Implementation of Chaotic Neural Key Generation Algorithm
For IoT Devices
ZIED GUITOUNI1, MOHSEN MACHHOUT1
1Electronics and Micro-Electronic Laboratory, Faculty of Sciences of Monastir, TUNISIA.
Abstract: - This paper presents a new method for generating encryption keys for Internet of Things (IoT)
devices. This method combines chaos theory with neural networks to create secure and efficient keys. We use
the Lorenz chaotic system to generate complex patterns and a Convolutional Neural Network (CNN) to learn
and predict these patterns. This approach is designed to address the unique security challenges of IoT devices,
which often have limited computing power. We tested our method with different key sizes and evaluated its
performance using accuracy, loss, entropy, and correlation metrics. The results show that key sizes between
256 and 512 bits offer the best balance between model performance and security for IoT devices. We also
conducted Diehard statistical tests, which our key generation method passed successfully, demonstrating its
ability to produce high-quality random keys.
Key-Words: - Internet of Things, Cryptographic Key Generation, Chaotic Systems, Neural Networks,
Convolutional Neural Networks, Lorenz System, Randomness.
Received: April 4, 2024. Revised: September 9, 2024. Accepted: September 26, 2024. Published: October 24, 2024.
1 Introduction
The Internet of Things (IoT) has emerged as a
transformative paradigm, interconnecting billions of
devices and revolutionizing various sectors
including healthcare, agriculture, and smart cities
[1]. However, the proliferation of IoT devices has
introduced significant security challenges,
particularly in cryptographic key generation and
management [2]. The resource-constrained nature of
many IoT devices, combined with their vulnerability
to physical and remote attacks, necessitates novel
approaches to ensure robust security measures [3].
Secure key generation is a cornerstone of IoT
security, providing the foundation for encryption,
authentication, and data integrity [4]. Traditional
key generation methods often prove inadequate for
IoT environments due to their computational
intensity or lack of sufficient randomness [5]. This
paper presents a novel approach to address these
challenges: a Chaotic Neural Key Generation
Algorithm specifically designed for IoT devices.
Chaos theory, with its inherent properties of
sensitivity to initial conditions and unpredictability,
offers a promising avenue for cryptographic
applications [6]. Chaotic systems can generate
highly complex and seemingly random behavior
from simple deterministic equations, making them
ideal candidates for key generation [7]. When
combined with the adaptive learning capabilities of
neural networks, chaos theory presents an
opportunity to create a robust, efficient, and secure
key generation mechanism.
Neural networks, inspired by biological neural
systems, have demonstrated remarkable capabilities
in pattern recognition, adaptation, and complex non-
linear mapping [8]. By leveraging these properties,
neural networks can potentially enhance the quality
and efficiency of key generation processes [9]. The
integration of neural networks with chaotic systems
creates a synergistic approach that addresses the
unique security requirements of IoT devices.
This paper proposes a new method for generating
encryption keys for IoT devices. Our method
combines the unpredictability of chaotic systems
with the learning capabilities of neural networks.
Specifically, we use a type of chaotic system called
the Lorenz system to create complex patterns [6].
We then use a Convolutional Neural Network
(CNN) to learn and predict these patterns, which
helps us generate encryption keys [7].
The remainder of this paper is organized as
follows: Section 2 describes the background of
Chaotic Systems in Cryptography and the CNN
architectures. Section 3 outlines the proposed
algorithm for chaotic neural network-based key
generation. In Section 4, we present the
experimental results from implementing the
algorithm, including the training process evaluation
and the security analysis. Finally, Section 5
concludes the paper.
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.27
Zied Guitouni, Mohsen Machhout
E-ISSN: 2769-2507
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Volume 6, 2024
2 Background
2.1 Chaotic Systems in Cryptography
Chaotic systems are complex mathematical models
that are very sensitive to their starting conditions
[12]. This means that even a tiny change in the
beginning can lead to very different results over
time. This property makes chaotic systems useful
for cryptography, where we need to create
unpredictable patterns [7].
One popular chaotic system is the Lorenz
system, first described by Edward Lorenz in 1963
[13]. It's a set of three equations that model weather
patterns, which are given by:
dx/dt = 𝜎 * (y - x) (1)
dy/dt = x * (𝜌 - z) – y (2)
dz/dt = x * y - 𝛽 * z (3)
where x, y, and z represent the system's state
variables, and sigma, rho, and beta are parameters.
The chaotic sequence is generated by iterating the
equations using a given seed value.
