q1, and Q2 are F×6M, F×(2N−6M), F×6M, and F×(2N−6M) respectively.

Step 2: I1, Q1 are performed tRNA encoding, and I2, Q2 are performed DNA encoding. The tRNA and DNA encoding rules of I1, I2, Q1, Q2 are determined by using the above-mentioned HRNS I1H, I2H, Q1H, Q2H. We denote the encoded matrices as I'1, I'2, Q'1, and Q'2.

Step 3: I'1, Q'1 are performed chaotic tRNA translation. Three consecutive bases are considered as one codon, so the number of codons for I'1, Q'1 is F×M. These codons are translated into corresponding amino acids according to Table 1.

We use the generated key as the chaotic initial value. The chaotic sequences {x1}, {x2}, {x3} are generated by 1-D logical chaotic map.

$${\textrm{x}_{i + 1}} = \mu {x_i}({1 - {x_i}} )$$
where i represents the i-th iteration, xi (xi∈[0,1]) represents the result of the i-th iteration, and μ represents the bifurcation parameter. When μ∈(3.57,4), the 1-D logical chaotic map shows a good chaotic state.

The chaotic values are processed by Eq. (8). {x1}, {x2} are transformed into chaotic matrices X1, X2 of size F×M, and {x3} is transformed into chaotic matrix X3 of size F×3M.

$$x_i^{\prime} = mod ({{x_i} \times {{10}^{15}},8} )+ 1$$

An amino acid may correspond to several codons, so we have grouped amino acids for encryption, as shown in Table 1. According to the X1, X2, new codons are randomly selected for the amino acids in I'1, Q'1.

$$codo{n^{\prime}} = rcycle({codon,{X_{i,j}}} )$$
where codon is the original codon, codon’ is the new codon selected in the amino acid group, and rcycle(c, d) returns the new codon after the original codon is shifted to the right by d in the amino acid group. Then we can get new base matrices I''1, Q''1. According to X3, each base corresponds to different decoding rules, I''1 and Q''1 are decoded into binary matrices I'''1, Q'''1 of size F×6M. An example of the chaotic tRNA translation is shown in Fig. 3.

 figure: Fig. 3.

Fig. 3. The chaotic tRNA translation.

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Step 4: I'2, Q'2 are performed the chaotic DNA base complementation and the selection mapping. Each DNA base has a unique corresponding base in the DNA base complementary principle [26].

$$\left\{ \begin{array}{l} {b_i} \ne B\textrm{(}{b_i}\textrm{)} \ne B\textrm{(}B\textrm{(}{b_i}\textrm{))} \ne B\textrm{(}B\textrm{(}B\textrm{(}{b_i}\textrm{)))}\\ {b_i} = B\textrm{(}B\textrm{(}B\textrm{(}B\textrm{(}{b_i}\textrm{))))} \end{array} \right.$$
where bi∈(A, T, C, G) represents four bases, B(·) returns a DNA base after a complementary operation. According to Eq. (10), six base complementary rules can be obtained, as shown in Table 4.

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Table 4. DNA Base Complementary Rules

DNA has two kinds of symmetric algebraic operations: addition and XOR, as shown in Tables 5 and 6.

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Table 5. DNA Base Addition Operation

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Table 6. DNA Base XOR Operation

The chaotic sequences {y1}, {y2}, {z1}, {z2} are generated by Eq. (7) and processed according to Eqs. (11) and (12). Two primer matrices Y1, Y2 of size F×(N−3M) can be obtained. Then we perform DNA encoding on every two bits of the processed sequences {z1}, {z2} and obtain two chaotic matrices Z1, Z2 of size F×(N−3M) as the scrambling matrices for the selection mapping.

$$y_i^{\prime} = mod ({{y_i} \times {{10}^{15}},26} )+ 1$$
$$z_i^{\prime} = \left\{ \begin{array}{l} 0, \cdots \cdots {z_i} \le 0.5\\ 1, \cdots \cdots {z_i} > 0.5 \end{array} \right.({1 \le i \le n} )$$

