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Related Concept Videos

Algebraic Expressions01:26

Algebraic Expressions

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Algebraic expressions are essential in mathematics. They represent relationships through variables, constants, and operations. These expressions help describe patterns and solve problems in various mathematical fields. Understanding their components, classifications, and operations allows for efficient simplification and manipulation.Each algebraic expression consists of individual parts, including numbers and symbols, that work together to form meaningful mathematical statements. The numerical...
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SFG Algebra01:16

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In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
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The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as:  with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...
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In the middle of the nineteenth century, it was observed that two trains passing each other at a high relative speed get pulled towards each other. The same occurs when two cars pass each other at a high relative speed. The reason is that the fluid pressure drops in the region where the fluid speeds up. As the air between the trains or the cars increases in speed, its pressure reduces. The pressure on the outer parts of the vehicles is still the atmospheric pressure, while the resultant...
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There are many devices and situations in which fluid flows at a constant height and so can be analyzed using Bernoulli's principle. These devices include, but are not limited to, entrainment devices and fluid flow measuring devices.
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Pseudorandom number generator based on the Bernoulli map on cubic algebraic integers.

Asaki Saito1, Akihiro Yamaguchi2

  • 1Department of Complex and Intelligent Systems, Future University Hakodate, 116-2 Kamedanakano-cho, Hakodate, Hokkaido 041-8655, Japan.

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Summary

This study introduces a novel pseudorandom bit generator utilizing chaotic orbits of the Bernoulli map. It offers superior statistical properties and avoids sequence overlaps, outperforming the Mersenne Twister.

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Area of Science:

  • Number Theory
  • Chaos Theory
  • Cryptography

Background:

  • Pseudorandom bit generators are crucial for simulations and secure communication.
  • Existing generators like Mersenne Twister have limitations.
  • Chaotic systems offer a potential source for high-quality randomness.

Purpose of the Study:

  • To develop a novel pseudorandom bit generator based on chaotic dynamics.
  • To address limitations of current pseudorandom number generators.
  • To ensure unbiased seed selection and prevent sequence overlaps.

Main Methods:

  • Utilizing chaotic true orbits of the Bernoulli map on real cubic algebraic integers.
  • Developing a specific seed selection method for unbiased initial points.
  • Analyzing the memory usage and growth of points on true orbits.

Main Results:

  • The generator precisely simulates the Bernoulli map, producing ideal random binary sequences.
  • A method for unbiased seed selection and overlap avoidance was established.
  • Upper bounds for memory usage related to orbit point representation were determined.
  • Extensive tests showed good statistical properties, outperforming Mersenne Twister MT19937.

Conclusions:

  • The developed generator offers a high-quality alternative for pseudorandom binary sequence generation.
  • The method provides a robust approach to seed selection, enhancing sequence reliability.
  • This chaotic system-based generator demonstrates a promising advantage over established methods.