1.1. Problem formulation

The traditional PC-based encryption solutions need many resources, and they are unsuitable for IoT devices with limited resources. A simplified version of conventional methods might be used to overcome these obstacles and provide secure communication in IoT devices with constrained resources and lightweight cryptography. The following are the main problems in integrating traditional cryptography in IoT devices, as shown in Fig 2 [4]. Classic cryptographic algorithms such as AES, DES, and RSA are not optimal for constrained devices due to their computational expense, larger memory requirements, and energy inefficiency. Lightweight cryptographic primitives consume reduced power, such as PRESENT and LED block ciphers, along with SPONGENT and PHOTON lightweight hash functions, serve as two exemplars. They have incorporated permutation layers, modify S-boxes, and implement padding techniques, all of which require supplementary memory and computing capacity. For instance, even lightweight block ciphers must undergo multiple rounds of substitution and permutation. This indicates that they are ineffective for real-time data encryption on resource-constrained sensor nodes. Lightweight hash-based techniques for authentication and key derivation are effective for data protection and integrity verification; however, they are suboptimal for rapid symmetric encryption and efficient keystream generation during streaming. Conversely, stream ciphers operate exclusively on a single bit or byte at any given moment. This indicates that they can encrypt data rapidly and with minimal memory usage. This indicates their suitability for IoT applications that require minimal power, memory, or CPU resources and have low latency requirements.

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Fig 2. Key issues with traditional cryptography.

https://doi.org/10.1371/journal.pone.0330976.g002

Furthermore, existing lightweight cryptographic systems such as Trivium [5], MICKEY [6], and Grain series ciphers [7,8] are a few of the primary stream ciphers that may exhibit insufficient resistance to modern attack vectors or fail to achieve an acceptable balance between security and performance. Stream ciphers designed for resource-limited environments must provide low latency and minimal resource usage while preserving high unpredictability, nonlinearity, and cryptographic strength. Achieving this equilibrium remains difficult. A significant demand exists for lightweight encryption models that minimize computing complexity while incorporating robust diffusion, dynamic key evolution, and improved entropy. Over time, the decoding science has made significant progress, and it has now been shown that certain lightweight stream ciphers are dangerous [9]. Extensive key search attacks could be more effective against Grain v1. To address these challenges, there is a pressing need for a novel lightweight stream cipher architecture that:

• Ensures robust security through high nonlinearity, resistance to statistical and algebraic attacks, and strong keystream randomness.
• Operates efficiently on constrained IoT devices by minimizing computational overhead, memory usage, and energy consumption.
• Improves upon existing models such as Grain, Trivium, and other chaos-based designs by offering better entropy, faster encryption, and full NIST randomness compliance.
• Incorporates dynamic and adaptive cryptographic structures, such as chaotic maps and multiplexer-based nonlinear mixing, to enhance confusion and diffusion without compromising performance.

1.2. Contribution

This work integrates the nonlinear Feedback Shift Register (NLFSR), Linear Feedback Shift Register (LFSR), and the logistic chaos function to provide resistance against different kinds of attacks. Cryptographers are beginning to embrace chaotic cryptography as a revolutionary theory of cryptography. Chaotic cryptography is widely used in neural networks, economics, and secure communication [10,11]. However, only some studies have attempted to apply chaotic structures to lightweight cryptography. Researchers have been examining structurally modified chaotic maps to address the issues associated with the standard logistic map, including short periodicity in digital implementations and diminished Lyapunov exponents. The study referenced in [12] employs a multi-parameter hybrid chaotic map to enhance the sensitivity and reduce the unpredictability of image encryption. The research in [13] employed a Logistic-Sine connected system to enhance resistance against statistical attacks. This study deliberately selects the standard logistic map due to its minimal computational requirements, consistent parameter responses, and compatibility with LFSR and MUX logic. This is ideal for encrypting concise IoT SMS communications. The subsequent phase involves examining adaptive or hybrid chaotic systems to determine their potential to further enhance cryptography. In the past, many studies have been conducted on the integration of chaotic systems with stream ciphers. For instance, NLFSR Kumari & Mondal in [14], and Wang et al. [15]. The majority of existing research has focused on enhancing key sensitivity and fortifying PRNGs against attacks. Conversely, the LWLCM model is an adaptive amalgamation that optimizes resource utilization in response to its environment. It was specifically designed for IoT edge devices.

Using a thorough analysis of other lightweight stream ciphers, this work combines a chaotic system with NLFSR and LFSR to create a novel chaos-based lightweight stream cipher system supported by multiplexer units to introduce enhanced confusion and diffusion properties. Avalanche analysis and NIST procedures are applied to assess the lightweight stream cipher performance, being able to validate the encryption’s features. The results demonstrate the superior performance of the more straightforward encryption used here. LWLCM’s design is the same as that of Grain v1, including a multiplexer and logistic chaos as a logistic round module to increase security. The following have been highlighted as this paper’s main contributions:

• LWLCM is an innovative stream cipher that employs a chaotic pseudo-random number generator based on the Logistic Map to amalgamate NLFSR and LFSR for keystream generation. The chaotic component enhances nonlinearity and improves statistical unpredictability, distinguishing it from conventional PRNGs.
• Due to our modular architecture, we can conduct ablation experiments to evaluate the impact of each component on the quality of the keystream and the execution speed. This illustrates the significance of each component.
• This study highlights the enhancement of statistical security through Shannon entropy and the reduction of correlation coefficients, introducing a novel lightweight stream cipher, LWLCM, tailored for IoT environments.
• The main aim of this work is to produce extremely random ciphertexts with optimal unpredictability, thus enhancing resistance to statistical and linear attacks.
• Encryption is more resistant to attacks, such as linear and differential cryptanalysis, when complex non-linear Boolean functions that involve XOR, AND, and multiplexer operations are used. These functions improve the cipher’s security against sophisticated cryptanalytic techniques by adding a level of non-linearity and complexity that is challenging to reverse. With a maximum nonlinearity of 19, the filtering function is a symmetric Boolean computation with eight variables and seven orders.
• An extra degree of complexity and security is added by using multiplexers to regulate the selection of operations based on the state of particular bits. This design decision strengthens the cipher’s resistance to algebraic and fault attacks by making any straight linear approximation more difficult.
• Experimental analysis demonstrates that the proposed LWLCM cipher achieves its primary design objective, enhancing randomness and diminishing statistical correlation in ciphertext generation through efficiency. Across various plaintext sizes, LWLCM consistently produces entropy values near the optimal value of 8.0 and correlation coefficients nearing zero. These findings indicate that the cipher can yield significantly random and statistically independent outputs, which are essential indicators of robust encryption. The superior performance in statistical security measures justifies the trade-off, despite its encryption and decryption rates being somewhat higher than those of AES-256 and Trivium.