The specific selection mapping operation of each base of I'2, Q'2 is determined according to the primer matrices Y1, Y2. The operating instructions of Y1, Y2 are shown in Table 7. If algebraic addition and XOR operations are required, the operation is carried out with the base at the corresponding position of Z1, Z2. Then we can obtain two new matrices I''2, Q''2 after the selection mapping. Next, I''2, Q''2 are converted into binary matrices I'''2, Q'''2 of size F×(2N−6M) by randomly selecting the decoding rules according to X3. An example of the chaotic DNA base complementation and the selection mapping is shown in Fig. 4.

 figure: Fig. 4.

Fig. 4. The chaotic DNA base complementation and the selection mapping.

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Table 7. The Selection Mapping Operation Instructionsa

Step 5: I'''1 and Q'''1 are combined, I'''2 and Q'''2 are combined, and then the encrypted matrices I’ and Q’ can be obtained. The I’ and Q’ are combined to obtain the encrypted QAM matrix P1en.

In the end, the specific steps of the IQ tRNA-DNA encoding are over.

There may be unchanged bases in the encoding process. To ensure all data encryption at the physical layer, the second layer cubic permutation encryption is carried out. The matrix P1en is converted into a 3-D cube structure of subcarrier, symbol and time. The specific steps of the cubic permutation are as follows:

Step 1: The chaotic sequences {γ1}, {γ2}, {γ3}, {ω1}, {ω2}, {ω3} are obtained, which are used to generate the original coordinates and the new coordinates.

$$\left\{ \begin{array}{l} a = mod \textrm{(}{\gamma_{1i}} \times \textrm{1}{\textrm{0}^{\textrm{15}}}\textrm{,}{max_{sub}}\textrm{)} + 1\\ b = mod \textrm{(}{\gamma_{2i}} \times \textrm{1}{\textrm{0}^{\textrm{15}}}\textrm{,}{max_{sym}}\textrm{)} + 1\\ c = mod \textrm{(}{\gamma_{3i}} \times \textrm{1}{\textrm{0}^{\textrm{15}}}\textrm{,}{max_{tim}}\textrm{)} + 1 \end{array} \right.$$
$$\left\{ \begin{array}{l} {a^{\prime}} = mod \textrm{(}{\omega_{1i}} \times \textrm{1}{\textrm{0}^{\textrm{15}}}\textrm{,}{max_{sub}}\textrm{)} + 1\\ {b^{\prime}} = mod \textrm{(}{\omega_{2i}} \times \textrm{1}{\textrm{0}^{\textrm{15}}}\textrm{,}{max_{sym}}\textrm{)} + 1\\ {c^{\prime}} = mod \textrm{(}{\omega_{3i}} \times \textrm{1}{\textrm{0}^{\textrm{15}}}\textrm{,}{max_{tim}}\textrm{)} + 1 \end{array} \right.$$
where a, b, and c are the value of the subcarrier, symbol, and time dimension of the original coordinate respectively, a’, b’, and c’ are the value of the new coordinate, and maxsub, maxsym, and maxtim are the maximum size of subcarrier, symbol, and time dimension respectively in the cubic structure.

Step 2: For the original QAM symbol “Q0”, the encrypted QAM symbol “Qe” is obtained by exchanging the two coordinates, as shown in Fig. 5.

$${Q_e} = exchange\textrm{((}a\textrm{,}b\textrm{,}c\textrm{),(}{a^{\prime}}\textrm{,}{b^{\prime}}\textrm{,}{c^{\prime}}\textrm{))}$$
where exchange(·) represents the exchange of the two coordinates.

 figure: Fig. 5.

Fig. 5. The cubic permutation.

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In the end, the specific steps of the cubic permutation are completed, the encryption matrix P2en is obtained for transmission.

