Random Variable Generation with Infinite Outcomes
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Solution Overview
Problem
Conventional random number generators face challenges in generating numbers from an infinite range due to the impossibility of achieving a uniform probability distribution and physical hardware constraints, such as large numbers exceeding available memory space.
Innovation Solution
A computer-implemented method using a convergent infinite series to create a discrete probability distribution with an infinite sample space, assigning equal probabilities to finite elements and derived probabilities to infinite elements, and estimating the probability of failure through integration approximation, allowing for the generation of discrete random variables within hardware limitations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a random number generator is designed to generate numbers from an infinite range, then the entropy and security of the generated keys are improved, but a uniform probability distribution cannot be achieved and hardware storage constraints are violated
Solution Approach 1:
The patent applies local quality by creating different probability distribution characteristics for different ranges of the infinite sample space. Specifically, it uses a convergent infinite series (such as geometric series) to assign probabilities that decrease as values increase, creating a non-uniform distribution that is locally optimized for both security and hardware compatibility. This resolves the contradiction by accepting non-uniform distribution globally while maintaining high entropy through the infinite range.
Solution Approach 2:
The patent changes the probability distribution parameter from uniform to a convergent series-based distribution. By using parameters from a convergent infinite series (where the sum of probabilities equals 1), the system can generate numbers from an infinite range while ensuring the probability distribution is mathematically valid and computationally manageable within hardware constraints.
2Reliability
If a random number generator is designed to generate numbers from an infinite range, then the entropy and security of the generated keys are improved, but the generated numbers exceed available memory space
Solution Approach 1:
The patent applies partial action by generating random numbers from an infinite theoretical range but practically limiting the output to values that fit within hardware memory constraints. The convergent infinite series naturally concentrates probability mass on smaller values, so most generated numbers will be small enough to store, while the theoretical infinite range provides the entropy benefit. This resolves the contradiction by achieving partial utilization of the infinite range that satisfies both entropy requirements and storage limitations.
3Volume of stationary object
If conventional random number generators use finite range with uniform distribution, then hardware storage constraints are satisfied, but the entropy and security are limited
Solution Approach 1:
The patent transitions from a finite-dimensional uniform distribution to an infinite-dimensional convergent series distribution. By moving to another mathematical dimension (from finite to infinite sample space), the system achieves higher entropy while the convergent nature of the series ensures that practical outputs remain within hardware storage capabilities. This dimensional change resolves the contradiction between storage limits and entropy requirements.
Data Source
AI summary
Embodiments of the invention provide random number generators and methods that are able to generate numbers with infinite possible outcomes while being able to estimate efficiently the probability of random number generation failure due to hardware constraint(s).