This paper is divided into several Sections. Section 2 includes the literature review, while Section 3 describes the design specification. The Design consideration is defined in Section 4. At the same time, the proposed work LWLCM model and algorithmic template, is discussed in Section 5. The results and discussion are covered in Section 6 with complete observation, followed by security analysis, which is covered in Section 7. The statistical test is shown in Section 8, and the limitations of the proposed work have been discussed in Section 9. Finally, the conclusion and future directions are covered in Section 10.

3.1. Components

The algorithm’s primary components are a Logistic round module, two 80-level FSRs, and four multiplexers. LWLCM is composed of 192 bits that are distributed over LFSR, NLFSR, and the Logistic round module. Both the registers LFSR and LFSR are specified over the Galois field (2⁸⁰), and the contents of both registers are designated by (p₀, p₁,..............,p₈₀) and (β₀, β₁..............,β₈₀) respectively, as illustrated in Fig 3 and the Logistic round module’s contents are designed by (f₀, f₁,.........,f₃₂) and updated by the logistic chaos function.

3.1.1. Logistic chaos function.

Cryptography has made extensive use of the chaos theory of nonlinear research. Chaotic systems offer beneficial cryptographic properties, including long-term unpredictability, pseudo-random behavior, and extreme sensitivity to initial conditions. These properties are connected to modern cryptography’s diffusion and confusing ideas [28]. An approach to chaotic digitization is proposed to address the problem of limited accuracy. Here is how to express the logistic chaotic map given in Equation 1.

(1)

The initial parameters, α and x₀, are variables to maintain uncertainty and security. Rather, they are generated dynamically during the initialization process as follows:

• Initial Seed . Generated using a portion of the secret key. Specifically, the ASCII values of the first few characters of the key are normalized to the range as:

(2)

where is the character of the key and is the key length.

• Logistic Parameter : Derived using a combination of IV and key entropy using:

(3)

This ensures that , maintaining chaotic behavior while introducing sensitivity to IV changes. Fig 4 shows that the chaotic map has more variability across the interval 3.6 ≤ α ≤ 4. However, we have to consider that digital degradation can significantly affect the performance of the logistic map, especially in digital systems where absolute numbers are represented with finite precision. Quantization and rounding errors are minor errors that can compound over iterations and cause deviations from the expected chaotic behavior; in specific scenarios, this degradation can result in a loss of chaos, where the system turns into less practical applications that require strong randomness, such as cryptography. Limited accuracy in mathematics can also result in overflow or underflow mistakes, which further ruins the chaotic structure of the logistic map [29]. Due to its high sensitivity to initial conditions, the map is especially susceptible to digital degradation, where even small adjustments can result in considerable differences in output. This decrease in randomness may jeopardize the logistic map’s security and efficacy in encryption applications, as small mistakes can propagate and amplify across iterations, decreasing the map’s practical dependability.

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Fig 4. Bifurcation diagram of logistic map.

https://doi.org/10.1371/journal.pone.0330976.g004

In the proposed LWLCM system, the chaotic parameters α and x₀ are neither stored nor transmitted across the communication channel. Both parameters are generated in real time on the receiver’s side, utilizing a shared secret key and an IV. The recipient can independently ascertain α and x₀, as the key and IV are provided in advance via a secure method for identification verification. This indicates they are not required to store or transmit these numbers in multiple locations. Attackers cannot recover α or x₀ without the secure key and IV, rendering it difficult for them to retrieve the parameters. This also reduces the volume of communication required, which is crucial in IoT environments where resources are limited.

3.1.2. LFSR.

An LFSR is a sequential shift register in which its previous state dictates a linear function of its feedback. Except for the first flip-flop, which receives input from a linear function based on the prior state, the configuration comprises a sequence of flip-flops, each receiving input determined by the output of its antecedent. XoR operations on designated bits of the register often fulfill the role. LFSRs have numerous benefits in cryptography and computing contexts because of their simplicity and efficiency, which are greatly valued. Possessing fewer logic gates than alternative pseudo-random number generators (PRNGs), they exhibit considerable efficiency for hardware implementations, characterized by diminished circuit complexity and lower power consumption. Fundamental XOR and shift operations enable LFSRs to perform swiftly, rendering them suitable for high-speed applications such as cryptographic stream ciphers like Grain-128a and Trivium. They effectively generate pseudo-random sequences, which are valuable for Monte Carlo simulations, data obfuscation, and cryptographic key creation. LFSRs, constructed from a fundamental polynomial, yield an extended periodic sequence before repetition, which is crucial for security applications because it generates a maximum-length sequence of 2^n-1. Their reduced processing demands render them more power-efficient than linear congruential generators among conventional pseudorandom number generators. Key components of stream ciphers, particularly A5/1 and A5/2, utilized in GSM encryption, comprise LFSRs. Frequently used alongside NLFSRs, they enhance security in lightweight cryptographic systems.

The 80-bit LFSR utilized in the proposed encryption is constructed with a primitive polynomial defined over the Galois field GF(2⁸⁰), which is used by Grain v1 given by Equation 2, ensuring a maximum period of 2⁸⁰−1, hence providing optimal periodicity and cryptographic strength. This guarantees that, to prevent predictability in the keystream, the LFSR state will not repeat until the entire cycle is finished. The taps employed are chosen based on recognized elementary polynomials documented in literature and cryptographic standards [30]. The primitive polynomial and state update function of the LFSR are illustrated by Equations 4 and 5.