3. Experiment setup

The experiment setup of the proposed scheme is shown in Fig. 6. A PRBS with a length of 9.6×104 is input at the OLT. After S/P and QAM modulation, the signal is converted into a QAM matrix P with the size of 120×200. We divide the real and the imaginary parts of the QAM symbol to obtain two matrices I and Q of the same size, both of which are 120×200. Then we take a positive integer M=30. The sizes of I1, Q1 are 120×90, and the sizes of I2, Q2 are 120×110. According to the hash values of these four submatrices, four HRNS I1H, I2H, Q1H, and Q2H are equal to 1, 6, 3, and 8 respectively. The proposed scheme needs five chaotic sequences, so we set the coefficient matrices Κ, H as follows:

$${\rm K}\textrm{ = }\left[ {\begin{array}{{cccc}} 5&3&2&7\\ 1&8&3&5\\ 6&2&{10}&1\\ 9&4&6&7\\ 7&1&2&8 \end{array}} \right]$$
$${\rm H}\textrm{ = }\left[ {\begin{array}{{cccc}} {0.1152687741}&{0.62587552256}&{0.769542356988}&{0.88569976}\\ {0.254698752}&{0.42658996333}&{0.6958741256}&{0.92658745154}\\ {0.3154685214}&{0.15264552667}&{0.63254897558}&{0.5897456288}\\ {0.896542879}&{0.9658741235}&{0.96587452121}&{0.36587745569}\\ {0.3256887752}&{0.3955669852}&{0.2698528775}&{0.6987745223} \end{array}} \right]$$

 figure: Fig. 6.

Fig. 6. The experiment setup (AWG: arbitrary waveform generator; LD: laser diode; MZM: Mach-Zehnder modulator; SSMF: standard single-mode fiber; PSC: passive splitter couple; TOA: tunable optical attenuator; PD: photodetector; OLT: optical line terminal; ONU: optical network unit).

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The OLT pre-shares the four HRNS and coefficient matrices with ONU. Then the encrypted OFDM signal is generated offline by MATLAB. The length of IFFT is 256. In order to ensure the generation of real value signals, a data frame with a Hermitian symmetry structure is used, in which 120 subcarriers carry encrypted data and another 120 subcarriers load corresponding complex conjugate data. A CP with a length of 1/16 of the OFDM symbol is added to the data sequence to reduce inter-symbol interference (ISI). The signal is uploaded to the arbitrary waveform generator (AWG, Keysight M8196A) with a sampling rate of 20 GSa/s to complete the digital-to-analog conversion (DAC). A tunable laser diode (LD) is used as the optical source. The wavelength of the LD is set to 1552 nm and 1542 nm. The encrypted signal is modulated onto the optical carrier by a Mach-Zehnder modulator (MZM) with a bandwidth of 10 GHz. The optical signal is transmitted over the 25-km standard single-mode fiber (SSMF). At the ONU, a tunable optical attenuator (TOA) is used to control the received optical power. When the optical signal is detected by a photodetector (PD) with a bandwidth of 10 GHz, the digital storage oscilloscope (DSO Keysight Z594A) with a sampling rate of 40 GSa/s is used as an analog-digital converter (ADC) to record it. The signal demodulation and decryption are also performed offline by MATLAB.

4. Results and discussions

4.1 Dynamic security key

First, we analyze the randomness of the security key. The key generated using the dynamic key agreement based on mRNA codebook is controlled by the key parameter set. We assume that the values of [η1, η2, η3, η4] are the same. The scatter diagram of the relationship between the security key and the processing coefficient η is shown in Fig. 7. We can see that the security key generated using this scheme has strong randomness. Even if the processing coefficients are the same, when the position of the start index s is changed, the key generated is different. Besides, when the transmitted data changes, the HRNS will change with the characteristics of the signal, and the coefficient matrices Κ, H can also be changed in real time according to the user needs, which achieves the dynamic update of the security key. It reduces the probability of illegal attackers directly intercepting the security key. Assuming that an illegal ONU has monitored the channel for a long time, and has eavesdropped on the security key, the OLT can also dynamically modify the pre-shared key parameter set to achieve the purpose of changing the security key dynamically, so that the illegal ONU can not obtain the correct security key.

 figure: Fig. 7.

