To meet the increasing demand for underwater activities, such as ocean explorations and rescue missions, underwater wireless sensor networks (UWSNs)[
UWOC is customarily regarded as highly secure compared with UAC since the light source is highly directional and has limited penetration distance in common waters[
A UWOC system does not inherently provide a secure transmission link, making it easy for attackers to capture information. In seawater, especially for long-reach transmission, the scattering effect will make the received light spot much larger than the detection area, thereby increasing the risk of signal eavesdropping[
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In this Letter, we present a security-enhanced orthogonal frequency division multiplexing (OFDM) scheme based on three-layer chaotic encryption and chaotic discrete Fourier transform (DFT) precoding in a UWOC system, which can simultaneously guarantee sufficiently high security and transmission performance. The application of multiple hyperchaotic maps and multi-fold data encryption can improve the key space and reduce the risk of the scrambling method and chaotic model being destroyed by statistical analysis. Multiple hyperchaotic maps generate masking factors, implementing bit stream diffusion encryption, in-phase/quadrature (IQ) encryption, time-frequency dimensional scrambling, and chaotic DFT precoding in OFDM. The chaotic DFT precoding matrix is generated to reduce the peak to average power ratio (PAPR) and bit error rates (BERs). The chaotic DFT precoding matrix is obtained by introducing chaotic sequences into the standard DFT matrix for phase encryption and column permutation. Hence, it is more difficult to crack than the encrypted DFT matrix in Refs. [18,19]. To verify the feasibility of the scheme, a 3 Gbit/s encrypted 16-quadrature amplitude modulation (16-QAM) OFDM signal is successfully demonstrated over a 7 m UWOC link. The encryption system is tested and analyzed to have higher security with a key space of and can resist brute force attacks (BFAs) and CPAs, achieving the higher confidentiality of information transmission.
The concept of the proposed security-enhanced OFDM system for UWOC based on three-layer chaotic encryption and chaotic DFT precoding is shown in Fig. 1. The key-driven hyperchaotic maps are used to generate masking factors. It has been proved that signals encrypted by low-dimensional chaotic maps are not always safe[
Figure 1.Block diagram of the secure OFDM-UWOC based on three-layer chaotic encryption and chaotic DFT precoding.
2.1. Diffuse encryption
Bidirectional diffusion in cryptography makes each bit in the plaintext affect many bits in the ciphertext. Here, a four-dimensional (4D) hyperchaotic Chen system is applied to generate chaotic sequences for bidirectional diffusion[
When , , , , and , the system is in a chaotic state. From Eq. (1), four chaotic sequences , , , and can be obtained. Key1 of bidirectional diffusion is . The specific diffusion process is as follows.
The function returns the remainder divided by , is rounding down. and sequences, both with the length of , consist of integers in the range of 0 to 255.
Step 2 can diffuse the plaintext into the ciphertext to different degrees but fails to spread globally due to the single direction of the diffusion, and the following plaintext cannot be diffused to the preceding ciphertext. Hence, using bidirectional diffusion, each part of the binary plaintext information is fully diffused into the ciphertext to generate an utterly dynamic ciphertext. When the plaintext is changed, the entire ciphertext will produce irregular changes, which can effectively resist the CPAs.
2.2. IQ encryption
Then, the first layer of encrypted data is converted to binary data for QAM mapping to obtain symbol sequence . The hyperchaotic logistic mapping is used for IQ encryption and is defined as[
The encryption for the th QAM symbol in the symbol sequence can be expressed as
2.3. Time-frequency dimensional scrambling
After completing the IQ encryption in the second layer, the OFDM frames are scrambled in the time-frequency dimension[
Figure 2.Schematic diagram of time-frequency scrambling[
The data matrix after IQ encryption can be expressed as
Equation (9) defines the row vectors of the data matrix as . Before the time-frequency permutation, the sequence is partitioned into parts, and then each part is ranked in ascending order separately to return and record the dynamic indices. position index sequences obtained by are used to reorder the frequency-domain data of the OFDM symbols, respectively, to realize row scrambling operation. The frequency-domain scrambled matrix can be represented by column vectors . The same operation is used to process to obtain position index sequences and then scramble time-domain data of subcarriers, respectively. Time-frequency permutation is similar to bit interleaving, which can reduce the BER to some extent in the case of burst noise.
2.4. Chaotic DFT precoding
In this work, chaotic DFT precoding is adopted to reduce PAPR and increase the security of UWOC additionally[
According to the above equation, the standard DFT matrix of is row-phase encrypted using different values in the sequence generated by Eq. (8), i.e., each row is subtracted by a different value , while the column-phase is encrypted using a constant , which is from . Finally, the sequence is used to perform a column scrambling on the whole of the phase encrypted DFT matrix to obtain our final chaotic encrypted DFT matrix . Column scrambling of the DFT matrix is equivalent to input data scrambling.
