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Shannon Entropy Loss in Mixed-Radix Conversions
1Hume Center for National Security and Technology, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
This study models converting base-2 pseudorandom number generators (PRNGs) for mixed-radix applications like card shuffling. It precisely quantifies entropy loss in this conversion, optimizing parameters for casino shuffling applications.
Area of Science:
- Cryptography and Information Theory
- Applied Mathematics
Background:
- Pseudorandom number generators (PRNGs) are crucial for simulations and games.
- Mixed-radix systems are used in applications like card shuffling.
- Entropy loss during data conversion impacts the randomness of generated sequences.
Purpose of the Study:
- To model the translation of base-2 PRNGs to mixed-radix domains.
- To precisely calculate Shannon entropy loss in mixed-radix conversion.
- To optimize parameters for applications like card shuffling in casinos.
Main Methods:
- Developed a translation model for base-2 PRNGs to mixed-radix domains.
- Derived a precise formula for Shannon entropy loss in surjective mappings.
- Analyzed the impact of domain size (2^J) on entropy loss.
- Validated the formulation using a card-shuffling algorithm simulation.
Main Results:
- Calculated a more precise formula for Shannon entropy loss, accounting for variable radix 'n'.
- Derived a tighter bound on entropy loss for surjective mappings.
- Demonstrated that increased source domain size (J) leads to decreased entropy loss.
- Specified optimal parameters for simulating card shuffling with different PRNGs.
Conclusions:
- The derived formula provides a more accurate assessment of entropy loss in mixed-radix conversions.
- Increased source domain size is key to minimizing entropy loss.
- The findings are applicable to low-power implementations in casino environments, ensuring quantifiable randomness.
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