Fig. 7. The relationship between the security key and the processing coefficient η.

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Second, we calculate the key storage space. The start index s is determined by the HRNS and the reference coefficients according to Eq. (2). Assuming that the HRNS and reference coefficients are set as the maximum values, the mRNA codebook needs contain 10×8×4 + 4×3 = 332 parameters stored locally by ONU and OLT. Since the encryption scheme requires five chaotic sequences, five chaotic initial values need to be generated. The OLT and the ONU pre-share four HRNS and the coefficient matrices Κ, H of size 5×4. Therefore, a total of 332 + 4+5×4×2 = 376 parameters are needed. The comparisons between the dynamic key agreement proposed by this scheme and other key generation schemes are shown in Table 8. As the number of the ONUs supported by the OLT increases, the key storage space consumed by the physical layer security services will also increase. The curve of the key storage space with the number of the ONUs is shown in Fig. 8. It can be seen from the above results that the traditional schemes only need to store the chaotic initial values required for encryption in advance. The operation is simple and the key storage space is very small. However, since the security key is directly transmitted on the channel, it is more vulnerable to steal by illegal attackers. Compared with other existing key generation schemes, the proposed scheme has a smaller key storage space and slower growth rate, and it does not need complex post-processing to compare whether the OLT and the ONU have the same key. In addition, since the key generated by this scheme is plaintext-related, it can be changed in real-time according to transmitted signal, which further increases the randomness and security.

 figure: Fig. 8.

Fig. 8. The curve of the key storage space with the number of ONUs.

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Table 8. The Comparisons between the Proposed Scheme and other Key Generation Schemes

4.2 Security performance

First, we analyze the sensitivity of the security key. The HRNS I1H, I2H, Q1H, Q2H, and the coefficient matrices Κ, H are pre-shared and stored locally between OLT and ONU. The chaotic initial values are obtained through pre-agreed key generation rules. When the key parameter set changes, the chaotic initial values also change, so testing the sensitivity of the chaotic sequences is the basis of evaluating the sensitivity of the encryption system to the key parameter set. When the value of I1H is changed from 1 to 2 and the other parameter values remain unchanged, the chaotic initial value x is changed from 0.230110915062263 to 0.185358067838114, and the sensitivity of {x} is shown in Fig. 9(a). When the κ23 of the K is changed from 3 to 4 and the other parameter values remain unchanged, the chaotic initial value y is changed from 0.295792966570490 to 0.293376048711866, and the sensitivity of {y} is shown in Fig. 9(b). When the η32 of the H is changed from 0.15264552667 to 0.152645526670001 and the other parameter values remain unchanged, the chaotic initial value z is changed from 0.19410638532357 to 0.194106638533358, and the sensitivity of {z} is shown in Fig. 9(c). When the values of the pre-shared parameters remain unchanged, the decoding rule of the anti-codons conversion to binary is changed from rule 1 to rule 2 according to Table 3 in the pre-agreed key generation rules, the chaotic initial value γ is changed from 0.40153334703362 to 0.334575060291988, and the sensitivity of {γ} is shown in Fig. 9(d). We can see that the chaotic initial values and the trajectories of two chaotic sequences are completely different by randomly changing one of the key parameter set or the pre-agreed decoding rule, which indicates that the encryption system is highly sensitive to the change of the key parameter set. The BER curve with a tiny change in the chaotic initial value when the received optical power is −12dBm is shown in Fig. 10. It can be seen that when the chaotic initial value differs by 10−15, the BER is significantly improved (∼0.5), which is much higher than the FEC threshold (@10−3). The constellation diagrams after decrypting with the correct key and the wrong key with a difference of 10−15 are shown in the insets (a) and (b) of Fig. 10. The receiver must have the same key parameter set as the sender to decrypt the data correctly, which indicates that the security key in the proposed scheme is highly sensitive.

 figure: Fig. 9.

