Advanced Cryptography Using Nanoantennas in Wireless Communication

Abstract

This work presents an end-to-end encryption–decryption framework for securing electromagnetic signals processed through a nanoantenna. The system integrates amplitude normalization, uniform quantization, and Reed–Solomon forward error correction with key establishment via ECDH and bitwise XOR encryption. Two signal types were evaluated: a synthetic Gaussian pulse and a synthetic voice waveform, representing low- and high-entropy data, respectively. For the Gaussian signal, reconstruction achieved an RMSE = 11.42, MAE = 0.86, PSNR = 26.97 dB, and Pearson’s correlation coefficient = 0.8887. The voice signal exhibited elevated error metrics, with an RMSE = 15.13, MAE = 2.52, PSNR = 24.54 dB, and Pearson correlation = 0.8062, yet maintained adequate fidelity. Entropy analysis indicated minimal changes between the original signal and the reconstructed signal. Furthermore, avalanche testing confirmed strong key sensitivity, with single-bit changes in the key altering approximately 50% of the ciphertext bits. The findings indicate that the proposed pipeline ensures high reconstruction quality with lightweight encryption, rendering it suitable for environments with limited computational resources.

1. Introduction

In recent decades, wireless communication technology has made significant strides, while nanotechnology and nanoscience have captured remarkable attention. These fields have become some of the most compelling areas of modern technology, paving the way for innovative solutions across diverse sectors such as energy, information technology, defense, and industry [1].

The 4G mobile system’s era has transformed the way we communicate, bringing a vast array of new features to our fingertips, such as email, text messaging, Wi-Fi connectivity, and even home and car security [2]. Moving forward, 5G technology aims to achieve speeds up to 100 times faster and a 1000 times greater bandwidth to support an expanding array of applications for future devices [2]. The increasing demand for devices that consume large amounts of bandwidth and require higher data rates and lower latency has prompted researchers to begin designing the vision for 6G networks [3].

Among these technological advances, nanoantennas, also known as optical antennas, emerge as promising and practical structures with the potential to revolutionize wireless communication. Their small size relative to the wavelength of optical signals allows nanoantennas to play a crucial role as signal emitters and receivers [1]. The utilization of the surface plasmon polariton (SPP) enhancement mechanism is a pivotal aspect of their approach, as it leads to a substantial augmentation in the intensity of the electromagnetic field at the interface between nanoantennas and surrounding media. This, in turn, results in a notable improvement in signal transmission efficiency. However, while beneficial in improving signal strength, this mechanism also exposes nanoantennas to vulnerabilities such as eavesdropping and signal interception, making them susceptible to security breaches in sensitive communication systems [1].

Consequently, the focal point of this project is the analysis of the signals transmitted by nanoantennas and the exploration of their intrinsic vulnerabilities, with a particular emphasis on those stemming from the SPP mechanism. The objective of this research is to develop and evaluate cryptographic protocols that effectively integrate with the physical properties of nanoantennas. The present study will assess the impact of these protocols on communication efficiency and performance by drawing on prior studies in cryptography applied to electromagnetic signals. These prior studies have shown promising results in securing wireless communications.

This paper is structured as follows: Section 2 presents the principles of nanoantennas, approaches security in wireless communication and presents the concept of cryptography and the different kinds of methods to enhance security through cryptography. Section 3 provides a comprehensive review of related works, highlighting key advancements in these domain. Section 4 describes the experimental setup and simulation methodology employed to evaluate the system’s performance with both Gaussian and voice input signals. Section 5 presents and analyses the obtained results, focusing on reconstruction accuracy and robustness against distortions. Section 6 discusses the implications of these results, highlighting the framework’s strengths and limitations. Finally, Section 7 draws the main conclusions and outlines directions for future work.

2. Background

2.1. Nanoantennas in Wireless Communications

Antennas are critical components in wireless information transmission technologies, serving as devices that convert electric and magnetic currents into electromagnetic waves and vice versa [4]. The development of nanoantennas is the result of the emergence of nano-optics, which focuses on the transmission and reception of optical signals at the nanometer level [5]. These antennas, typically made from gold or silver nanoparticles, are designed to resemble traditional Radio-Frequency (RF) antenna structures but operate on a much smaller scale, often much smaller than the wavelength of the incident light [6].