(4)(5)

3.1.3. NLFSR.

NLFSR, a version of LFSR, utilizes non-linear feedback mechanisms rather than basic XOR-based linear processes, making it more robust against cryptanalysis. NLFSRs utilize AND, OR, and majority logic to incorporate non-linearity, unlike LFSRs that produce predictable sequences via linear recurrence relations, thus markedly improving security. NLFSRs are ideal for cryptographic applications, such as lightweight stream ciphers like Grain-128a and Trivium, because of their non-linearity, which enhances resistance to algebraic and correlation attacks. Improved statistical randomization and increased unpredictability ensure enhanced key generation and encryption security. The 80-bit NLFSR used in the proposed work enhances its resilience against correlation attacks through the use of several nonlinear tap functions and cross-product terms. While NLFSRs do not conventionally employ primitive polynomials, their nonlinear feedback functions are meticulously designed to augment nonlinearity and complexity, hence boosting the unpredictability and diffusion characteristics of the output keystream. The feedback polynomial used by NFSR, which has an 80-bit width, is a modified version of Grain [7]. The following is the update function of the NLFSR is given by Equation 6:

(6)

3.1.4. Multiplexer unit.

Cryptography utilizes a 2 × 1 multiplexer (MUX) to select one of two input signals according to a control bit, enhancing security, efficiency, and diversity. Stream ciphers, substitution-permutation networks (SPNs), PRNGs, and fault-tolerant cryptographic circuits are extensively employed. By altering feedback routes, a 2 × 1 multiplexer enhances non-linearity and unpredictability in Grain and Trivium stream ciphers, increasing their resistance to cryptanalysis. It facilitates dynamic modifications of block ciphers, enhancing dispersion and confusion. It also safeguards against side-channel attacks by concealing power and timing analysis vulnerabilities. It’s hardware efficiency renders it appropriate for lightweight IoT cryptography since it utilizes minimal logic resources and energy while accelerating encryption. MUX-based redundancy enhances the fault tolerance of cryptographic hardware, guaranteeing dependable and secure encryption. Contemporary cryptographic systems depend on the 2x1 multiplexer due to its ability to lower computing expenses, improve resilience to attacks, and facilitate regulated randomization, hence augmenting security. The M₁, M₂, M₃, and M₄ multiplexers make up the 2 × 1 multiplexer unit [31]. The input bits for the M₁ originate from f_i+4 and f_i+8 bits of the Logistic Round Module; the selection bits for the M₁ come from β_i+19 bit of the NFSR, as shown by Equation 7. While the input bits for M₂ come from f_i+10 and f_i+16 bits of the Logistic Round module, the selection bits for M₂ come from β_i+27 bits of the NFSR, as shown by Equation 8. In the same way, the input bits for M₃ come from f_i+20 and f_i+24 bits of the Logistic round module, and the selection bits for M₃ come from p_i+11 bit of the LFSR, as shown by Equation 9. The selection bits for M₄ come from p_i+79 bits of the LFSR, whereas the input bits come from f_i+30 and f_i+31 bits of the Logistic round module, as shown by Equation 10. A two-choice multiplexer that accepts f₁ and f₂ as input signals and stands for the selection signal is defined as MUX (f₁, f₂, s).

(7)(8)(9)(10)

3.1.6. Filter function.

The data in the two shift registers and the Logistic round module represent the cipher’s state. This state gives nine variables to the Boolean function h(γ). This filter function was selected due to its balance, first-order correlation immunity, and algebraic degree of eight. The nonlinearity for these functions is precisely 19, which is the maximum possible value. Both the register and the logistic chaotic module provide input. We define the function by Equation 11.

(11)

Where γ₀, γ₁, γ₂, γ₃, γ₄, γ₅, γ₆, γ₇, γ₈ correspond to the tap points p_i, p_i+25, p_i+46, p_i+64, β_i+63, β_i+79, f_i+15, f_i+20, and M₃. The filter function is concealed using bits β_i, M₄, and f_i+4 to generate the output function.

3.1.7. Output function.

The keystream bit at the time step is computed by a nonlinear mixing of bits derived from the chaotic sequence derived from the chaotic module by Equation 1, the NLFSR state , the multiplexer unit derived from Equation 10, is the filter function derived by Equation 11, and XOR operation. Formally, the LWLCM’s output function is described by Equation 12:

(12)

where C = {2,15,36,45,64,73,79}. This framework ensures that the keystream comprises state bits and dynamic random input that evolves. This renders it exceedingly difficult to decipher and resistant to linear cryptanalysis. is a robust output function due to the incorporation of a multiplexer, NLFSR, and chaotic map, which enhance its unpredictability and resistance to decryption attempts. Before any key creation occurs, the registers and the logistic round module must be initialized with the key, IV, and logistic chaos functions. Let’s say that ki stands for the key bits, where 0 ≤ i < 79, and IV_i stands for the IV bits, where 0 ≤ i ≤ 63. The following describes how the key is initialized. To fill up the remaining bits of the LFSR, p_i = 1, 64 ≤ i ≤ 79, load IV, p_i = IV_i, 0 ≤ i ≤ 63, into the first 64 bits of the LFSR first. Then, insert the key bits, βi = ki, 0 ≤ i ≤ 79, into the NFSR. Using the logistic chaos function, the logistic round module was initialized with α ∊ [3.6,4] and x₀ ∊ (0,1). Next, 160 clock cycles of the cipher are performed without producing a running key that looks like grain. Instead, the filter function’s output w(γ) is transmitted again and combined with the LFSR and NFSR inputs, as illustrated in Fig 5.

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Fig 5. Key initialization.

https://doi.org/10.1371/journal.pone.0330976.g005

5.1. Encryption

This section covers the encryption process, the IV, key, and plaintext, and the inputs used in the encryption process after initializing the encryption and “warming it up” with the clock function. The ciphertext is created by XORing the key stream produced by the keystream generation function with the binary plaintext. The binary string is returned in the form of ciphertext as shown in the encryption algorithm.

Encryption Algorithm

Input: Plaintext (P), α, x₀, key (k), Initialization Vector (IV), XOR (⊕)

Output: Ciphertext

1. Derived the initial parameters α, x₀ by Equations 2 and 3.

2. Initialize the logistic round module:

  for i = 0 to 32 do

  f[i] = logistic_chaos(x₀, α) # Compute logistic chaos values by Equation 1.

3. Initialize NLFSR:

  for i = 0 to 79 do

   nlfsr[i] = k[i] # Load key values into NLFSR

4. Initialize LFSR with IV:

  for i = 0 to 63 do

  fsr[i] = IV[i] # Load initialization vector values into LFSR

5. Continue initializing LFSR:

  for i = 64 to 79 do

  lfsr[i] = 1 # Set LFSR values from 64 to 79 to

6. Clock the cipher 160 times without generating a keystream:

  for j = 0 to 159 do

  clock() # Apply the clocking function using Equations 5, 6, and 11

7. Generate keystream:

  keystream = keyStreamGeneration() # Apply the clocking function using Equations 5, 6, 11, and 12

8. Encrypt plaintext:

  for i = 0 to length(P) - 1 do

  Ciphertext[i] = P[i] ⊕ keystream[i] # XOR plaintext with keystream

9. Return Ciphertext

5.2. Decryption

Encryption and decryption are the opposite processes. The decryption function initializes with the same IV and key, executes the clock function, and generates the same key stream. The binary ciphertext and key stream are XORed to return the original binary plaintext. This binary plaintext is then converted back into text using text_from_bits, resulting in the original message shown by decryption algorithms.