Fig. 9. The sensitivity of the security key. (a) Only change a hash ruled number; (b) Only change one of the K; (c) Only change one of the H; (d) Only change the pre-agreed decoding rule.

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 figure: Fig. 10.

Fig. 10. The BER curve with a tiny change in the chaotic initial value.

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Second, we calculate the key space. The HRNS, the coefficient matrices are pre-shared as the security key. The key space provided by the four HRNS is 4×8 = 32. The sensitivity of dynamic key agreement based on mRNA codebook to a single parameter change in the coefficient matrices can bring a key space of 1020×[(1–0)×1015]20=10320. Five chaotic sequences provide a key space of (1015)5=1075. The total key space of the encryption system is 32×10320×1075=3.2×10396. If an illegal attacker cracks the encryption system at the computational speed of 3.38×1017TFlop/s of Tianhe-2 supercomputer, it will take at least 9.47×10378 years to obtain the correct key, which is sufficient to resist exhaustion attacks. Compared with the encryption scheme that directly transmits the key, the key space is expanded by about 10321 times when the same encryption scheme is used. Besides, if the mRNA codebook used by ONU and OLT simultaneously changes, the key space will be expanded to (32×10320)12×1075=1.15×103933. The key space comparison with other encryption schemes is shown in Table 9. The proposed scheme provides a huge key space, enriches the key sequence of the system, and can realize the dynamic update of the security key.

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Table 9. The Key Space Comparison

Third, we evaluate the computational complexity. Assuming the length of an encrypted data is N, and n (n<<N) chaotic initial values need to be generated for encryption. The total complexity of the encryption scheme comes from two aspects: key generation and data encryption, as shown in Table 10. We can see that the computational complexity mainly comes from data encryption. In this scheme, n=5, Table 11 is the computational complexity comparison of this scheme and other encryption schemes. It can be seen that the total complexity of the scheme does not increase too much, but it is slightly higher than the traditional DNA-only scheme since the RNA encoding is expanded. DNA is a stable double helix structure connected by a large number of hydrogen bonds, while RNA is a single-stranded structure, and the mutation is more flexible. Therefore, combining DNA and RNA can increase the randomness and security of data encryption and improve the ability to resist attacks.

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Table 10. The Computational Complexity

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Table 11. The Computational Complexity Comparison

4.3 Transmission performance

First, we simulate the complementary cumulative distribution function (CCDF) of the peak to average power ratio (PAPR), as shown in Fig. 11. As we can see, the CCDF curve of the encrypted signal is a little lower than that of the original signal since the chaotic tRNA-DNA encoding changes the phase relationship between constellation points. Therefore, the proposed scheme can slightly improve the signal transmission performance.

 figure: Fig. 11.

Fig. 11. The PAPRs of original and encrypted signals.

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Second, we compare the BER curves of two legal ONUs and one illegal ONU under different received optical power, as shown in Fig. 12. When the received optical power is −12dBm, the constellation diagram of the encrypted signal is shown in the insert of Fig. 12. For the legal ONUs on the channels with different wavelengths, the BER curves are basically the same. Therefore, the wavelength change of the channel does not affect transmission performance, and OFDM-WDM-PON is compatible with WDM-PON. The BER curve of the encrypted signal are lower than that of the original signal under the same received optical power, which is the influence of the phase change between constellation points. The BER performance of signals transmitted through the back-to-back (BTB) system is about 1dB (BER@10−3) received optical power lower than that of SSMF transmission, which is mainly due to the fiber loss and dispersion. For the illegal ONU, the BER is always about 0.5 since the correct key and the encryption scheme are not known, which indicates that the illegal ONU can not obtain useful information. Therefore, this scheme can effectively resist illegal attacks. The comparisons of BER results of different encryption schemes are shown in Fig. 13. Figure 13(a) is the comparison under different OSNR. Figure 13(b) is the comparison under different received optical power through 25-km SSMF transmission. It can be seen that the BER curve using this scheme is basically the same as the BER curve using tRNA-DNA encryption only. The BER performance using this scheme is about 0.8dB (BER@10−3) lower than that of the original signal, is better than that of the signal encrypted only by DNA and the signal encrypted only by cubic permutation. Therefore, compared with the traditional signal encrypted only by DNA, the proposed scheme not only enhances the signal transmission performance but also further improves the scrambling degree of the signal and increases the security of signal transmission.

 figure: Fig. 12.