Nanoantennas are based on the principles of electromagnetic theory, described by Maxwell’s equations in their macroscopic and microscopic forms [7]. In 1998, Ebbesen demonstrated that metallic nanostructured arrays exhibited radiation spectra with intensities higher than those predicted by classical theories, describing this phenomena as Extraordinary Optical Transmission (EOT). In the same study, Ebbesen identified Surface Plasmonic Polaritons (SPPs) as the primary contributors to this effect [8].

Nanoantennas work by exciting SPPs, which are collective oscillations of free electrons at the interface between a metal and a dielectric material when interacting with electromagnetic radiation [8]. When light or any other electromagnetic signal is applied to a nanoantenna, it can be converted into an SPP wave that propagates along the metal–dielectric interface before being lost due to absorption in the metal or radiation into free space, as shown in Figure 1.

In a material with permittivity, $\epsilon$, permeability, $\mu$, and no external sources, the behavior of electromagnetic waves can be described by the wave equation for the electric field [10]:

$${\nabla }^2\mathbf{E}-{\displaystyle \frac{\epsilon }{c^2}}{\displaystyle \frac{{\partial }^2\mathbf{E}}{\partial t^2}}=0,$$

(1)

where ${\nabla }^2$ is the Laplace operator, representing the spatial variation of the field, $\mathbf{E}$ is the electric field vector, $\epsilon$ is the permittivity of the material, c is the speed of light in vacuum, and ${\displaystyle \frac{{\partial }^2\mathbf{E}}{\partial t^2}}$ is the second partial derivative of the electric field with respect to time [10].

The efficiency of this conversion depends directly on the resonant frequency of the nanoantenna and its geometric properties, including size, shape, and material composition [11].

The excitation of an SPP requires a matching of the wave vector of the incident electromagnetic wave to that of the plasmonic wave [11]. This matching condition is governed by the dispersion relation of the SPP at the metal–dielectric interface.

For a metal–dielectric interface, the dispersion relation of the SPP is given by Equation (2):

$$k_{\mathrm{SPP}}={\displaystyle \frac{\omega }{c}}\sqrt{{\displaystyle \frac{{ϵ}_{\mathrm{m}}{ϵ}_{\mathrm{d}}}{{ϵ}_{\mathrm{m}}+{ϵ}_{\mathrm{d}}}}},$$

(2)

where $k_{\mathrm{SPP}}$ is the wave vector of the surface plasmon, $\omega$ is the angular frequency of the incident light, c is the speed of light in vacuum, ${ϵ}_{\mathrm{m}}$ is the permittivity of the metal, and ${ϵ}_{\mathrm{d}}$ is the permittivity of the dielectric [11].

The amplification phenomenon occurs because SPPs generate highly localized electric and magnetic fields with energy densities much higher than that of the incident field [12]. The concentration of this energy at the nanoscale leads to an increase in the intensity of the transmitted signal, which is particularly useful in applications requiring signal transmission or processing over very short distances or at nanoscale dimensions [12].

Field enhancement by SPPs is a key feature exploited in plasmonic applications, enabling efficient energy transfer [13]. This phenomenon can be described by the field distribution in the near-field region of the surface plasmon. The field near the surface of a thin metal film can be approximated as in Equation (3):

$$E(x,z)=E_0\exp (-\kappa z)\cos \left(k_{\mathrm{SPP}}x\right),$$

(3)

where $E(x,z)$ is the electric field, $E_0$ is the field amplitude at the surface, $\kappa$ is the decay constant in the dielectric, and x and z are the spatial coordinates along the interface and perpendicular to the surface, respectively [13].

The interaction of light with nanoantennas can be tuned to amplify signals at specific frequencies [6]. This frequency-selective amplification is a powerful feature for communications applications, where frequency modulation is essential for data encoding and transmission [6]. By controlling the plasmonic resonance of the nanoantennas, it is possible to amplify signals at specific wavelengths, enabling higher bandwidth and more efficient communication networks. This capability makes nanoantennas particularly promising for use in high-capacity communication networks where signal amplification and wavelength tuning are critical [6]. This amplification goes beyond simply increasing signal intensity as it can also involve manipulation of other signal properties such as phase and polarization.

