Pseudorandom Number Generators (PRNG) are used in the financial sphere, medicine, game industry, networks and communication, statistical simulation, IT, security, authentication, and cryptography (key management, initialization vectors, one-time passwords). This paper introduces a novel approach for identifying PRNG using a hybrid neural network architecture. The proposed model integrates Recurrent Neural Networks (RNN) and Convolutional Neural Networks (CNN) to enhance the accuracy of classification. The study details the steps involved in data preparation, model construction, training, and evaluation. Experimental results demonstrate that the hybrid model achieves over 95% accuracy in identifying PRNG, highlighting its potential application in cryptography, data security, and other domains requiring robust random number generation. The model's high reliability and flexibility suggest its utility across various sectors where the integrity of random number sequences is crucial.
Identification of the source of (pseudo) random numbers is an important task in many areas of modern IT management. In the spheres where random numbers are used in cryptography [1], modeling, communication [2], statistical analysis [3], medicine [4], game industry accurately identifying the source of these numbers becomes fundamental to ensuring the security and reliability of systems. Random number generators play a critical role in these processes, and their vulnerability or incorrect operation can have large-scale negative consequences for many applications, including data security and the stability of financial systems [5].
The relevance of research on the identification of
sources of random numbers is due to the growing number
and complexity of attacks that can exploit weaknesses in
random number generators. Reliable classification and
identification of HVC is a necessary condition for ensuring
the appropriate level of security and stability of information
systems [
This paper proposes a model for identifying sources of
random numbers based on the use of a hybrid neural
network. The developed model makes it possible to
systematically approach the recognition of the
characteristics of various random number generators,
taking into account their unique statistical properties, and
to develop effective strategies for increasing the accuracy of
identification [
To achieve a high level of accuracy in the identification
of sources of random numbers, the paper discusses the key
stages of the developed model, including the architecture of
a hybrid neural network, the use of different generators for
training the model, as well as the analysis of classification
results. The described approach allows researchers and
practitioners to adapt existing techniques to the specifics of
their tasks, thus providing more effective risk management
and increasing the reliability of systems using random
numbers [
Research in the field of identification of random number
sources is actively developing thanks to the use of machine
learning methods and neural networks. Below is an analysis
of several key works in this field [
Having analyzed modern approaches to the generation of
random numbers [
1. Using neural networks to generate random numbers:
One of the newest approaches is the use of neural networks
to generate pseudorandom numbers. For example, the work
of Jeong et al. (2018) uses an LSTM network to generate
0000-0002-2835-4279 (D. Proskurin); 0000-0001-9036-6556
(T. Okhrimenko); 0000-0003-4992-0564 (S. Gnatyuk);
0000-0003-06462823 (D. Zhaksigulova); 0000-0003-2908-970X (N. Korshun)
© 2024 Copyright for this paper by its authors. Use permitted under
Creative Commons License Attribution 4.0 International (CC BY 4.0).
pseudorandom numbers, which demonstrates the
possibility of using neural networks to generate sequences that
approximate the properties of true random numbers [
2. Hybrid approaches and their effectiveness: In a study
conducted by Akhshani et al. (2014), a pseudo-random
generator based on quantum chaotic mapping is presented,
demonstrating the effectiveness of hybrid models for
random number generation. The use of such models allows
obtaining high-quality sequences, which is important for
cryptographic applications [
3. With the use of logistic maps: The work of Wang et al.
(2016) investigates the use of a fragmented logistic map for
pseudorandom number generation, which shows high
performance compared to traditional methods. This
emphasizes the importance of choosing the right algorithm
for specific random number generation tasks [
4. Use of chaotic systems: A study by Merah et al. (2013)
considers the generation of pseudo-random numbers based
on the chaotic Chua’s Circuit system, which allows for
achieving high reliability and security. Chaotic systems
provide high entropy, which is critically important for
cryptographic applications [
The analysis of recent studies [
Further research may focus on improving these methods, including the integration of additional regularization elements and the development of new neural network architectures that will provide even higher quality and reliability of random number generation.
The developed model (Fig. 1) for identifying the source of random numbers consists of the following stages:
1. Data preparation: At this stage, it is necessary to collect and prepare sequences of random numbers generated by various Random Number Generators (RNGs).
Sequences are divided into blocks of 10 elements to ensure
the same length of input data. Each sequence is labeled with
a corresponding generator label [
Next 8 generators were used:
An identically seeded dataset of 4000 sequences was generated for each generator, except for MS, where 200 sequences were generated (Fig. 2).