Figure 1 shows a 3D representation of the Lorenz
attractor, generated using the Lorenz equations with
parameters 𝜎 = 10, 𝜌 = 28, and 𝛽 = 2.667. The
figure displays a butterfly-shaped pattern, a well-
known characteristic of the Lorenz system. The
trajectory is plotted over 10,000 time steps, with a
step size of 0.01, starting at the point (0, 1, 1.05). As
the system evolves, the path never repeats, though it
remains confined within a specific region of the
phase space.
Figure 1. Lorentz Attractor
The two lobes of the attractor, resembling
butterfly wings, reflect the system's oscillation
between two semi-stable states. This pattern
illustrates the deterministic but unpredictable nature
of chaotic systems, where small variations in initial
conditions can lead to drastically different
outcomes. The continuous, non-overlapping path
emphasizes the system's sensitivity to starting points
and its complex, non-linear behavior. This
visualization effectively demonstrates the dynamics
of chaotic systems and their potential applications in
fields like cryptography and secure communication.
2.2 Convolutional Neural Networks (CNNs)
CNNs are a powerful type of machine learning tool
that are great at finding patterns in data. They're
well-known for their use in image recognition, but
CNNs have also proven to be valuable in various
fields, including cryptography.
The structure of a CNN is like a series of
building blocks, each with its specific role. The first
blocks are convolutional layers. These layers use
filters that move across the input data, searching for
specific features. It's similar to how our eyes might
scan a picture, noticing things like edges or shapes.
After the convolutional layers, we have pooling
layers. These layers reduce the data, retaining only
the most crucial information. This not only speeds
up the network but also helps it focus on the bigger
picture instead of getting caught up in minor details.
The final part of a CNN consists of fully connected
layers. These function as the brain of the network,
taking all the information gathered by the earlier
layers and using it to make decisions, such as
classifying an image, making a prediction, or
solving a complex problem.
What sets CNNs apart is how they learn. As they
process more data, they improve at recognizing
patterns, even in new information they haven't
encountered before. This ability to learn and adapt
makes CNNs a valuable tool in many areas of
research and technology. The image in Figure 2
illustrates how a CNN is constructed, emphasizing
the role of each component in pattern recognition.
Figure 2. Convolutional Neural Networks Architecture
Our study utilizes a specialized CNN to handle
chaotic data for generating encryption keys. The
network begins with two layers that identify
patterns. The first layer has 32 small pattern-finders,
while the second has 64. These layers employ ReLU
to enhance the network's understanding of complex
patterns. After detecting patterns, the network
organizes the information into a simple list. This list
then undergoes two additional processing steps. The
first step, with 256 units, further refines the patterns.
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.27
Zied Guitouni, Mohsen Machhout
E-ISSN: 2769-2507
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Volume 6, 2024
The final step, also with 256 units, determines the
likelihood of each potential outcome.
In the following section, we introduce an
innovative approach to creating encryption keys.
Our method combines two powerful concepts:
chaotic systems and neural networks. By bringing
these two concepts, we've developed a way to
generate secure keys from random data. The chaotic
system provides unpredictability, while the neural
network learns to work with this randomness
efficiently. What makes our method special is that
it's designed to work well on devices with limited
processing power. This is particularly useful for
Internet of Things (IoT) devices, which often have
constraints on their computing capabilities.
3 Chaotic Neural Key Generation
Algorithm
Our key generation method combines chaos theory
and machine learning to create secure encryption
keys. The main steps in the key generation process
outlined by this method are as follows:
Chaotic Sequence Creation: We use the Lorenz
system, a type of chaotic math model, to make a
long sequence of unpredictable numbers. We start
with a seed value and use special equations to
generate this sequence.
Data Preparation: We divide the chaotic
sequence into smaller chunks, each containing 8
numbers. These chunks become our input data. The
next number after each chunk is our target output.
We adjust these numbers to make them easier for
our neural network to process.
Neural Network Setup: We use a CNN for our
task. This type of network is good at finding
patterns in data. Our CNN has layers that look for
patterns and layers that make decisions based on
those patterns.
Training the Network: We teach our CNN using
the prepared data. The network learns to predict the
next number in the sequence based on the previous
8 numbers. We use a method called categorical
cross-entropy to measure how well the network is
learning.
Checking the Network: After training, we test the
CNN with new data to make sure it can accurately
predict numbers in the chaotic sequence. This step
ensures our network works well and isn't just
memorizing the training data.
Making the Encryption Key: Once we're sure our
network works well, we use it to predict new
numbers based on our chaotic sequence. We convert
these predictions to binary (1s and 0s) and mix them
with some additional random bits. This creates our
final encryption key.
This proposed method is particularly useful for
devices with limited processing power, like many
Internet of Things (IoT) devices. It creates strong,
secure keys without requiring a lot of computational
resources. The combination of chaos theory and
neural networks makes the keys hard to predict,
enhancing security.