2.2. Security in Wireless Communication

As wireless technologies become increasingly integrated into a wide range of activities, including personal communications and vital industrial operations, the security of these networks becomes a critical concern [14]. In this context, there are areas that are of particular importance including Physical Layer Security (PLS) approaches, the identification of threats and vulnerabilities specific to wireless networks, and antenna-based security measures.

2.3. Criptography in Eletromagnetic Signals

As wireless communications take place using radio frequencies, the risk of interception is greater than that with wired networks [15]. If a message is not protected or encrypted, an eventual attacker can read it, thereby compromising confidentiality [15].

Cryptography is the method of transforming data into an unreadable format so that only the authorized recipient can understand and be able to decode it [16].

This work aims to study two categories of cryptography: public key cryptography and secret key cryptography.

2.3.1. Public Key Encryption

Public key cryptography, also known as asymmetric cryptography, uses a pair of keys for each user involved in the communication process [17]. This two-key system consists of a public key and a private key. The public key is openly shared with anyone, while the private key is kept confidential and not disclosed to others [18].

In this system, when someone wants to send a secure message, they encrypt it using the recipient’s public key [17]. This key is accessible to everyone but is designed in such a way that the encrypted message can only be decrypted by the corresponding private key, which only the recipient possesses [17]. Upon receiving the encrypted message, the recipient uses their private key to decrypt the message and convert it back into its original, readable format [17]. The described concept is shown in Figure 2.

2.3.2. Secret Key Encryption

Secret key cryptography concept employs a single secret key for both the encryption and decryption processes [18]. In this methodology, the sender encrypts the data using an exclusive key, thereby converting it into an encoded format that is not easily interpretable [18]. Similarly, the recipient utilizes the same key to decrypt the information, thus restoring it to its original, intelligible form [18], as represented by Figure 3.

This process is commonly referred to as symmetric encryption, and despite its simplicity, it shows a massive vulnerability related to the key’s management [19]. The necessity for the sender and recipient to share the same key introduces substantial security risks [18]. In the event that the key is mishandled or intercepted, it has the potential to result in unauthorized access and potential misuse, thereby significantly compromising the security of the data [19].

3. Related Work

3.1. Electromagnetic Analysis for Cryptography

The author Gunathilake and his collaborators in [20], established the importance of lightweight cryptography in Internet of Things devices, which are limited by their processing power, memory, and energy consumption. The study posits the vulnerability of these devices to side-channel attacks due to physical leakages. It introduces the cipher “PRESENT” as a potential solution, with its small block and key sizes designed for efficiency in constrained environments [20].

The EM emissions from the PRESENT cipher are analyzed to assess its vulnerability to side-channel attacks, specifically through electromagnetic analysis. The author delineates the methodological framework and the practical implementation of capturing electromagnetic emissions from the cipher during its operation to detect potential data leakages. Through the use of mathematical models, Hamming weight and distance, to hypothesize potential information leakage and conducting two types of EM analysis, Simple Electromagnetic Analysis and Correlation Electromagnetic Analysis, in the time and frequency domains obtained, EM analysis can effectively identify potential leakages in cryptographic implementations like the PRESENT cipher [20].

The observations encompass variations in the electromagnetic field strength during distinct cipher operations, which may be indicative of varying internal states of the cipher [20]. Moreover, the observations accentuate particular instances where the EM emissions exhibit a robust correlation with theoretical predictions of data leakage, thereby suggesting the potential for the extraction of sensitive information [20].

3.2. Elevating Security Using ECC and Advanced Encryption Standard (AES) Algorithms

ECC is a notable instrument in the repertoire of cryptographic techniques suitable for wireless sensor networks. Fundamentally, ECC utilizes the algebraic properties of elliptic curves over finite fields to offer robust security with relatively brief key lengths [21]. The AES is a foundational component in the field of symmetric key encryption, playing a pivotal role in ensuring the security of data across a wide range of domains. In contrast to ECC, the AES utilizes a shared secret key for both the encryption and decryption processes, thereby enhancing computational efficiency [21].