Decryption Algorithm

Input: Cipher (C), α, x₀, key (k), Initialization vector (IV), XOR (⊕)

Output: Plaintext

1. Derived the initial parameters α, x₀ by Equations 2 and 3.

2. Initialize logistic chaos module

  for i = 0 to 32 do

  f[i] = logistic_chaos(x₀, α) # Compute logistic chaos values by Equation 1.

3. Initialize NLFSR

  for i = 0 to 79 do

  nlfsr[i] = k[i]

4. Initialize LFSR with IV

  for i = 0 to 63 do

  lfsr[i] = IV[i]

5. Further initialize LFSR

  for i = 64 to 79 do

  lfsr[i] = 1

6. Clock the 160 times #using Equations 5, 6, and 11 ciphers without generating a keystream

  clock()

7. Generate the keystream # using Equations 5, 6, 11, and 12

  keystream = keyStreamGeneration()

8. Decrypt the ciphertext

  for i = 0 to length(Cipher) do

  Plaintext[i] = Cipher[i] ⊕ keystream[i]

9. Return Plaintext

6.1. Time complexity analysis

With n representing the bit count in the input plaintext or ciphertext, the proposed lightweight stream cipher defines its time complexity as O(n). The encryption process consists of five critical stages: first, the plaintext is converted into binary format, requiring O(n) time; second, the LFSR and NLFSR are initialized with the designated key and initialization vector (IV) in constant time, O(1); third, a warm-up phase of 160 fixed rounds is performed to diffuse the internal state, also in O(1) time; fourth, the keystream is generated with each bit calculated in constant time, resulting in an overall complexity of O(n); and finally, each bit of the plaintext is XORed with the corresponding keystream bit during encryption, which again necessitates O(n) time. The overall time complexity of the encryption and decryption processes is T(n) = O(n) + O(1) + O(1) +O(n) + O(n) ≈ O(n), which indicates that the method exhibits linear scalability for input size, making it particularly appropriate for resource-constrained environments such as IoT devices.

6.2. Encryption time

In IoT and real-time applications, encryption time is a critical metric of cryptographic efficiency, defined as the duration needed for an encryption method to transform plaintext into ciphertext. Further, based on the size of each data set, four sets of data are gathered, and the encryption time is evaluated to clarify whether the proposed model is suitable for IoT-based applications. To find the encryption time, 100 trials are performed for each input type. The average values of the final results have been considered and are shown in Table 2, and a comparison has been made in Fig 8 indicates that the proposed LWLCM cipher operates at a reduced speed compared to AES-256, Grain v1, and Trivium, mostly attributable to the incorporation of a nonlinear chaotic function and dynamic multiplexer logic within its architecture. By augmenting the internal complexity and computational depth of the methodology, these components enhance security attributes in the keystream, including statistical unpredictability, nonlinearity, and increased diffusion. This additional complexity is a calculated compromise to provide enhanced resilience to linear, differential, and algebraic attacks, hence augmenting the security of LWLCM in adversarial conditions. For all plaintext values, LWLCM demonstrates an encryption speed that is around 56–59% quicker than Grain-128 and nearly 94–95% faster than RSA. Grain-128 experiences prolonged processing times due to its enlarged state size and intricate feedback mechanisms, notwithstanding its security; RSA is fundamentally unsuitable for bulk data encryption because of its asymmetric nature and computational demands. Consequently, LWLCM outperforms Grain-128 and RSA in execution time while offering superior cryptographic protection compared to faster yet less sophisticated ciphers such as Grain v1 and Trivium, thereby optimizing lightweight efficiency with better security.

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Table 2. Encryption time (sec).

https://doi.org/10.1371/journal.pone.0330976.t002

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Fig 8. Encryption time (sec).

https://doi.org/10.1371/journal.pone.0330976.g008

6.3. Decryption time

The decryption process in the proposed model utilizes a stream cipher technique, in which the ciphertext is XORed with the keystream to obtain the original plaintext. Table 3 and Fig 9. The proposed LWLCM cipher consistently outperforms both Grain-128 and RSA in terms of decryption performance across all evaluated plaintext sizes. Specifically, LWLCM demonstrates a 56% to 59% reduction in decryption time compared to Grain-128, owing to its lightweight structure and efficient feedback mechanisms. When compared to RSA, the performance advantage is even more significant—LWLCM achieves a 75% to 85% faster decryption time, highlighting its suitability for resource-constrained environments where computational efficiency and low latency are critical. While the proposed work is marginally slower than Grain v1, especially for smaller plaintext sizes (10–14% slower), the difference disappears for bigger plaintexts and is less than 0.5 percent slower because of its complex nature. The proposed work strikes a compromise between security and efficiency, providing notable advancements over Grain-128 and RSA while maintaining parity with Grain v1, Trivium, and AES-256.

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Table 3. Decryption Time(sec).

https://doi.org/10.1371/journal.pone.0330976.t003

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Fig 9. Decryption time (sec).

https://doi.org/10.1371/journal.pone.0330976.g009

6.4. Throughput

Throughput in cryptography refers to the rate at which an encryption or decryption algorithm processes data. It determines how efficiently an algorithm can handle large volumes of data in real-time applications. The throughput of the algorithm grows as its performance grows because there is a direct correlation between the two [32]. The encryption/decryption method’s throughput can be ascertained using Equations 13 and 14.

(13)

(14)

Tables 4,5, and Figs 10 and 11 show that the LWLCM cipher consistently demonstrates superior encryption and decryption throughput compared to Grain-128 and RSA-1024 across all assessed plaintext sizes. LWLCM demonstrates a throughput enhancement of around 130% to 150%, surpassing Grain-128 and underscoring its design focused on lightweight efficiency. The throughput enhancement of 1800% is particularly significant when juxtaposed with RSA-1024, hence emphasizing the efficacy of LWLCM in low-resource settings. While Trivium attains the maximum raw encryption/decryption throughput, followed by AES-256 and Grain v1. LWLCM presents a judicious compromise among speed, randomness, and cryptographic strength due to its nonlinear chaotic value and multiplexer unit, with a tradeoff between security and efficiency. LWLCM performs admirably compared to Grain-128 and RSA-1024, providing a notably higher throughput at a reasonable cost compared to Grain v1.