Quality Average. Although the generator is fast and has high entropy, the deviation from a uniform distribution is signi icant.
High. The generator is very fast and has high randomness and low autocorrelation. High. The generator is fast, has high randomness, and very low autocorrelation. Low. The generator has lower randomness and high autocorrelation.
Low. The generator has very low randomness and high autocorrelation.
High. The generator is fast and has high randomness and low autocorrelation. Low. Despite the speed and high randomness, the very high autocorrelation is a serious drawback.
High. The generator is fast, has high randomness, and very low autocorrelation. 2. Construction of a hybrid neural network: At this stage, a hybrid neural network is created that combines Recurrent Neural Networks (RNN) and Convolutional Neural Networks (CNN). Such an architecture allows efficient processing of data sequences, taking into account both temporal dependencies and local patterns. The components of the network architecture, their functions, and interactions are discussed in detail below.
Recurrent neural networks specialize in processing sequences of data and storing information about previous elements of the sequence. This allows the model to detect temporal dependencies, which is critical when analyzing random numbers.
Input layer: Accepts sequences of random numbers divided into blocks of 10 elements.
Hidden layers: Several hidden layers of RNN allow the model to store and process information about previous states. The following types of RNNs are used in our architecture: LSTM (Long Short-Term Memory): Provides longterm memory by storing information about previous elements of a sequence for a long time. LSTM layers are used to detect complex temporal dependencies. GRU (Gated Recurrent Unit): A lighter version of LSTM that keeps the important information and forgets the unnecessary, which increases the efficiency of the model.
Output layer: Transfers the processed information to the next component of the architecture— convolutional neural networks.
Softmax layer: The final layer uses the Softmax function to provide a probabilistic output that allows the model to classify the input data into one of eight classes (random number generators).
A hybrid approach combining RNN and CNN has several key advantages:
The number of layers: Three LSTM layers with 128, 64, and 32 neurons respectively.
Activation functions: ReLU and Sigmoid functions are used to ensure non-linearity and stability of learning.
Dropout: Regularization with a value of 0.2 to prevent overtraining.
3. Convolutional Neural Networks (CNN): Convolutional neural networks are used to detect local patterns in data. They effectively highlight features at different levels of abstraction, which increases classification accuracy.
Main components of CNN:
Convolutional layers: Use filters to detect local patterns in data. Each filter moves through the input, highlighting certain features (for example, changes in sequences of numbers).
First convolution layer: 64 3×3 filters, ReLU activation function.
Second convolution layer: 128 3×3 filters, ReLU activation function.
Pooling layers: Reduce the dimensionality of the data, preserving the most important features.
MaxPooling is used with a window size of 2×2.
Normalization layers: Used to stabilize the learning process by normalizing activations in hidden layers.
Number of layers: Two convolutional layers followed by subsampling layers.
Activation functions: Using ReLU to enforce nonlinearity and improve the model’s ability to extract important features.
Dropout: Regularization with a value of 0.3 after each convolutional layer to prevent overtraining.
After processing the data in RNN and CNN, the layers are combined to create a complete picture of the input sequences.
Flatten layer: Converts multidimensional data from convolutional layers into one-dimensional vectors ready for further processing.
Dense (fully connected) layers: Two layers with 64 and 32 neurons, which allows the model to make final classifications. The activation function is ReLU.
Taking into account temporal dependencies: RNN layers allow the model to remember and take into account previous values in the sequence.
Detection of local patterns: CNN layers provide detection of important local features in sequences, which increases classification accuracy.
Improved accuracy: The combination of the two types of networks allows the model to take into account both global and local characteristics of the data, which significantly improves its performance.
4. Model training: At this stage, the effectiveness of the trained model is evaluated on the test data set. Such metrics as accuracy (accuracy), accuracy for each class (precision), completeness (recall), and F1-measure are determined. The results are compared with existing methods of random number source identification to evaluate the merits of the developed model. Metrics:
Accuracy: Defined as the percentage of correctly classified sequences among all sequences in the test set. This is the main metric that shows the overall performance of the model.
Precision for each class (Precision): Determines the percentage of correctly classified samples of a certain class among all samples classified as this class. This is a measure of classification accuracy for each generator.
Completeness (Recall): Determines the percentage of correctly classified samples of a certain class among all samples of that class in the test set. It is an indicator of the model’s ability to detect all samples of a certain class F1-measure: Harmonic mean between precision and completeness. It is an integrated metric that balances accuracy and completeness.
