Transcendental Equation Pseudo Random Number Generator
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing random number generators, particularly pseudo random number generators (PRNGs), suffer from poor statistical behavior and limited sequence length, which can lead to repetition and inadequate randomness for various applications, including cryptographic and simulation purposes.
Innovation Solution
The method involves determining algebraic input parameter values for transcendental equations, calculating solutions to these equations, and generating pseudo random numbers based on the solutions, which can produce high-quality, statistically robust random number sequences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional PRNG algorithms (such as LCGs) are used, then the generation process is simple and fast, but the statistical behavior is poor and sequences repeat quickly
Solution Approach 1:
The patent changes the fundamental mathematical parameters from algebraic operations to transcendental operations. By using transcendental functions (exponential, logarithmic, trigonometric) instead of algebraic operations, the system achieves superior statistical properties and extended sequence lengths while maintaining computational feasibility through modern processing units.
Solution Approach 2:
The patent substitutes traditional mechanical/computational PRNG mechanisms with a mathematical model based on transcendental equations. This replacement transforms the generation process from iterative algebraic calculations to solving transcendental equations, fundamentally improving statistical behavior and sequence duration.
2Duration of action of stationary object
If PRNGs with large state are used, then the sequence length before repetition increases, but the memory requirements and computational overhead increase
Solution Approach 1:
The patent changes the mathematical foundation from algebraic to transcendental equations, which inherently provide extended sequence lengths without requiring proportionally increased memory states. The transcendental nature of the equations creates a vastly larger effective state space.
Solution Approach 2:
The patent transitions from discrete algebraic state transitions to continuous transcendental function evaluations, effectively adding a dimensional aspect to the random number generation. This allows for extended sequences by utilizing the continuous domain properties of transcendental functions.
3Reliability
If complex iterated calculations are used in PRNGs, then the output appears more random, but the computational time and processing power increase
Solution Approach 1:
The patent replaces complex iterative algebraic calculations with direct transcendental function evaluations. This substitution maintains high randomness quality through the inherent complexity of transcendental functions while reducing computational overhead by eliminating multiple iteration cycles.
Solution Approach 2:
The patent skips the traditional iterative approach by directly evaluating transcendental functions to generate random numbers. This rushing through the generation process achieves both high randomness quality and improved generation speed by avoiding redundant iterative steps.
Data Source
AI summary
Described embodiments relate to a pseudo random number generator (PRNG) system and a method for generating pseudo random numbers. The PRNG systems comprises one or more processors and memory comprising a non-transitory machine-readable medium storing instructions which, when executed by the one or more processors, causes the system to a) determine at least one algebraic input parameter value for a transcendental equation, wherein the transcendental equation comprises a transcendental function that is capable of generating transcendental number outputs from algebraic number inputs, b) calculate at least one solution to one or more transcendental equations based on the at least one algebraic input parameter value; and c) generate one or more pseudo random numbers based on the solution.