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Table 4. Encryption throughput (Byte/sec).

https://doi.org/10.1371/journal.pone.0330976.t004

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Table 5. Decryption throughput (Byte/sec).

https://doi.org/10.1371/journal.pone.0330976.t005

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Fig 10. Encryption throughput (Kb/sec).

https://doi.org/10.1371/journal.pone.0330976.g010

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Fig 11. Decryption throughput (kb/sec).

https://doi.org/10.1371/journal.pone.0330976.g011

6.5. Avalanche analysis

In cryptography, the term “avalanche effect” is used to characterize a specific behavior of mathematical functions used in encryption. The avalanche effect is one of the desirable properties of any encryption method. A single-bit change in the key should result in a 50% change in the ciphertext or keystream. This characteristic is known as the “avalanche effect.” [33]. This quality is crucial in preventing opponents from using plaintext attacks or statistical analysis to take advantage of weaknesses in encryption. In the proposed algorithm, a single-bit flip was introduced at any i^th bit of the secret key, keeping the IV constant. This update changed how the NLFSR was set up. We looked at the ciphertext that came out and the original ciphertext to determine how many bits had changed. Examining LWLCM on both pairs of key-ciphertext and key-keystream, as shown in Tables 6 and 7, Figs 12 and 13, exposes a more noticeable avalanche impact than modern lightweight stream ciphers such as Grain v1, Trivium, and AES-256. The results show that above 50%, LWLCM consistently achieves an avalanche effect over the required security threshold on both pairs. The great unpredictability of the cipher strengthens its resilience by ensuring that small changes in input produce significant differences in ciphertext or keystream, complicating cryptanalysis greatly. The encryption model integrates the logistic chaos function to increase security by adding non-linearity and enhanced sensitivity to initial conditions. Including the chaotic function ensures that even small changes in the input generate drastically different keystreams, hence improving diffusion characteristics and preventing attackers from recognizing regular patterns. Figs 14 and 15 show that adding logistic chaos to LWLCM produces an improved average avalanche effect on both pairs of key-ciphertext and key-keystream and outperforms Grain v1, Trivium, and AES-256, increasing the cipher’s resistance against cryptographic attacks. The results conclude that the proposed approach significantly increases security while preserving efficiency, offering resilience to statistical and differential attacks. Its unpredictability, strong diffusion, and low computing cost make it a perfect solution.

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Table 6. Avalanche Effect (%) of Key- Keystream.

https://doi.org/10.1371/journal.pone.0330976.t006

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Table 7. Avalanche effect (%) Key- Cipher text.

https://doi.org/10.1371/journal.pone.0330976.t007

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Fig 12. Key-Keystream Avalanche effect.

https://doi.org/10.1371/journal.pone.0330976.g012

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Fig 13. Key-Cipher Text Avalanche effect.

https://doi.org/10.1371/journal.pone.0330976.g013

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Fig 14. Average Avalanche effect for Key-Keystream.

https://doi.org/10.1371/journal.pone.0330976.g014

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Fig 15. Average Avalanche effect for Key-Cipher text.

https://doi.org/10.1371/journal.pone.0330976.g015

6.6. Memory usage

In the domain of IoT, where devices operate with constrained memory, power, and computational resources, efficient memory management is a critical factor in evaluating the feasibility of cryptographic algorithms. Any algorithm’s lowest and maximum memory usage, quantified in kilobytes (KB), directly affects its suitability for real-time IoT applications. Fig 16 depicts the variance in memory utilization among LWLCM, Grain v1, Grain-128, and Trivium, highlighting the compromise between security and resource efficiency. The integration of a multiplexer and logistic chaos map intensifies code complexity, leading to heightened memory usage. However, this heightened complexity significantly enhances security, making the proposed method more resilient than traditional lightweight algorithms. The balance between memory optimization and security robustness is essential for developing scalable, energy-efficient, and attack-resistant cryptographic solutions in IoT environments.

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Fig 16. Memory usage (Kb).

https://doi.org/10.1371/journal.pone.0330976.g016

6.7. Energy consumption

Energy consumption is essential in assessing how well algorithms operate in limited settings. The efficiency with which the algorithm functions with constrained resources like battery-operated devices is amply demonstrated by this [34]. We can evaluate how well the suggested approach balances security and cost by monitoring energy usage. We can calculate energy consumption by using Equation 15.

(15)

V is the potential difference, I is the current, and t is the total time. The LWLCM’s energy usage demonstrates how well it balances efficiency and improved security measures, as shown in Table 8 and Fig 17. It uses more energy than Grain v1, Trivium, and AES-256 due to its complex nature. However, this difference is offset by the more sophisticated security features that provide better defense against intrusions. All plaintext sizes combined show that LWLCM is still substantially more energy-efficient than Grain-128 and RSA-1024. Because of this, LWLCM is an efficient cipher that provides strong security without requiring as much energy as more complicated ciphers like Grain-128 and RSA-1024. Its effectiveness in situations where security and efficiency are critical for solid encryption procedures is highlighted by its capacity to deliver robust digital privacy while consuming reasonable energy.

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Table 8. Energy consumption (Joule).

https://doi.org/10.1371/journal.pone.0330976.t008

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Fig 17. Energy consumption (Joule).

https://doi.org/10.1371/journal.pone.0330976.g017

Analyzing the proposed cipher’s efficacy reveals an essential equilibrium between security and velocity. Despite prioritizing lightweight operations, which may sacrifice some cryptographic complexity, ciphers such as Trivium, Grain v1, and AES-256 demonstrate enhanced encryption and decryption speeds alongside improved throughput. This trade-off enhances rapid data processing but may slightly diminish advanced randomization or vulnerability to certain attacks. The proposed LWLCM encryption exhibits greater structural complexity through the utilization of a logistic chaos function and dynamic multiplexer logic. Statistical analyses indicate that these components markedly enhance the overall unpredictability, diffusion effectiveness, and resilience against cryptanalytic assaults of the cipher, despite a slight prolongation of the encryption duration. The proposed LWLCM cipher significantly surpasses Grain-128 and RSA-1024 in terms of encryption speed during benchmarking. The extended processing times of Grain-128 and RSA-1024 are attributable to their elevated state dimensions and inherently complex computations. While LWLCM enhances security layers, it preserves a superior speed compared to conventional approaches, therefore affirming its efficiency. Ultimately, LWLCM attains an optimal equilibrium: it is marginally slower than Trivium, Grain v1, and AES-256, while significantly faster than Grain-128 and RSA, hence enhancing cryptographic security. This equilibrium renders LWLCM an advantageous option for restricted environments such as IoT for immediate, secure communication.