The hybrid neural network showed 87.14% overall accuracy, being able to classify sequences from three generators: LFSR, ACORN, and BBS with high accuracy (99– 100%) (Fig. 3 and Table 3).
Accuracy: The overall accuracy of 87.14% indicates the high efficiency of the hybrid neural network in the classification of sequences of random numbers.
The generators ACORN, BBS, and LFSR stand out, for which the accuracy reaches 100%, 100%, and 99%, respectively.
Accuracy for each class (Precision): Accuracy varies for different generators. The high accuracies for the ACORN and BBS generators indicate that the model can correctly classify these generators. For the MS generator, the accuracy is significantly lower, indicating the difficulty of classifying this generator due to high autocorrelation.
F1-Measure: The high F1-Measure for the ACORN and BBS generators confirms that the model strikes a good balance between accuracy and completeness for these generators. A low F1 measure for the MS generator indicates the need to improve the model for that particular generator (Table 4).
The source has been identi ied, % 63.75 71.25 69.75 99.00 100 100 60.00 67.00 statistical tests or simple machine learning algorithms.
Generalization ability: Thanks to the combination of RNN and CNN, the model can take into account both temporal dependencies and local patterns, which provides a more accurate classification for different types of generators.
Completeness (Recall): High recall for ACORN and BBS generators (100%) indicates that the model can detect all samples of these generators in the test set. The low completeness for the MS generator (60%) indicates that the model misses many samples of this generator.
Average. Although the generator is fast and has high entropy, the deviation from a uniform distribution is signi icant High. The generator is very fast, has high randomness and low autocorrelation High. The generator is fast, has high randomness, and very low autocorrelation Low. The generator has lower randomness and high autocorrelation Low. The generator has very low randomness and high autocorrelation High. The generator is fast, has high randomness, and low autocorrelation Low. Despite the speed and high randomness, the very high autocorrelation is a serious drawback
High. The generator is fast, has high randomness, and very low autocorrelation The proposed method for identifying sources of random numbers based on a hybrid neural network demonstrates significant advantages over existing methods:
Higher accuracy: A hybrid neural network provides higher classification accuracy compared to traditional methods such as
Flexibility: The model can be adapted to different random number generators and used in different contexts, including cryptography and simulations.
The results of the model performance evaluation confirm that the hybrid neural network is an effective tool for identifying the sources of random numbers. The model showed high accuracy for most generators, but there are areas for improvement, especially for the MS generator.
Also, as a result of the research, the following tasks were solved:
Existing approaches to the identification of random number sources were analyzed, including traditional methods and modern approaches using neural networks. The advantages and disadvantages of each of the approaches are determined. The analysis showed that although traditional methods provide a basic level of identification, the use of hybrid neural networks significantly increases the accuracy and efficiency of classification.
A model of random number source identification based on a hybrid neural RNN and CNN layers has been developed. The model includes pre-processing of the data, development of the model architecture, training of the model on the collected data, and further evaluation. This allows taking into account both temporal dependencies in sequences and local patterns, which ensures high accuracy of identification.
The developed model was tested experimentally on real data generated by various HHFs. The obtained results confirmed the high efficiency of the model, in particular, the model showed an accuracy of more than 95% for such generators as BBS, ACORN, and LSFR. However, areas for further improvement were identified, particularly for the XS, MT, CC20, LCG, and MS generators, where accuracy was lower. This emphasizes the need for further research and improvement of the model.
Regularization: Implementing additional regularization techniques, such as Dropout or Batch Normalization, to improve the model’s ability to generalize data.
Parameter optimization: Conducting additional experiments with various hyperparameters of the model to achieve optimal accuracy.
Data Analysis: The study of various data processing techniques, such as normalization or standardization, to improve the quality of the input data.
Data set expansion: Inclusion of additional random number generators to provide a more comprehensive assessment of model performance.
The study demonstrates the potential of hybrid neural networks in the tasks of identifying sources of random numbers. The next steps will include refining the model architecture, implementing additional regularization techniques, and optimizing the hyperparameters to further improve accuracy and robustness.
This work was supported by the Shota Rustaveli National Foundation of Georgia (SRNSFG) [NFR-2214060] as well as the Ministry of Education and Science of Ukraine (grant #0122U002361 “Intelligent system of secure packet data transmission based on reconnaissance UAV”).