Dayana et al. [21] proposed a system that combines both cryptographic techniques. In this system, ECC generates a pair of keys a private key and a public key. For symmetric encryption, an AES key is generated. The model was tested by firstly encrypt the “Sample” data using the AES. After the first step, an ECC signature is then generated using the private key and the concatenated message of the “Sample” data and the AES-encrypted data, to ensure both the integrity and authenticity of the data. Upon receiving the encrypted data, the recipient separates the AES-encrypted data and ECC signature. The ECC signature is verified using the ECC public key, and if valid, the AES algorithm will decrypt data to retrieve the original data.

The results of the model proposed by Dayana and his collaborators achieved an Authentication Success Rate of 96%, outperforming ECC and the AES separately. Another metric of performance evaluated was the Data Confidentiality Verification Rate, in which the method of ECC+AES obtained a very high effectiveness, as shown in Figure 4.

4. Proposed Model

In this work, we propose a multi-stage framework aimed at enhancing the security of wireless communications by leveraging nanoantenna technology combined with cryptographic techniques. The proposed system architecture is composed of four sequential blocks, each contributing to the secure transmission and reconstruction of the electromagnetic signal:

• Block 1—Nanoantenna Response Characterization:
  The process initiates with the design and full-wave modeling of a nanoantenna, developed from fundamental principles. The structure is used to amplify the signal transmitted.
• Block 2—Signal Quantization and Error Correction:
  The electromagnetic response at the output of the nanoantenna is captured, normalized, and quantized, resulting in a digital bitstream. Subsequently, the stream undergoes processing by an error correction module that is based on Reed–Solomon (255,223) coding. This coding provides resilience against transmission errors.
• Block 3—Key Generation and Bitwise Encryption:
  Symmetric key generation is performed using the ECDH (Elliptic Curve Diffie–Hellman) protocol, followed by a bit-by-bit encryption process using the XOR operation. The derived key is then applied cyclically to the data sequence, thereby ensuring the confidentiality of the transmitted signal.
• Block 4—Decryption and Signal Recovery:
  The signal is decrypted by applying the XOR operation again with the same symmetric key, which allows the original data stream to be recovered. Subsequently to decryption, the signal undergoes reconstruction through the inversion of quantization and normalization, thereby restoring the original continuous signal.

4.1. Block 1—Nanoantenna Response Characterization

The nanoantenna concept outlined in this study was developed and simulated using professional EM simulation software. The structure consists of a rectangular metallic film made of gold (Au) deposited on a dielectric substrate and patterned with a periodic square array of sub-wavelength apertures. The thickness of the dielectric and metallic layers is 100 nm.

The array, as shown in Figure 5, is composed of $3\times 6$ square apertures, each with the side length $\lambda /9=88.89\mathrm{nm}$, where $\lambda =800\mathrm{nm}$ corresponds to the central design wavelength. The apertures are spaced by the same distance ($\lambda /9$) in both the x and z directions, ensuring periodicity and enabling strong surface plasmon polariton (SPP) excitation in optical range, namely in visible spectral region. The total length of the nanoantenna structure is $L=1\mathsf{\mu }\mathrm{m}$.

The nanoantenna block is designed to amplify and concentrate the signal to be transmitted. Prior to integration into the communication pipeline, a detailed electromagnetic analysis is conducted to evaluate the spatial distribution of the electric field on a predefined observation plane. The aim of this evaluation is to identify the precise spatial location at which the electric field exhibits its maximum amplitude response and the frequency at which this peak occurs.

By isolating this optimal point, which corresponds to the maximum local field enhancement, it becomes possible to characterize the nanoantenna’s behaviour with high fidelity. In particular, the transfer function of the antenna is computed exclusively at this spatial location, thereby capturing the frequency-dependent transformation that an input signal undergoes as it propagates through the nanoantenna.

Following this amplification and transfer function evaluation, the output signal at the selected point is subjected to a normalization and quantization process.

In order to facilitate comprehension of the proposed structural design, please refer to

Table 1. Geometric and material parameters used in the nanoantenna design.