6.8. Ablation study on component impact

We performed an ablation study to assess the influence of each element of the LWLCM cipher on the efficacy of the data encryption process. We gradually removed the NLFSR, the chaotic module, and the MUX, yielding three simplified ciphers. We ensured equitable outcomes by utilizing uniform sizes of plaintext and settings for each configuration test. From Table 9, the results show that removing any of the modules speeds up the encryption process, notably when the chaotic function is not present. In this case, it takes 4.7270 seconds to encrypt 2¹² bytes of plaintext with the complete LWLCM and 2.242 seconds without the chaos module. The same patterns still show up if we remove the MUX (0.860 s) or the NLFSR (0.863 s). This shows that these modules make arithmetic a lot harder. Now, in the case of the decryption process, the same thing has been observed from Table 10. On removing each individual module, the decryption time decreases.

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Table 9. Encryption time(sec) in the absence of each component at a time.

https://doi.org/10.1371/journal.pone.0330976.t009

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Table 10. Decryption time(sec) in the absence of each component at a time.

https://doi.org/10.1371/journal.pone.0330976.t010

Further, the throughput has also been calculated to check the efficiency of each module. Table 11 demonstrates that the LWLCM model may encrypt data using four alternative approaches. The results demonstrate that dropping the chaotic module markedly optimizes throughput. The thorough model can process 4096 bytes at a velocity of 866.71 bytes per second. The new model is capable of processing 1826.74 bytes per second. The performance improves slightly when the MUX and NLFSR are removed. Certain electrical equipment operates more efficiently with increased data transmission; yet, this results in diminished randomness and linearity of the data. Incorporating chaos and multiplexing into the encryption process enhances complexity, hence complicating decryption and facilitating communication; however, it demands substantial computational resources. This indicates their necessity for the final design.

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Table 11. Throughput (byte/sec) in the absence of each component at a time.

https://doi.org/10.1371/journal.pone.0330976.t011

Other important parameters that evaluate the randomness of the keystream are entropy and the Avalanche effect to protect against different attacks. Table 12 presents the entropy of ciphertexts generated by the LWLCM cipher with various structural features deactivated. The fundamental concept is that the combined utilization of chaotic maps, MUX, and NLFSR consistently approaches the optimal entropy level of 8.0. This renders forecasting future events exceedingly challenging. Upon the removal of the chaotic module, the entropy values significantly diminish (for instance, 7.64 for a 2⁸-byte input), indicating a reduction in randomness. Removing the NLFSR also results in a decrease, albeit less significant. Removing the MUX somewhat increases the entropy; however, it remains marginally lower than that of the entire system. These results indicate that each module is crucial for ensuring the statistical security of the encryption. The chaotic function is crucial as it enhances bit-level diffusion and non-linearity. While in the case of the avalanche effect, the proposed LWLCM encryption consistently exhibits an avalanche effect nearing the optimal 50% threshold across all tested plaintext sizes. From Table 13, it can be observed that upon removal of the chaotic module, the impact of the avalanche diminishes by around 5–6%. This indicates that chaos is a crucial element in rendering the ciphertext less discernible and more dispersed. This means that chaos is an important part of making the ciphertext less clear and more spread out. When the avalanche’s performance drops to about 41–42% without the MUX, the difference becomes clearer. This shows that the multiplexer is necessary to make the encryption output less linear. Removing the NLFSR reduces the avalanche effect by around 3–4%. This complicates the interpretation of the input and obscures the clarity of the findings. These results demonstrate the efficacy of LWLCM’s architecture and the significance of each component in achieving robust statistical security. The integrated architecture ensures that even a minor alteration to the key will result in a significant, unforeseen change in the ciphertext. This complicates the ability of cryptographers to obtain the keys necessary for message decryption.

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Table 12. Entropy analysis in the absence of each component.

https://doi.org/10.1371/journal.pone.0330976.t012

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Table 13. Avalnche analysis(%) in the absence of each components at a time.

https://doi.org/10.1371/journal.pone.0330976.t013

7.1. Linear approximation attack

According to the reference [36], Grain cipher cryptography will withstand the linear_approximation_attack if the NFSR employed with the cryptography system’s output function has strong nonlinearity and high elasticity. The suggested method successfully prevents linear cryptanalysis by utilizing complex feedback loops, multiplexer operations, and non-linear Boolean functions. Its feedback mechanisms use XOR, AND, and multiplexer operations to break linear relationships that could be used as an opening for these kinds of attacks. The multiplexers add substantial complexity and non-linearity by introducing conditional logic, whose outputs depend on control bits. LFSR and NLFSR are two examples of complex feedback mechanisms that use non-linear combinations to distribute the influence of a single bit across several others. By enhancing the cipher’s diffusion and mixing features, this design strengthens it against analyses that aim to take advantage of more straightforward, linear patterns by guaranteeing that slight changes in the input have wide-ranging, unpredictable impacts on the output. The result indicated a bias of less than 0.01, demonstrating the robustness of the system against a linear approximation attack.

7.2. Correlation attack

The bits in the LFSR are (almost) exactly balanced due to the statistical properties of maximum length LFSR sequences,“ the developers of Grain v1. This may not be true when an NFSR is driven autonomously [37]. Yet, the bits in the NFSR are balanced because an LFSR state is used to obtain the feedback. Keep in mind that the NFSR function is also balanced. In light of this, one may argue that the NFSR and LFSR bits are uncorrelated. That is the case for LWLCM, where there is also a nonlinear logistic round module, and the maximum-length FSR, LFSR, and NFSR correspond to the LFSR and NFSR of Grain, respectively. The significance of the filtering function is good balancedness, nonlinearity, and resiliency properties, to resist correlation assaults and quick correlation attacks. According to section 3.1.4, LWLCM has a more robust output function than the original Grain family. While Grain v1 and Grain-128a have output functions defined over 12 variables and 1536 and 61440, respectively, and with the nonlinearity of 274877906943, their output function is defined over 38 variables. Our encryption system is less vulnerable to correlation attacks because the LWLCM output function is more balanced and nonlinear, and the correlation coefficient is closer to zero.

