Random Number Sequence Periodicity Detection via Wigner Distribution
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Solution Overview
Problem
Current random number generators, both true and pseudorandom, face challenges in ensuring complete randomness due to biases and deterministic nature, with existing testing methods failing to effectively identify and correct periodicities in generated sequences.
Innovation Solution
A system and method that applies transformations such as the Wigner distribution and Hilbert transform to identify periodic segments in random number sequences, analyzing intensity values to detect deviations and correct periodicities, thereby enhancing the randomness of the generated sequences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If statistical tests are applied to verify random number generator output quality, then the ability to detect lack of randomness is improved, but the complexity of the testing system increases
Solution Approach 1:
The patent divides the random number sequence into segments and applies the Wigner distribution function to each segment to detect periodicities. This segmentation allows complex periodic patterns to be identified through localized analysis, improving detection accuracy without requiring analysis of the entire sequence at once.
Solution Approach 2:
The patent introduces the Wigner distribution function as an intermediary tool that transforms the random number sequence into a time-frequency representation. This intermediary transformation enables the detection of periodicities that are not immediately apparent in the original sequence, enhancing measurement precision while maintaining manageable system complexity.
2Reliability
If true random number generators are used to generate random numbers, then the randomness quality is improved, but sensitivity to external influences and hardware errors increases
Solution Approach 1:
The patent applies statistical tests and the Wigner distribution analysis as feedback mechanisms to detect periodicities and biases in the random number sequence. When periodicities are detected, the system can identify and correct these issues, providing feedback that improves reliability while monitoring for harmful external influences.
Solution Approach 2:
The patent replaces direct hardware-based random number generation with a software-based detection and correction system. By using the Wigner distribution function and statistical analysis, the system substitutes mechanical/hardware randomness with computational methods that can detect and correct periodicities, reducing sensitivity to hardware vulnerabilities.
3Stability of the object's composition
If pseudorandom number generators are used, then the deterministic nature is improved for reproducibility, but the ability to pass statistical randomness tests deteriorates
Solution Approach 1:
The patent applies preliminary statistical testing and Wigner distribution analysis to detect periodicities in the pseudorandom sequence before it is used. By performing this analysis in advance, the system can identify and correct deterministic patterns that would otherwise cause failure in statistical randomness tests, allowing PRNGs to maintain both reproducibility and test passage.
Data Source
AI summary
A system comprising at least one hardware processor and a non-transitory computer-readable storage medium having stored thereon program code, the program code executable by the at least one hardware processor to receive a sequence comprising n bits, apply a transformation to the sequence to obtain a time-frequency signal representation of the sequence, analyze the signal to measure one or more intensity values of the transformed sequence, and determine the presence of a periodic segment within the sequence when one of the intensity values deviates from a specified value range.