Fig. 12. The BER performance of two legal ONUs and an illegal ONU on different wavelength channels under different received optical power.

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 figure: Fig. 13.

Fig. 13. The BER comparison results of different encryption schemes (a) under different OSNR; and (b) under different received optical power.

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5. Conclusion

An encryption scheme of combining chaos with RNA and DNA coding was firstly proposed for security OFDM-WDM-PON. In this scheme, we adopt the dynamic key agreement based on mRNA codebook, and the two-level encryption of the IQ tRNA-DNA encoding and the cubic permutation. We define the plaintext-related HRNS to select the start codon on the mRNA codebook stored locally. The key parameter set is pre-shared instead of transmitting the key directly. The key generated using the proposed scheme is plaintext-related and the key generation rules are confidential to illegal ONUs, which increases the randomness and security of the key. The key space can reach up to 3.2×10396, which is beneficial to resist exhaustion attacks. Besides, the values of the key parameter set can be changed in real-time according to the needs of the users, which realizes the dynamic update of the security key. The diversity of the correspondence between tRNA and amino acids in biology is utilized, and the selection mapping relationship of DNA base complementary rules is extended. It increases the diversity of the encryption process. Compared with the traditional DNA encoding for PRBS, the proposed scheme encodes the QAM symbols, which expands the application range of DNA encoding. The encoding rules selected are plaintext-related, the decoding rules for each base are generated randomly and different from each other, which effectively improves the security of the communication system and the ability to resist known/chosen plaintext attacks. In addition, the cubic permutation is added to ensure all data encryption on the physical layer. The encrypted signals of 35.29 Gb/s on different wavelength channels have been successfully transmitted over a 25-km SSMF and a BTB system. The wavelength change of the channel has no effect on the communication system. OFDM-WDM-PON is compatible with traditional WDM optical networks. The proposed scheme can enhance the security and transmission performance.

Funding

National Natural Science Foundation of China (61571092, 62071088); National Key Research and Development Program of China (2018YFB1801302); Project for Innovation Team of Guangdong University (2018KCXTD033); Project for Zhongshan Social Public Welfare Science and Technology (2019B2007); Research Project for Talent of UESTC Zhongshan Institute (418YKQN07); Science and Technology Planning Project of Guangdong Province (2021A0101180005).

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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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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Figures (13)

Fig. 1.
Fig. 1. The proposed schematic diagram of the chaotic RNA and DNA encryption in OFDM-WDM-PON (OM: optical multiplexer; OS: optical splitter).
Fig. 2.
Fig. 2. The dynamic key agreement based on mRNA codebook. (a) The security key is generated; (b) The key parameter set is pre-shared.
Fig. 3.
Fig. 3. The chaotic tRNA translation.
Fig. 4.
Fig. 4. The chaotic DNA base complementation and the selection mapping.
Fig. 5.
Fig. 5. The cubic permutation.
Fig. 6.
Fig. 6. The experiment setup (AWG: arbitrary waveform generator; LD: laser diode; MZM: Mach-Zehnder modulator; SSMF: standard single-mode fiber; PSC: passive splitter couple; TOA: tunable optical attenuator; PD: photodetector; OLT: optical line terminal; ONU: optical network unit).
Fig. 7.
Fig. 7. The relationship between the security key and the processing coefficient η.
Fig. 8.
Fig. 8. The curve of the key storage space with the number of ONUs.
Fig. 9.
Fig. 9. The sensitivity of the security key. (a) Only change a hash ruled number; (b) Only change one of the K; (c) Only change one of the H; (d) Only change the pre-agreed decoding rule.
Fig. 10.
Fig. 10. The BER curve with a tiny change in the chaotic initial value.
Fig. 11.
Fig. 11. The PAPRs of original and encrypted signals.
Fig. 12.
Fig. 12. The BER performance of two legal ONUs and an illegal ONU on different wavelength channels under different received optical power.
Fig. 13.
Fig. 13. The BER comparison results of different encryption schemes (a) under different OSNR; and (b) under different received optical power.

