تقرير
Pseudo-random number generation with $\beta$-encoders
| العنوان: | Pseudo-random number generation with $\beta$-encoders |
|---|---|
| المؤلفون: | Kalle, Charlene, Verbitskiy, Evgeny, Zeegers, Benthen |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems |
| الوصف: | The $\beta$-encoder is an analog circuit that converts an input signal $x \in [0,1]$ into a finite bit stream $\{b_i\}$. The bits $\{b_i\}$ are correlated and therefore are not immediately suitable for random number generation, but they can be used to generate bits $\{a_i\}$ that are (nearly) uniformly distributed. In this article we study two such methods. In the first part the bits $\{a_i\}$ 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 $b_1, \ldots, b_m$ are needed to correctly determine the first $n$ bits $a_1,\ldots,a_n$. 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 $b_1,\ldots,b_m$ using modern cryptographic techniques. Comment: 12 pages, 2 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2303.13170 |
| رقم الأكسشن: | edsarx.2303.13170 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |