CC BY
1
№ 9 (126)
сентябрь, 2024 г.
DOI - 10.32743/UniTech.2024.126.9.18205
PROBLEMS IN GENERATING PSEUDORANDOM NUMBER SEQUENCES
AND THEIR SOLUTIONS
Alisher Salaev
Assistant at the Department of Information Security,
Urgench branch
of the Tashkent University of Information Technologies named after Muhammad al-Khorezmi, Uzbekistan, Urgench
ПРОБЛЕМЫ ГЕНЕРАЦИИ ПОСЛЕДОВАТЕЛЬНОСТЕЙ ПСЕВДОСЛУЧАЙНЫХ ЧИСЕЛ
И ИХ РЕШЕНИЯ
Салаев Алишер Куралбаевич
ассистент кафедры «Информационная безопасность»,
Ургенчский филиал
Ташкентского университета информационных технологий
имени Мухаммада ал-Хорезми, Республика Узбекистан, г. Ургенч
ABSTRACT
The generation of pseudorandom number sequences is a critical aspect of many computational processes, including cryptography, simulations, and statistical sampling. However, generating truly random sequences using deterministic algorithms poses significant challenges. One of the primary issues is the potential for seed selection, which can result in easily guessable sequence. Additionally, many PRNGs suffer from short periods, meaning the sequence eventually repeats, which is undesirable in many applications, particularly in cryptography where predictability can lead to security vulnerabilities. Another challenge is the bias in PRNGs, where certain numbers or patterns appear more frequently than others, undermining the uniformity of the sequence.
АННОТАЦИЯ
Генерация последовательностей псевдослучайных чисел является критически важным аспектом многих вычислительных процессов, включая криптографию, моделирование и статистическую выборку. Однако генерация действительно случайных последовательностей с использованием детерминированных алгоритмов создает значительные проблемы. Одной из основных проблем является потенциальный выбор начального числа, который может привести к легко угадываемой последовательности. Кроме того, многие PRNG страдают от коротких периодов, что означает, что последовательность в конечном итоге повторяется, что нежелательно во многих приложениях, особенно в криптографии, где предсказуемость может привести к уязвимостям безопасности. Еще одной проблемой является смещение в PRNG, где определенные числа или шаблоны появляются чаще других, что подрывает однородность последовательности.
Keywords: sequence generation, pseudorandom numbers, solutions.
Ключевые слова: генерация последовательностей, псевдослучайные числа, решения.
1. Introduction
Pseudorandom number sequence are foundation to many digital processes, powering applications from encryption and simulations to randomized algorithms and gaming. These sequences are generated by pseudorandom number generation (PRNGs), which, despite their deterministic nature, strive to produce sequences that closely resemble true randomness. However, the task of generating these sequences is fraught with challenges, including predictability, bias, and security vulnerabilities. This article explorers the key problems in generating pseudorandom number sequences and the solutions that have been developed to address them.
2. Key problems in generating pseudorandom number sequences
1. Predictability of sequences: PRNGs operate on deterministic algorithms, meaning that the sequences they generate are inherently predictable if the initial seed is known. This predictability is a major issue, particularly in cryptography, where the security of encrypted data depends on the unpredictability of the keys used. If an attacker can guess or determine the seed, they can potentially recreated the entire sequence and compromise the system.
2. Seed selection and reuse: The quality of a pseudorandom sequence is heavily dependent on the choice of the seed. A poorly chosen seed, such as one
Библиографическое описание: Salaev A. PROBLEMS IN GENERATING PSEUDORANDOM NUMBER SEQUENCES AND THEIR SOLUTIONS // Universum: технические науки : электрон. научн. журн. 2024. 9(126). URL: https://7universum.com/ru/tech/archive/item/18205
№ 9(126)
ceffraGpb, 2024 r.
that is predictable or reused across multiple instances, can lead to sequences that are vulnerable to attack. Seed reuse is especially problematic in cryptographic contexts, where the same sequence of "random" numbers could be exploited to break encryption schemes.
3. Finite Periodicity: Every PRNG has a finite period, after which the sequence of numbers it generates begins to repeat. While this period can be extremely long in well-designed generators, it remains a limitation. In applications requiring extensive or continuous streams of random numbers, periodicity can introduce undesirable patterns of correlations that affect the outcome of simulations or the security of cryptographic systems.