Name	Value	Unit	Description
E	$1\times {10}^{-7}$	m	Metal thickness
$subs$	$1\times {10}^{-7}$	m	Dielectric thickness
$\lambda$	$8\times {10}^{-7}$	m	Design wavelength
L	$1\times {10}^{-6}$	m	Total length of structure
$hole\text{\_}l$	$8.8889\times {10}^{-8}$	m	Side length of apertures
$dist$	$8.8889\times {10}^{-8}$	m	Spacing between apertures
$W_b$	$8.8889\times {10}^{-8}$	m	Aperture width
$num\text{\_}h\text{\_}x$	3	–	Number of apertures along x
$num\text{\_}h\text{\_}z$	6	–	Number of apertures along z

, which delineates the parameters that have been stipulated to guide the conceptualization and design of the nanoantenna.

4.2. Block 2—Signal Quantization and Error Correction

Subsequently to the normalization of the filtered signal to the interval [0, 1], the signal undergoes uniform quantization into 8-bit unsigned integers, resulting in 256 discrete amplitude levels. Each quantized sample is then decomposed into its binary representation using a most significant-bit first-order, producing a binary stream suitable for digital encoding. This binary stream is segmented into contiguous blocks of 8 bits and reassembled into bytes, forming the data payload to be protected against transmission errors. To ensure robustness and reliability, a Reed—Solomon (255,223) error correction code is applied. This encoded bitstream serves as the foundation for subsequent secure transmission.

4.3. Block 3—Key Generation and Bitwise Encryption

In this stage, the system establishes a secure encryption key using the Elliptic Curve Diffie–Hellman (ECDH) protocol, which offers strong security with relatively low computational overhead, making it suitable for lightweight communication systems.

4.3.1. Key Generation with ECDH

The process commences with both communicating entities independently generating their private keys, each being a large random integer selected securely. In the proposed implementation, the secp256r1 elliptic curve is utilized, also known as NIST P-256, as it is a widely adopted cryptographic standard due to its optimal balance of performance and security.

Each private key, $d\in [1,n-1]$, where n is the order of the base point G, is used to compute a public key through scalar multiplication:

$$Q=d·G$$

where Q is the public key (a point on the curve), d is the private key, and G is the base point defined by the elliptic curve parameters.

After exchanging the public keys $Q_A$ and $Q_B$, both parties compute a common shared secret point using scalar multiplication:

$$K_A=d_A·Q_B\mathrm{and}{K}_B=d_B·Q_A$$

Due to the commutative property of scalar multiplication over elliptic curves, both $K_A$ and $K_B$ yield the same point, K, which constitutes the shared secret. From the shared point $K=(x,y)$, only the x-coordinate is used to derive a symmetric key. The coordinate is encoded as a byte array and passed through the SHA-256 hash function:

$$\mathrm{key}\text{\_}\mathrm{raw}=\mathrm{SHA}\text{-}256\left(x\right)$$

The output is a 256-bit digest, from which the first 128 bits are selected to form the symmetric encryption key:

$$\mathrm{shared}\text{\_}\mathrm{key}=\mathrm{key}\text{\_}\mathrm{raw}[1:16]$$

This ensures that the final key is both cryptographically secure and compatible with lightweight symmetric encryption schemes.

4.3.2. Bitwise XOR Encryption

The process of deriving a symmetric encryption key via the ECDH protocol and subsequent SHA-256 hashing is followed by the application of a lightweight encryption procedure based on the bitwise XOR operation to the encoded data. This stage aims to ensure the confidentiality of the transmitted signal with minimal computational overhead, thereby ensuring its suitability for nanoantenna systems.

Let the decoded byte stream from the previous error correction stage be denoted as

$$\mathbf{D}=\{d_1,d_2,\dots ,d_n\},d_i\in \{0,1,\dots ,255\}$$

and let the derived symmetric key be

$$\mathbf{K}=\{k_1,k_2,\dots ,k_{16}\},k_i\in \{0,1,\dots ,255\}$$

where $\mathbf{K}$ is a 128-bit key obtained from the SHA-256 hash of the shared elliptic curve point.

