Monday, October 30, 2017

Logistic Map, Chaos, Randomness and Quantum Algorithms

The logistic map is the most basic recurrence formula exhibiting various levels of chaos depending on its parameter. It has been used in population demographics to model chaotic behavior. Here we explore this model in the context of randomness simulation, and revisit a bizarre non-periodic random number generator discovered 70 years ago, based on the logistic map equation. We then discuss flaws and strengths in widely used random number generators, as well as how to reverse-engineer such algorithms. Finally, we discuss quantum algorithms, as they are appropriate in our context.
  • Java, Perl and Excel random number generators compared
  • Historical considerations
  • Backdoor planted by the NSA in some of these systems
  • Original material on complex random number generators
  • Image encryption
  • Periodicity detection, disctinctness quantum algorithm (big data)  
  • Practical solutions
  • Need for new programming language for quantum computing
  • Cool animated gif
  • Post-quantum cryptography
  • Generators based on irrational numbers
The article is not too long, as most of the technical details are provided in the numerous references. It covers many topics ranging from computer science, algorithms, big data, to probability theory and mathematics. The level is simple enough to be read by non-experts, yet of great value for the experts as well. Click here to read this new article.

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