To the logical foundations of random number generator construction.
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| Title: | To the logical foundations of random number generator construction. |
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| Authors: | Enikeev, Ruslan1 (AUTHOR) |
| Source: | Journal of Logic & Computation. Jun2025, Vol. 35 Issue 4, p1-39. 39p. |
| Subjects: | Random number generators, Random numbers, Common misconceptions, Probability theory, Signal processing |
| Abstract: | This study explores fundamental aspects of probability theory within the framework of constructing random sequences or random number generators. We propose an interpretation of probability spaces and operations on formal events through the theory of formal languages, utilizing string manipulation techniques. As part of the research, we present a direct implementation of the discussed concepts in the form of a program that generates random numbers of the required type by processing signals from a sound card. Additionally, the problem of primality testing, which is particularly relevant to practical cryptographic applications, is addressed. We critically examine common misconceptions regarding the properties of Carmichael numbers and the application of Fermat's Little Theorem. Furthermore, we propose an efficient primality testing algorithm. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Abstract: | This study explores fundamental aspects of probability theory within the framework of constructing random sequences or random number generators. We propose an interpretation of probability spaces and operations on formal events through the theory of formal languages, utilizing string manipulation techniques. As part of the research, we present a direct implementation of the discussed concepts in the form of a program that generates random numbers of the required type by processing signals from a sound card. Additionally, the problem of primality testing, which is particularly relevant to practical cryptographic applications, is addressed. We critically examine common misconceptions regarding the properties of Carmichael numbers and the application of Fermat's Little Theorem. Furthermore, we propose an efficient primality testing algorithm. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 0955792X |
| DOI: | 10.1093/logcom/exae075 |