To apply encryption, the key $\mathbf{K}$ is repeated cyclically to match the length n of the data stream. This results in a derived keystream:

$${\mathbf{K}}^{*}=\{k_1,\dots ,k_{16},k_1,\dots ,k_r\},\mathrm{with}r=nmod16$$

The encryption is then performed bytewise using the bitwise XOR operation:

$$\mathbf{C}=\{c_1,c_2,\dots ,c_n\},\mathrm{where}{c}_i=d_i\oplus k_i^{*}$$

The XOR operation, denoted by ⊕, is a fundamental binary operation defined as

$$a\oplus b=\left\{\begin{array}{cc}0,\hfill & \mathrm{if}a=b\hfill \\ 1,\hfill & \mathrm{if}a\ne b\hfill \end{array}\right.$$

This operation ensures that each ciphertext byte, $c_i$, encapsulates the difference between the original data byte $d_i$ and the corresponding key byte $k_i^{*}$.

The resulting ciphertext $\mathbf{C}$ is then transmitted or stored and can be decrypted by any authorized receiver in possession of the same shared key.

4.4. Block 4—Decryption and Signal Recovery

Upon reception of the encrypted data stream, the system initiates the decryption process by regenerating the same symmetric key that was used for encryption.

This objective is accomplished by reapplication of the ECDH key agreement protocol, a process which ensures that both communicating entities, having exchanged public keys and retained their private keys, independently derive the same shared secret point. The symmetry of this process ensures that no additional information exchange is required for key regeneration at the receiver.

Because the XOR operation is its own inverse, applying it again with the same key reverses the encryption:

$$\mathrm{original}\text{\_}\mathrm{byte}=\mathrm{ciphertext}\text{\_}\mathrm{byte}\oplus \mathrm{key}\text{\_}\mathrm{byte}$$

This process enables the receiver to fully restore the protected byte stream to its pre-encryption state.

The recovered byte stream is then converted back to its binary representation by decomposing each byte into a sequence of eight individual bits. These components are then reshaped into a matrix that maintains the same structure used during the quantization stage. This ensures that the digital formatting process is accurately reversed.

Subsequently, the system reconstructs the original quantized signal levels by interpreting each group of eight bits as an unsigned eight-bit integer. These values correspond to discrete quantization levels in the range of 0 to 255, as originally obtained from the uniform quantizer. To recover the continuous-time analog signal, the quantized values are mapped back into their original amplitude range using the inverse of the normalization transformation.

The final result is a time-domain signal that approximates the original waveform as it was after propagation through the nanoantenna.

5. Results

The initial objective was to ascertain the spatial point at which the electric field attained its maximum amplitude, as this location was considered the most indicative of the nanoantenna’s peak electromagnetic response.

To identify the point of maximum electric field intensity, a frequency sweep ranging from 0.1 to 3 THz was conducted. For each frequency, the total field amplitude was reconstructed from the complex components $E_x$, $E_y$, and $E_z$.

The maximum value across all frequencies was identified, and the corresponding spatial coordinates were extracted, as shown in Figure 6. This particular point, where the electric field reached its maximum, was selected for subsequent transfer function analysis. This selection was made on the basis that it represented the location of the most significant field enhancement near the nanoantenna.

Subsequently to the identification of the point of maximum electric field intensity, it was necessary to characterize the nanoantenna’s frequency response at that specific location.

This objective was accomplished by calculating the transfer function, defined as the projection of the complex electric field vector onto the direction of the incident wave, across the frequency range of interest. The resulting complex response was then normalized and decomposed into magnitude and phase components.

The parameters in the fitted transfer function

$$H\left(f\right)\approx \left(a{e}^{-bf}+c\right)·e^{j(mf+b_{\varphi })}$$

were obtained by fitting the simulated transfer function $H\left(f\right)$, computed from the projection of the complex electric field vector at the location of maximum total energy onto the normalized incident field direction, to simple analytical models for magnitude and phase.

The magnitude $\left|H\right(f\left)\right|$ was fitted to an exponential decay model, $a{e}^{-bf}+c$, by minimizing the sum of squared residuals. The unwrapped phase was fitted to a linear model, $mf+b_{\varphi }$, using least-squares linear regression. This procedure yielded the parameters reported above, and the group delay was calculated as ${\tau }_g=-m/\left(2\pi \right)$.

In order to facilitate its use in analytical models, the fitted transfer function was expressed in closed form as

$$H\left(f\right)\approx \left(1.6063·e^{-0.0768f}+0.0431\right)·e^{j(-0.0628f-0.6555)}$$

where the magnitude is represented by an exponential decay function and the phase by a linear trend. This formulation allowed the extraction of key parameters such as the group delay, which was found to be ${\tau }_g\approx 9.9999\mathrm{ps}$.