7.3. Algebraic attack

Initially introduced at the EUROCRYPT2003 conference, the predictable cipher cryptanalysis method is known as the algebraic attack. The basic concept behind this methodology is to express a cryptographic method’s security as the solution to a group of overdetermined nonlinear equations. Formulating and resolving multivariable, huge-scale nonlinear problems is a significant factor in determining the difficulty of mathematical attacks. Extensive multivariable nonlinear formula solutions are a significant area of algebraic calculation. With the introduction of algebraic assaults, a new Boolean function cryptography criterion known as algebraic immunity is established. For further information on research on algebraic immunity [38]. The proposed method’s advanced usage of multiplexer operations, recursive feedback systems, and complex Boolean functions provides a defense against algebraic attacks. The cipher generates a highly complicated and nonlinear algebraic structure by integrating multiplexer functions, AND, and XOR operations. The multiplexer, in particular, adds conditional branching to every operation, increasing the algebraic complexity and creating a system of equations that is difficult to solve efficiently. The feedback loops in the LFSR and NLFSR make these equations more difficult, which produces recursive dependencies that disperse changes throughout the cipher’s state. This combination creates a complex web of high-degree polynomial equations that prevent algebraic attacks by increasing the computational effort needed to find meaningful solutions. This protects the cipher from advanced cryptanalytic attacks.

7.4. Guess and determine attack

Unlike Grain-128a and Grain v1, which have 12 and 17 variables, LWLCM has 38 variables that govern its output function. If the LFSR is questioned, the output relies entirely on the NFRS and the logistic round module, exhibiting significant nonlinearity [36]. Say an attacker chooses to guess 20 bits of the 80-bit key in the proposed encryption, which uses a 64-bit IV. Because of the cipher’s complex architecture, this scenario lessens the uncertainty in the remaining 60 critical bits without greatly simplifying the work. The formula for the initial state is S₀ = Initial (IV, Key). This state is created by integrating the IV and the key, which may be mathematically represented by Equation 16.

(16)

Whether or not the key bits are guessed, these feedback mechanisms and the cipher’s non-linear operations guarantee that every bit of the key is fully mixed into the state, hiding obvious links between the key bits and the cipher output. Effectively using partial key guesses is computationally challenging due to the complexity and reliance caused by the initial mixing and subsequent state transitions through non-linear Boolean functions and multiplexers. This solution provides strong security even against advanced cryptanalytic techniques by fortifying the cipher against guess-and-check attacks by guaranteeing that partial knowledge of the key does not impair the overall encryption process.

7.5. Fault attack

A cryptography chip gadget produces erroneous results when an encryption algorithm flaw is introduced. Then, by scrutinizing the imprecise outcomes, the key is discovered. These attempts to break Grain ciphers have been effective [37]. The cipher’s complicated feedback loops involving LFSR and NLFSR, recursive state dependencies, and non-linear Boolean functions are the main reasons for its strong resilience to fault attacks. Using non-linear operations like XOR, AND, and multiplexer functions guarantees that any introduced flaws spread in unforeseen ways, making any direct cryptanalysis attempts by adversaries far more complex. The architecture deftly diffuses the impact of faults throughout the whole state through feedback mechanisms that distribute the influence of a single fault across numerous state elements and several cycles. Let us examine a fault that induces a state S_t, where the fault modifies this state to S_t′. The following state S_t+1 is expressed in Equation 14. If a failure causes S_t to change to S_t’, the following situation would presumably occur, which is shown in Equation 17.

(17)

Because of the broad distribution and recursive dependencies in the cipher, errors are difficult to identify and pinpoint, which makes it highly challenging for adversaries to derive valuable information from manipulated outputs. As a result, the cipher’s design provides natural defense against the standard techniques used in fault attacks, boosting its security and integrity in a dangerous situation

7.6. Known plain text attack

A type of cryptanalysis known as known-plaintext attacks (KPA) occurs when an attacker obtains access to both the plaintext and the ciphertext that goes along with it [39]. Based on this knowledge, the attacker tries to deduce the encryption key or decode more plaintexts. Assume that an attacker possesses identical plaintext-ciphertext combinations, (P₁, C₁) and (P₂, C₂), but each encryption process additionally incorporates an IV, which varies for every encryption session. The LFSR component of the cipher depends on the IV to initialize the state or to influence how it functions. One possible beginning for the encryption of P₁ would be S₀ initial state; IV₁, E is the encryption function, and key (K) would impact this. The cipher’s operations would then process this to generate C_1, such as C₁= E (P₁, Init (IV₁, K)). Likewise, C₂ is generated as follows: C₂= E (P₂, Init (IV₂, K)).

It is effectively ensured that distinct ciphertexts are produced from the same plaintext encrypted under multiple IVs by using a different IV for each encryption instance. Because of this unpredictability, it is more difficult for an attacker to identify recurring patterns or connections between P and C that indicate K. By distributing the impact of the plaintext and key throughout the cipher’s operations, the IV obscures any direct connections between the plaintext and the ciphertext. The altering IV for another encryption instance (let’s say P₂ and IV₂) resets the internal state differently, upending the cryptographic landscape and making it difficult for an attacker to deduce K even if they are aware of P₁ and C₁.

7.7. Side-channel attacks

The proposed LWLCM cipher employs a 2 × 1 multiplexer governed by a chaotic logistic function, resulting in significant nondeterminism in internal state transitions and output generation. This unpredictable switching technique obscures distinct computational patterns, hence impeding attackers’ attempts to derive keys using power analysis or timing-based side-channel attacks. Moreover, the minimal electromagnetic and power leakage due to the compact and stable hardware footprint of LWLCM significantly diminishes exposure.

7.8. Reply attack

Employing a confidential key and a dynamic Initialization Vector (IV), LWLCM’s initial phase guarantees that the keystream is unique to each session. The initialization vector (IV) varies with each session and is cryptographically linked to the output, preventing an attacker’s ability to effectively reuse previous ciphertexts or intercepted keystreams, thus mitigating replay attacks. This is particularly critical in the IoT as interconnected systems occasionally pose safety risks.