4. Bias in generated sequences: Ideally, a PRNG should produce a uniform distribution of numbers, with each possible value having an equal chance of appearing. However, some PRNGs exhibit bias, where certain numbers or sequences occur more frequently than others. This lack of uniformity can skew results in simulations, lead to biased statistical analyses, and reduce the security of cryptographic protocols by making certain outputs more predictable.
5. Security vulnerabilities: Beyond simple predictability, PRNGs can be vulnerable to various attacks if their internal states can be inferred or influenced. Cryptographically secure pseudorandom number generators (CSPRNGs) are designed to resist these attacks, but flaws in implementation, inadequate entropy sources, or weaknesses in the underlying alrorithm can still lead to significant security breaches.
3. Solutions to improve pseudorandom number generation
1. Improved seed generation techniques: A critical step in enhancing the security and quality of pseudorandom sequences is ensuring that the seed is truly random and unpredictable. Techniques for better seed generation include using entropy sources such as physical noise, user inputs, or hardware-based random number generators (RNGs). Additionally, seeds should be sufficiently large to prevent brute-force attacks and should never be reused across different instances or applications.
2. Use of cryptographically secure PRNGs (CSPRNGs): CSPRNGs are specifically designed to produce sequences that are indistinguishable from true random sequences and are resistant to prediction or reverse engineering. Algorithms like the Fortuna, Yarrow, and those based on cryptographic primitives such as AES or SHA-2 provide strong security guarantees. CSPRNGs are essential for applications where the quality of randomness is tied to security, such as in key generation, digital signatures, and secure communications.
3. Combining multiple PRNGs: Another approach to improving the robustness of pseudorandom sequence is to combine the outputs of multiple PRNGs. By mixing the outputs of different generators, it becomes more difficult for an attacker to predict the sequence, even if one of the generators is compromised. This method can also extend the effective period of the sequence and reduce bias by averaging out the weaknesses of individual PRNGs.
4. Hardware-based random number generators (HRNGs): HRNGs, which rely on physical processes
such as thermal noise or radioactive decay, offer a way to generate truly random seeds or augment the entropy of PRNGs. While HRNGs are typically slower and less practical for generating large quantities of random numbers, they are invaluable for seeding PRNG or providing additional randomness in high-security applications.
5. Periodically reseeding and entropy pooling: To mitigate the issue of finite periodicity, PRNGs can periodically reseeded with new, unpredictable values. Reseeding ensures that even if a sequence were to start repeating, new entropy would disrupt the pattern. Entropy pooling, where randomness is collected from various sources over time, can also help maintain the unpredictability of the PRNG's output.
6. Rigorous testing and validation: PRNGs must undergo extensive testing to ensure they meet the necessary standards for randomness, uniformity, and security. Tests like the Diehard tests, NIST randomness test, and TestU01 suite can be used to evaluate the quality of pseudorandom sequences. Cryptographic PRNGs should also be reviewed and validated by independent experts to detect any potential vulnerabilities or weaknesses in their design or implementation.
4. Conclusion
The generation of pseudorandom number sequence is a critical yet challenging task that underpins a wide array of applications, from cryptography and simulations to statistical modeling and gaming. The inherent difficulties in producing sequence that are both unpredictable and unbiased, while also secure against potential attacks, highlight the complexity of this endeavor. Problems such as seed predictability, finite periodicity, and biases can significantly undermine the reliability and security of systems that rely on pseudorandom numbers.
However, the development of advanced techniques and algorithms has provided effective solutions to these challenges. Improved seed generation methods, the use of cryptographically secure pseudorandom number generators (CSPRNGs), and the incorporation of hardware-based randomness are among the key strategies that have enhanced the quality and security of pseudorandom sequences. Combining multiple PRNGs and periodically reseeding with fresh entropy further bolsters the robustness of these sequences.
Despite the progress made, the continuous evolution of technology, especially with the advent of quantum computing, presents new challenges that must be addressed to maintain the integrity of pseudorandom number generation. Ongoing research, rigorous testing, and validation are essential to ensure that PRNGs remine effective in providing the randomness necessary for secure and reliable digital systems.
In conclusion, while the problem associated with generating pseudorandom number sequences are significant, the solution developed thought a combination of mathematical rigor, algorithmic innovation, and practical engineering offer a robust foundation for addressing these challenges. As technology advances, the field must remine vigilant adapting and evolving to meet the demands of increasingly complex and security-critical applications.
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