Pseudo-random number generation with -encoders
The [Formula: see text]-encoder is an analog circuit that converts an input signal [Formula: see text] into a finite bit stream [Formula: see text]. The bits [Formula: see text] are correlated and therefore are not immediately suitable for random number generation, but they can be used to generate b...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2024-12-01
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| Series: | International Journal of Mathematics for Industry |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2661335224500266 |
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| author | Charlene Kalle Evgeny Verbitskiy Benthen Zeegers |
| author_facet | Charlene Kalle Evgeny Verbitskiy Benthen Zeegers |
| author_sort | Charlene Kalle |
| collection | DOAJ |
| description | The [Formula: see text]-encoder is an analog circuit that converts an input signal [Formula: see text] into a finite bit stream [Formula: see text]. The bits [Formula: see text] are correlated and therefore are not immediately suitable for random number generation, but they can be used to generate bits [Formula: see text] that are (nearly) uniformly distributed. In this paper, we study two such methods. In the first part the bits [Formula: see text] are defined as the digits of the base-2 representation of the original input x. Under the assumption that there is no noise in the amplifier we then study a question posed by Jitsumatsu and Matsumura on how many bits [Formula: see text] are needed to correctly determine the first n bits [Formula: see text]. In the second part, we show this method fails for random amplification factors. Nevertheless, even in this case, nearly uniformly distributed bits can still be generated from [Formula: see text] using modern cryptographic techniques. |
| format | Article |
| id | doaj-art-855edb482fe94d66b04dcfec664a90a0 |
| institution | Kabale University |
| issn | 2661-3352 2661-3344 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | International Journal of Mathematics for Industry |
| spelling | doaj-art-855edb482fe94d66b04dcfec664a90a02025-01-31T06:15:28ZengWorld Scientific PublishingInternational Journal of Mathematics for Industry2661-33522661-33442024-12-01160110.1142/S2661335224500266Pseudo-random number generation with -encodersCharlene Kalle0Evgeny Verbitskiy1Benthen Zeegers2Mathematisch Instituut, Leiden University, Niels Bohrweg 1, 2333CA Leiden, The NetherlandsMathematisch Instituut, Leiden University, Niels Bohrweg 1, 2333CA Leiden, The NetherlandsMathematisch Instituut, Leiden University, Niels Bohrweg 1, 2333CA Leiden, The NetherlandsThe [Formula: see text]-encoder is an analog circuit that converts an input signal [Formula: see text] into a finite bit stream [Formula: see text]. The bits [Formula: see text] are correlated and therefore are not immediately suitable for random number generation, but they can be used to generate bits [Formula: see text] that are (nearly) uniformly distributed. In this paper, we study two such methods. In the first part the bits [Formula: see text] are defined as the digits of the base-2 representation of the original input x. Under the assumption that there is no noise in the amplifier we then study a question posed by Jitsumatsu and Matsumura on how many bits [Formula: see text] are needed to correctly determine the first n bits [Formula: see text]. In the second part, we show this method fails for random amplification factors. Nevertheless, even in this case, nearly uniformly distributed bits can still be generated from [Formula: see text] using modern cryptographic techniques.https://www.worldscientific.com/doi/10.1142/S2661335224500266-encoderbinary expansionsLochs’ Theoremrandom number generation |
| spellingShingle | Charlene Kalle Evgeny Verbitskiy Benthen Zeegers Pseudo-random number generation with -encoders International Journal of Mathematics for Industry -encoder binary expansions Lochs’ Theorem random number generation |
| title | Pseudo-random number generation with -encoders |
| title_full | Pseudo-random number generation with -encoders |
| title_fullStr | Pseudo-random number generation with -encoders |
| title_full_unstemmed | Pseudo-random number generation with -encoders |
| title_short | Pseudo-random number generation with -encoders |
| title_sort | pseudo random number generation with encoders |
| topic | -encoder binary expansions Lochs’ Theorem random number generation |
| url | https://www.worldscientific.com/doi/10.1142/S2661335224500266 |
| work_keys_str_mv | AT charlenekalle pseudorandomnumbergenerationwithencoders AT evgenyverbitskiy pseudorandomnumbergenerationwithencoders AT benthenzeegers pseudorandomnumbergenerationwithencoders |