5.1. Nanoantenna Response to Signals

After obtaining the transfer function $H\left(f\right)$, the temporal response of the nanoantenna to incident signals was investigated.

As an initial test case, a Gaussian pulse was selected due to its simplicity and well-defined spectral content. The input signal was transformed into the frequency domain via FFT, and the previously computed $H\left(f\right)$ at the point of maximum response was applied as a frequency-domain filter. The resulting spectrum was then transformed back to the time domain using IFFT, allowing observation, shown in Figure 7, of the antenna-induced distortion on the temporal waveform. This procedure validated the expected system behavior and served as a foundation for future analysis involving more complex signal structures.

After the initial validation using a Gaussian pulse, we proceeded to evaluate the response of the nanoantenna to a more realistic and complex signal. This signal was generated as amplitude-modulated white noise to emulate the spectral and temporal dynamics of human speech.

By mapping the audio frequencies into the antenna’s operating band and applying the transfer function $H\left(f\right)$ in the frequency domain, was obtained the output signal corresponding to the antenna’s response, as shown in Figure 8.

The result, converted back to the time domain, provided insight into the distortion and filtering effects induced by the nanoantenna when processing real-world signals.

5.2. Proposed Cryptography Model Test

Subsequently to an analysis of the antenna’s impulse response to a Gaussian pulse, a comprehensive encryption and decryption pipeline for the output signal was developed, incorporating the previously proposed model.

A quantitative analysis was conducted to evaluate the performance of the proposed pipeline when applied to the Gaussian input signal and the voice signal. This analysis was based on widely used signal quality and security metrics. The objective of this assessment was to characterize the system’s reconstruction fidelity and cryptographic robustness. The metrics considered for the analysis included the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Peak Signal-to-Noise Ratio (PSNR), Pearson correlation coefficient, signal entropy, and avalanche effect.

Figure 9 illustrates a segment of the Gaussian input signal and its corresponding encrypted version, restricted to the first 50 bytes for visual clarity.

Subsequently to the encryption process, the Gaussian input signal underwent a decryption process. Figure 10 contains the result after the decryption of the first 50 bytes.

Following the decryption process, the Gaussian input signal was recovered. Figure 11 and Figure 12 shows a comparison between the original quantized signal that was amplified by the nanoantenna and the signal that was recovered at the receiver end, respectively.

The results confirm a very high reconstruction fidelity, with an RMSE of 11.4235, MAE of 0.8574, and PSNR of 26.97 dB. The Pearson correlation coefficient between the original quantized signal and the reconstructed signal reached 0.9087, indicating a strong linear relationship.

The entropy values of the original and reconstructed signals were 2.4746 and 2.5292, respectively, suggesting that the statistical distribution of the signal values was well preserved. From a security perspective, the avalanche effect for a single-bit change in the key was 0.5052, which is close to the ideal value of 0.5.

After the encryption and reconstruction stages with the Gaussian test pulse, the full processing chain was applied to a synthetic voice signal, providing a more complex and realistic evaluation scenario.

Figure 13 illustrates the encryption process for the first 50 bytes of the quantized voice signal, highlighting the transformation from the original digital representation into its encrypted form.

The subsequent decryption process restored the encrypted bytes back to their original digital values. This result is shown in Figure 14, which depicts the decrypted output for the same 50 byte segment.

The complete reconstruction of the synthetic voice signal at the receiver end is presented in Figure 15 and Figure 16. Figure 15 displays the original quantized signal after nanoantenna amplification, while Figure 16 shows the corresponding signal reconstructed after transmission, encryption, and decryption.

The comparison between the original and reconstructed voice signals, alongside the quantitative metrics described earlier, provides an effective measure of both the signal fidelity and the robustness of the proposed cryptographic framework in handling more complex, time-varying inputs.

The results confirm a high reconstruction fidelity, with an RMSE of 15.1256, MAE of 2.5213, and PSNR of 24.54 dB. The Pearson correlation coefficient between the original quantized signal and the reconstructed signal reached 0.8062, indicating a strong linear relationship.

