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Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences.

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Summary

Researchers explored auto-correlation functions for m-bit random numbers derived from chaotic binary sequences. They found that m-bit sequence auto-correlations can be controlled by adjusting the properties of the underlying binary sequences.

Keywords:
auto-correlation functionchaotic binary sequencem-bit sequencerandom number generation

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Area of Science:

  • Chaos theory
  • Information theory
  • Cryptography

Background:

  • Understanding the statistical properties of random number sequences is crucial for various applications, including cryptography and simulations.
  • Auto-correlation functions are key metrics for assessing the randomness and predictability of sequences.
  • Chaotic systems offer a potential source for generating high-quality random numbers.

Purpose of the Study:

  • To theoretically derive and numerically verify the auto-correlation functions of m-bit random numbers generated from m chaotic binary sequences.
  • To demonstrate the controllability of auto-correlation properties in m-bit sequences by manipulating the underlying binary sequences.
  • To investigate the distribution properties of the generated m-bit sequences.

Main Methods:

  • Theoretical derivation of the auto-correlation function for m-bit sequences based on the auto-correlation functions of constituent binary sequences.
  • Generation of m chaotic binary sequences using one-dimensional nonlinear maps with prescribed auto-correlation properties.
  • Numerical experiments to compute and compare theoretical and experimental auto-correlation values, and to analyze sequence distributions.

Main Results:

  • A simple formula for the auto-correlation function of m-bit sequences was derived, showing direct dependence on the auto-correlation of binary sequences.
  • Numerical experiments confirmed that generated m-bit sequences exhibit auto-correlation properties matching theoretical predictions.
  • Uniform distribution of m-bit sequences was achieved when the underlying binary sequences were balanced and independent.

Conclusions:

  • The auto-correlation properties of m-bit random sequences generated from chaotic binary sequences are controllable.
  • One-dimensional chaotic maps can be utilized to generate m-bit sequences with desired auto-correlation characteristics.
  • Balanced and independent binary sequences lead to uniformly distributed m-bit sequences, essential for robust random number generation.