Tables (11)

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Table 1. The Correspondence between Amino Acid and Codon

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Table 2. DNA Encoding and Decoding Rules

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Table 3. RNA Encoding and Decoding Rules

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Table 4. DNA Base Complementary Rules

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Table 5. DNA Base Addition Operation

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Table 6. DNA Base XOR Operation

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Table 7. The Selection Mapping Operation Instructions a

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Table 8. The Comparisons between the Proposed Scheme and other Key Generation Schemes

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Table 9. The Key Space Comparison

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Table 10. The Computational Complexity

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Table 11. The Computational Complexity Comparison

Equations (17)

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

{ I 1 H = m o d ( b i n 2 d e c ( E x t r a c t 10 ( S H A 256 ( I 1 ))),8) + 1 I 2 H = m o d ( b i n 2 d e c ( E x t r a c t 10 ( S H A 256 ( I 2 ))),8) + 1 Q 1 H = m o d ( b i n 2 d e c ( E x t r a c t 10 ( S H A 256 ( Q 1 ))),8) + 1 Q 2 H = m o d ( b i n 2 d e c ( E x t r a c t 10 ( S H A 256 ( Q 2 ))),8) + 1
s = κ 1 × I 1 H + κ 2 × I 2 H + κ 3 × Q 1 H + κ 4 × Q 2 H
x = ( m 1 64 × η 1 × 0 .9 +  m 2 64 × η 2 × 0 .99 +  m 3 64 × η 3 × 0 .9 +  m 4 64 × η 4 × 0 .99)/4
S = [ s 1 s 2 s n ] T
K  =  [ κ 11 κ 12 κ 13 κ 14 κ 21 κ 22 κ 23 κ 24 κ n 1 κ n 2 κ n 3 κ n 4 ]
H  =  [ η 11 η 12 η 13 η 14 η 21 η 22 η 23 η 24 η n 1 η n 2 η n 3 η n 4 ]
x i + 1 = μ x i ( 1 x i )
x i = m o d ( x i × 10 15 , 8 ) + 1
c o d o n = r c y c l e ( c o d o n , X i , j )
{ b i B ( b i ) B ( B ( b i )) B ( B ( B ( b i ))) b i = B ( B ( B ( B ( b i ))))
y i = m o d ( y i × 10 15 , 26 ) + 1
z i = { 0 , z i 0.5 1 , z i > 0.5 ( 1 i n )
{ a = m o d ( γ 1 i × 1 0 15 , m a x s u b ) + 1 b = m o d ( γ 2 i × 1 0 15 , m a x s y m ) + 1 c = m o d ( γ 3 i × 1 0 15 , m a x t i m ) + 1
{ a = m o d ( ω 1 i × 1 0 15 , m a x s u b ) + 1 b = m o d ( ω 2 i × 1 0 15 , m a x s y m ) + 1 c = m o d ( ω 3 i × 1 0 15 , m a x t i m ) + 1
Q e = e x c h a n g e (( a , b , c ),( a , b , c ))
K  =  [ 5 3 2 7 1 8 3 5 6 2 10 1 9 4 6 7 7 1 2 8 ]
H  =  [ 0.1152687741 0.62587552256 0.769542356988 0.88569976 0.254698752 0.42658996333 0.6958741256 0.92658745154 0.3154685214 0.15264552667 0.63254897558 0.5897456288 0.896542879 0.9658741235 0.96587452121 0.36587745569 0.3256887752 0.3955669852 0.2698528775 0.6987745223 ]
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