8.1. NIST test

This study validates the statistical performance of the LWLCM using NIST SP 800−2, the test kit issued by the US National Institute of Standards &Technology [40]. The test program consists of a statistical package with sixteen different testing techniques. Using software & hardware for secret random number producers, techniques may be used to evaluate the randomness of binary sequences of arbitrary length. Finding any instances of potential non-randomness in encryption is the primary goal of these testing techniques. The P-value determines the outcome of every test. It is determined that the stream cipher is non-random if the p-value is smaller than 0.01. A stream cipher is considered random if the p-value is more significant than 0.01. To assess the robustness and randomness of the keystream generated by the proposed LWLCM stream cipher, we produced a keystream of 1,500,000 bits for each test case. The entire test suite was executed 100 times, each instance utilizing a novel set of keys and a randomly selected IV. We examined whether the mean p-values for each of the 16 statistical tests were consistent across all 100 iterations. This was to ensure the absence of bias in the selection of specific keys or IV. The keystream generated by the proposed LWLCM successfully passed the whole NIST test. Table 14 presents the results, indicating that, well over the 0.01 threshold, all 16 tests were successful, with P-values surpassing 0.01 in each instance. This verifies that the cipher is appropriate for cryptographic applications in IoT contexts, as it provides highly unpredictable and statistically secure output.

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Table 14. NIST test.

https://doi.org/10.1371/journal.pone.0330976.t014

8.2. Shannon entropy

Claude invented entropy H (also called information entropy). E Shannon in 1948 and published in “A Mathematical Theory of Communication. “In cryptanalysis, we can use the entropy as a “Cost function” to rate a text. It is measured for the uncertainty of random variables and quantifies the expected value of information [41]. Entropy H(Y) of a discrete random variable X with possible values {y₁, y₂, y₃,………..,y_n}, where the probability of each yi is p(yi) value is between 0 and 1, and . Information content/uncertainty of X is I(Y), and H(Y) is the expected value of I(Y), thus

(18)

(19)

The random variables in distribution X are unrelated to one another. Because the stream cipher system is binary, 2 is the log’s default base. The predicted code length for coding samples based on the actual distribution is shown in Equation 20.

(20)

Because binary stream ciphers only have two values. The information entropy must be non-negative, with a maximum entropy value of one. Table 15 shows that, out of all the state-of-the-art Grain v1 [7], Grain-128 [8], and Trivium [5], LWLCM has the highest entropy value, indicating a high degree of randomness and uncertainty. It will be highly challenging for the attacker to interpret the keystream pattern.

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Table 15. Shannon entropy analysis.

https://doi.org/10.1371/journal.pone.0330976.t015

8.3. Correlation coefficient analysis

The intensity, direction, and type of the linear relationship between two variables, the plaintext and the matching ciphertext, are measured statistically using the correlation coefficient. This coefficient ensures that the ciphertext differs significantly from the plaintext, which is essential for determining how well an encryption scheme can withstand statistical attacks. The coefficient has values between −1 and 1. A value of 1 denotes a solid linear correlation and the equivalence of the plaintext and ciphertext. On the other hand, a coefficient of −1 denotes a negative correlation and an inverse relationship between the plaintext and the ciphertext. Effective encryption is indicated by a zero coefficient, which implies no correlation and suggests that the ciphertext is independent of the plaintext [42]. The Correlation Coefficient can be determined with Equation 21

(21)

Where are the mean and standard deviation of plain text and ciphertext, respectively. The mean can be determined with Equations 22 and 23, respectively.

(22)

(23)

The standard deviation of plaintext and ciphertext can be calculated with Equations 21 and 22, respectively

(24)

(25)

The Proposed method offers remarkable encryption performance, as shown in Table 16; its adaptability and progressively better encryption as plaintext sizes increase are noteworthy. Correlation coefficients that trend toward zero and turn negative emphasize this trend, demonstrating the algorithm’s resilience.

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Table 16. Compare the correlation coefficients of the proposed work with other existing algorithms.

https://doi.org/10.1371/journal.pone.0330976.t016

The proposed method is the best option for various encryption requirements because of its versatility, which guarantees high security for a wide range of data sizes. Comparatively, existing algorithms, such as Grain128, likewise have strong encryption capabilities with low average correlation coefficients, but they lack the proposed algorithm’s constant improvement and adaptability. Their effectiveness is indicated by the averages, Proposed at −0.0103 and Grain128 at −0.0205. On the other hand, the proposed method is notable for having an opposing average, highlighting its more robust and reliable encryption performance compared to Grain v1 and Trivium, which have higher and less reliable averages. Based on this comparison, the proposed algorithm is proven to be a solid encryption solution that works well in all scenarios.

9.1. Scalability to high-throughput systems

The encryption is intended for a limited number of nodes within the IoT. In high-throughput or parallel-processing systems, such as edge servers or multi-core computers, the sequential nature of bitwise operations and the 160-round warm-up phase may induce latency, hence making it suboptimal without parallel enhancements.

9.2. Scope limited to textual data

The current implementation and assessment of the LWLCM encryption have solely utilized textual content. Multimedia inputs, such as photographs, audio, or video streams, prevalent in contemporary IoT devices like surveillance systems, smart homes, and telemedicine, have not been assessed in the model. Extending the model to include additional data types may necessitate further preprocessing layers and improved keystream flexibility to maintain both security and efficiency.

9.3. Focus on confidentiality, not full authentication

This work presents data secrecy based on secure stream encryption. However, it is devoid of digital signatures or Message Authentication Codes (MACs), which would enable verification of data integrity or validity. Practical applications, particularly in distributed IoT networks, rely on the verification of data source accuracy. Subsequent advancements will employ lightweight authenticated encryption techniques to ensure both authenticity and confidentiality.

9.4. Assumed trust in input data and environment

The model assumes that past breaches have not damaged the integrity of the input data or communication channels, therefore making them trustworthy. It ignores systems of data validation or confidence-building tools. In adversarial environments, this may be limited since encrypted illegal or counterfeit data could be accepted. Including anomaly detection or pre-authentication checks could help to solve this problem.

9.5. Evaluation against emerging cryptanalytic models

The encryption has undergone testing for linear, algebraic, and fault attacks, successfully passing all 16 NIST randomness tests to date; however, it has not yet been evaluated for its resilience against AI-based or differential attacks. These contemporary models are becoming increasingly significant, so their evaluation is crucial for forthcoming undertakings.

9.6. Hardware implementation not yet evaluated

The publication lacks a synthesized hardware implementation and FPGA performance metrics, despite the cipher’s design being evident for lightweight hardware applications. Metrics such as logic gate count, slated for further hardware validation phases, may facilitate practical implementation. While the encryption successfully meets all 16 NIST randomness criteria and withstands linear, algebraic, and fault attacks, the study does not now assess its resilience against artificial intelligence-driven or differential attacks. Future research will include evaluations of these creative models as they are increasingly pertinent.