4 Evaluation of the proposed method
In this section, we present the experimental
evaluation of the key generation method.
4.1 Evaluation Metrics
We evaluated and compared the neural network
architectures based on four key performance
metrics:
Accuracy: Accuracy measures the percentage of
predictions matching true labels. It is calculated as
the number of correct predictions divided by the
total number of samples. We tracked accuracy on
both the training and validation sets to gauge model
fitting and generalization respectively.
Loss: Loss quantifies the model's error during
training. We utilized categorical cross-entropy loss
which calculates the divergence between predicted
and true probability distributions. Lower loss values
indicate better fitting on the training data.
Validation Accuracy: To assess generalization,
we computed accuracy on a held-out validation set
not involved in training. This reflects the model's
ability to correctly generate cryptographic keys for
previously unseen input data, an important metric
for our application.
Validation Loss: Analogous to validation
accuracy, we measured loss on the validation set.
This allowed monitoring changes in out-of-sample
error to detect potential overfitting as training
progressed. A stable or decreasing validation loss
indicates the model is still learning useful patterns
rather than memorizing the training data.
We recorded accuracy and loss values at the end of
each training epoch and plotted them to visualize the
learning dynamics.
4.2 Training evaluation
To assess the sensitivity of the proposed algorithm
concerning key size, we conducted a series of
experiments using various key sizes. Figure 2 shows
the accuracy of our chaotic neural key generation
method for different key sizes
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.27
Zied Guitouni, Mohsen Machhout
E-ISSN: 2769-2507
234
Volume 6, 2024
Figure 3. Precision Variation with Varying Key Sizes
For all key sizes, we see a significant
improvement in accuracy as the model trains. The
256-bit key size performs best, reaching a final
training accuracy of 92.56% and a validation
accuracy of 91%. The 512-bit key size follows
closely, with 92.48% training accuracy and 91.10%
validation accuracy. The 128-bit and 1024-bit keys
also show good performance, with final training
accuracies above 91% and validation accuracies
above 88%. Interestingly, while larger key sizes
generally lead to better security, they don't always
result in higher accuracy in our model. This
suggests that a balance between key size and model
performance is crucial for optimal security in
resource-constrained IoT devices. Figure 4
illustrates the loss values for our chaotic neural key
generation method across different key sizes.
Figure 4. Loss Variation with Varying Key Sizes
According to Figure4, all key sizes show a
significant decrease in loss during training,
indicating that our model is learning effectively. The
256-bit key size demonstrates the best performance,
with the lowest final training loss of 0.2476 and
validation loss of 0.7513. The 512-bit key size
follows closely, achieving a final training loss of
0.2856 and the lowest validation loss of 0.4445.
Interestingly, while the 1024-bit key has the highest
initial loss, it still achieves a competitive final
training loss of 0.3102. However, its validation loss
remains higher at 1.3198, suggesting some
overfitting. The 128-bit key, despite its smaller size,
performs reasonably well with a final training loss
of 0.2532. These results suggest that medium-sized
keys (256 and 512 bits) offer the best balance
between model performance and potential security
for our IoT-focused key generation method.
Based on the results shown in Figures 3 and 4, we
can conclude that for IoT devices using our chaotic
neural key generation method, key sizes between
256 and 512 bits work best. These key sizes offer a
good balance between how well the model performs
and how secure the keys are. This balance is
important for IoT devices, which need strong
security.
4.3 Security Evaluation
In this subsection, we assess the security of the
key generation method. To evaluate the randomness
of the generated keys, we examine key aspects
including entropy variation, correlation variation,
and statistical tests using Diehard.
4.3.1 Entropy Variation
Entropy testing is a key metric for evaluating the
randomness and unpredictability of generated keys
[16]. Higher entropy values reflect a stronger degree
of randomness, which in turn enhances security. By
examining entropy variation, we can assess the
quality and strength of the chaotic neural key
generation process.
In our analysis, a chaotic system with a specific
seed was used to generate a series of chaotic values.
These values were fed into a neural network to
produce random keys. Entropy testing was then
performed on the keys generated for various key
lengths: 128, 256, 512, and 1024 bits.
Figure 5. Entropy Variation
International Journal of Electrical Engineering and Computer Science
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Figure 5 shows how entropy varies across these
different key sizes. The results provide important
insights into the security of our chaos-based neural
key generation method. We found a clear link
between key length and entropy: as the key length
increased, so did the entropy values, indicating
higher randomness and stronger security.