The entropy values of the original and reconstructed signals were 4.5371 and 3.9869, respectively, suggesting that the statistical distribution of the signal values was reasonably preserved. From a security perspective, the avalanche effect for a single-bit change in the key was 0.4992, which is close to the ideal value of 0.5.

The results obtained are summarized in

Table 2. Summary of results of the proposed model under two different signals.

	Gaussian Signal	Voice Signal
RMSE	11.4235	15.1256
MAE	0.8574	2.5213
PSNR	26.97 dB	24.54 dB
Pearson Correlation Coefficient	0.8887	0.8062
Entropy (Original Signal)	2.4746	4.5371
Entropy (Reconstructed Signal)	2.5292	3.9869
Avalanche effect (1-bit change)	0.5052	0.4992

, providing a comprehensive overview of the pipeline behavior under two different scenarios.

6. Discussion

As demonstrated in Table 2, the proposed model exhibited a high degree of reconstruction fidelity for both test signals. For the Gaussian signal, the RMSE of 11.4235 and MAE of 0.8574 were lower than those obtained for the voice signal, 15.1256 and 2.5213, respectively, indicating a more accurate reconstruction in the Gaussian case. This behavior was consistent with the lower complexity and higher regularity of the Gaussian waveform, which facilitated the preservation of its structure through the processing pipeline.

The PSNR values demonstrated a similar trend, with 26.97 dB for the Gaussian signal and 24.54 dB for the voice signal, thereby confirming that the Gaussian reconstruction retained a higher signal-to-distortion ratio. In a similar vein, the Pearson correlation coefficient exhibited a higher value for the Gaussian signal compared to the voice signal, thereby further underscoring a more pronounced linear relationship between the original and reconstructed versions in the more straightforward test case.

Entropy analysis revealed divergent behaviors between the two signals. In the case of the Gaussian model, the entropy of the reconstructed signal marginally exceeded that of the original signal. This finding suggests that the minor variations introduced during the processing stage contributed to a more uniform distribution of values.

On the other hand, for the voice signal, the entropy decreased from 4.5371 to 3.9869 after reconstruction, indicating a reduction in statistical variability. This is likely attributable to the impact of quantization and residual reconstruction errors on a signal with higher complexity.

The avalanche effect for a single-bit key change was close to the ideal value of 0.5 for both case, indicating that key perturbations consistently produced widespread changes in the encrypted data, regardless of the signal type.

7. Conclusions

This work presents an end-to-end encryption–decryption framework for the protection of electromagnetic signals, integrating physical-layer processing and lightweight cryptographic mechanisms. The model operates subsequently to signal processing through a nanoantenna, the transfer function of which is obtained from its response to a Gaussian excitation.

The pipeline incorporates a series of data processing steps, including amplitude normalization, uniform quantization, bitstream formatting, and Reed–Solomon forward error correction. These techniques are employed to ensure the pipeline’s resilience against bit-level errors. The establishment of a secure session key is achieved through the use of ECDH, which is then employed to generate a keystream for bitwise XOR encryption. This approach ensures low computational cost while maintaining compatibility with high-data-rate processing.

The validation process entailed the use of a synthetic Gaussian pulse and a synthetic voice waveform, with the former representing low-entropy signals and the latter representing high-entropy signals. The Gaussian reconstruction achieved a lower RMSE and MAE, higher PSNR, and stronger Pearson correlation coefficient, reflecting its simpler structure and lower susceptibility to quantization loss. The voice signal exhibited elevated reconstruction errors; nevertheless, it demonstrated acceptable PSNR and correlation, thereby confirming preserved fidelity despite the augmented complexity.

Entropy analysis revealed a marginal increase for the reconstructed Gaussian signal, indicating processing-induced uniformity, while the voice signal entropy exhibited a decrease, presumably attributable to quantization and residual reconstruction errors. Avalanche testing confirmed that single-bit changes to the encryption key affected approximately 50% of ciphertext bits, indicating strong key sensitivity.

The pipeline exhibited high reconstruction fidelity, predictable performance, and robust key sensitivity, rendering it suitable for scenarios necessitating lightweight encryption with minimal computational overhead. However, reliance on a static key and a non-secure pseudorandom generator remains a limitation for deployment in adversarial environments.