Compared with other single and common chaotic mappings, the multiple hyperchaotic mappings used have more dimensions, leading to increased complexity and security of the UWOC encryption system, similar to the seven-dimensional (7D) chaotic mappings applied in Ref. . However, once the encryption system is implemented in practical applications, we do not need to iterate multiple hyperchaotic systems or update the key sequence frequently until the key of the UWOC system changes. In this case, the major computation complexity would only come from the encryption at the system level[
|Our Scheme||Ref. [||Ref. [|
|Complex-valued multiplication||M2 + N2||M2||M2 + N2|
|Addition||M(M − 1) + N(N − 1)||3M(M − 1) + 2M × (2M − 1) + N(N − 1)||M(M − 1) + N(N − 1)|
Table 1. The Computation Complexity of Encryption Schemes
|Our Chaotic Systems||7D Chaos (Ref. [||Chaos Maps (Ref. [|
Table 2. The Computation Complexity of Chaos Systems
As mentioned above, there is a trade-off between security and complexity. It is worth mentioning that the UWOC encryption method in this Letter does not introduce any additional optical modules, and all of the encryption and decryption operations are performed in the digital signal processing (DSP), so the impact of the iterations of chaotic mapping is small[
3. Experimental Setup
The experimental setup of the proposed high-security OFDM system for UWOC based on three-layer chaotic encryption and chaotic DFT precoding is shown in Fig. 3. At the transmitter, the bit streams are encrypted and loaded into an arbitrary waveform generator (AWG, Tektronix 70002A) at a sampling rate of 3.125 GSamples/s. The voltage amplitude of the output signal is appropriately adjusted using an amplifier (AMP) and a variable electronic attenuator (ATT). Subsequently, the encrypted signal is superimposed on a bias tee (Bias-T) with a direct current (DC) of 0.3414 A, so that the drive signal operates within the linear region of the blue LD. The blue light is collimated by a collimating lens (CL) and emitted into a 7 m water tank filled with tap water. At the receiver, the blue light is incident on an avalanche photodiode (APD210) after passing through a focusing lens (FL) and a variable optical ATT (VOA). Finally, the detected encrypted signals are captured via a mixed signal oscilloscope (MSO, Tektronix MSO71254C) at a sampling rate of 25 GSamples/s and processed offline by a personal computer (PC). The final data transmission rate is about 3 Gbit/s. Table 3 shows the detailed OFDM parameters of the UWOC system.
|Number of effective subcarriers||256|
|Inverse fast Fourier transform (IFFT) size||1024|
|Number of cyclic prefix (CP)||64|
|Number of subcarriers for gap near DC||8|
|Number of OFDM symbols||520|
Table 3. Parameters of the OFDM-UWOC System
Figure 3.Experimental setup. Insets: (a) the transmitter module, (b) the water tank, and (c) the receiving module.
4. Performance and Safety Analysis
The PAPR and BER are utilized to evaluate the performance of our encryption scheme. Besides, image transmission is a typical digital communication application, so we tested the encryption scheme with image data to visualize the encryption performance. The complementary cumulative distribution functions (CCDFs) of PAPRs for the original and encrypted data are shown in Fig. 4.
Figure 4.Performance of PAPR for (a) original image data and (b) three-layer encrypted data under different conditions.
The PAPR decreases along with the auto-correlation coefficient of the input data reduction before the N-IFFT operation[
Figure 5.BER curves of normal and illegal receiver for (a) original image data and (b) three-layer encrypted data.
It can be further verified that our scheme can be used in UWOC with high confidentiality and solid BER performance. Figure 5 shows BER curves and constellation diagrams of the original image and the encrypted data. The legal receiver can correctly recover the data using the correct private key. In contrast, illegal receivers always obtain a BER of about 0.5 and cannot decrypt the message, even if they obtain most of the correct key, with only a slight difference of from of key1. In the case of BFAs, the attacker receives an annulary distributed constellation since the chaotic DFT has the effect of phase encryption, as in Fig. 5(a), which perceives the encryption operation in the UWOC link. In general, the attacker utilizes all possible methods to restore the normal constellation diagram. However, the proposed UWOC system is still highly secure with multiple chaotic encryptions because they cannot easily detect the encryption operations in the bit stream, QAM, and time-frequency domain.
The randomness of chaotic systems and their high sensitivity to initial conditions are the basis of our encryption algorithm. Multiple hyperchaotic mappings can create a larger key space and increase the difficulty for attackers to crack. According to the Institute of Electrical and Electronics Engineers (IEEE) floating-point standard[
It is worth noting that two-layer encryption without diffusion has a better BER performance than three-layer encryption in Fig. 5(b). Owing to the XOR operation in the diffusion, which associates the front and back plaintexts, noise accumulation will happen when the ciphertext is decrypted. However, diffusion encryption can generate dynamic ciphertexts to resist the most threatening and aggressive CPAs, so the performance penalty is acceptable. In this paper, to obtain higher information security and ensure transmission performance, chaotic DFT precoding is adopted to compensate for the loss, even improving the reception sensitivity by about 1 dB.
To verify the anti-CPA ability of our encryption system, we give the variations of the ciphertext when changing 1 bit of the plaintext, as shown in Fig. 6. The 10th bit of the original binary plaintext has been changed in Fig. 6(a). Figure 6(b) indicates great difference between the new ciphertext obtained after the corresponding plaintext change and the original one in the same OFDM subcarrier, implying that the plaintext information has been sufficiently spread out to nearly all the data during the ciphertext generation process in the OFDM-based UWOC system. For clarity, Fig. 6(b) only shows the difference of ciphertext change on the first 60 OFDM subcarriers. Consequently, the proposed encryption system can mix up the relationship between the original data and the ciphertext to resist CPAs.
Figure 6.(a) Change 1 bit in plaintexts. (b) The difference of ciphertext change on the first 60 OFDM subcarriers.
In this Letter, we have proposed a security-enhanced OFDM scheme for UWOC using three-layer chaotic encryption and chaotic DFT precoding. Although there is a trade-off between security and system complexity, the experiment in this paper validates the transmission performance and feasibility of this scheme, which is also an additional way to achieve UWOC secure transmission. The three-layer encryption operations of OFDM symbols are diffusion, IQ encryption, and time-frequency scrambling in turn. Finally, chaotic DFT precoding compensates for BER deterioration, and the key space reaches . Our encryption system can resist BFAs, statistical attacks, and CPAs, which has great potential for UWOC systems in the future with higher security requirements.
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 . Standard for binary floating-point arithmetic(1985).
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