According to Figure 5, the minimum entropy
values recorded were 0.75, 0.72, 0.90, and 0.99 for
key lengths of 128, 256, 512, and 1024 bits,
respectively. The maximum entropy values rose
from 0.99 for the 128-bit key to 1.0 for the 1024-bit
key. Similarly, the average entropy values followed
the same pattern, with 0.94, 0.86, 0.96, and 0.99 for
the respective key lengths.
These results emphasize the importance of using
longer key lengths in chaos-based neural key
generation to boost entropy and enhance security.
Longer keys provide a larger key space, making it
harder for attackers to guess the key through brute-
force or statistical methods. The higher entropy
associated with longer keys improves randomness
and increases resistance to cryptographic attacks.
4.3.2 Correlation Variation
The correlation values observed during
cryptographic key generation are important
indicators of the quality and security of the process
[17]. In our study, we generated 1000 keys and
analyzed their correlation values. The results,
presented in Figure 6, provide valuable insights into
the performance of the key generation process.
Figure 6. Correlation Variation
The minimum correlation value of -0.25 and the
maximum of 0.24 highlight the effectiveness of the
key generation process in achieving bit
decorrelation. These values, close to ±0.25, show
that the bits making up the keys are well-separated
from one another, which is essential for preventing
the prediction or partial reconstruction of one key
based on another. Additionally, the average
correlation value of -0.005 indicates an almost
perfect statistical independence between the bits.
This level of independence ensures high entropy and
confusion in the generated keys, further
strengthening their security.
4.3.3 Diehard Test
The Diehard Test includes a series of statistical tests
designed to identify weaknesses or vulnerabilities in
random number generators [18]. By analyzing the
results of these tests, we can assess the strength of
the key generation process and its ability to
withstand statistical attacks.
Table 1 presents the outcomes of 15 Diehard
tests conducted on the generated keys. The results
show that the key generation process successfully
passed all 15 tests. The p-values from each test are
higher than the significance threshold, indicating
that the keys demonstrate high-quality randomness
and meet the required standards. This consistent
performance across all tests reinforces the reliability
and effectiveness of the key generation method.
TABLE 1
Results of Diehard Tests for Key Generation Using FFNN
P-Value
Result
0.241
0.633
0.400
0.625
0.312
0.097
0.345
0.879
0.588
0.196
0.584
0.701
0.931
0.106
0.783
0.727
Passed
Passed
Passed
Passed
Passed
Passed
Passed
Passed
Passed
Passed
Passed
Passed
Passed
Passed
Passed
Passed
These findings are important for the security of
IoT devices, where randomness plays a critical role
in ensuring the confidentiality and integrity of
sensitive data. The results demonstrate that the
proposed algorithm generates random keys with
sufficient randomness, contributing to enhanced
security for IoT devices.
The positive Diehard test results boost
confidence in the proposed method, showing its
suitability for cryptographic applications in IoT
devices. Secure key generation enables IoT devices
to establish safe communication, authenticate users,
and protect sensitive data from unauthorized access
and cyberattacks. Therefore, these findings
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.27
Zied Guitouni, Mohsen Machhout
E-ISSN: 2769-2507
236
Volume 6, 2024
positively impact the overall security and privacy of
IoT ecosystems.
5 Conclusion
This paper introduced a new approach to
cryptographic key generation for IoT devices by
integrating chaotic systems with neural networks.
Our method addresses the specific security needs of
resource-limited IoT devices while ensuring strong
and efficient key generation. The evaluation of our
chaotic neural key generation algorithm produced
promising outcomes. For example, with a 256-bit
key, we achieved a training accuracy of 92.56% and
a validation accuracy of 91%. Entropy analysis
showed high levels of randomness, with mean
entropy values ranging from 0.86 for 256-bit keys to
0.99 for 1024-bit keys. Correlation testing revealed
an average correlation of -0.005, demonstrating
strong statistical independence between key bits.
Additionally, our method passed all 15 Diehard
statistical tests, proving its ability to generate high-
quality random keys. These findings indicate that
our approach offers an effective solution for secure
key generation in IoT environments. Its balance
between security and efficiency makes it well-suited
for devices with limited computational resources.
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International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.27
Zied Guitouni, Mohsen Machhout
E-ISSN: 2769-2507
237
Volume 6, 2024
.Contribution of individual authors to
the creation of a scientific article
(ghostwriting policy)
• Zied Guitouni and Mohsen Machhout proposed the
idea of the paper.
• Zied Guitouni carried out the simulation and
optimization of the proposed algorithm.
• All authors organized and executed the
experiments in Section 4.
• All authors were responsible for the paper's
writing and editing.
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.27
Zied Guitouni, Mohsen Machhout
E-ISSN: 2769-2507
238
Volume 6, 2024
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
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