Wave-Based Prime Factorization Using Zero-Crossing Detection

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Solution Overview

Problem

Traditional computers face increased computation times as the number of inputs grows, particularly in complex tasks like prime factorization, which is time-consuming for large integers and affects cryptographic protocols.

Innovation Solution

A wave-based computer system that generates prime waves and a dividend wave to detect zero-crossings, allowing for the determination of prime factors in a manner independent of input size, using oscillators, phase adjustors, and zero-crossing detectors.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If traditional binary logic computation is used, then the computer can perform various functions, but the computation time increases more quickly as the number of inputs increases

Engineering Contradiction:

Improvecomputational functionalityVSAvoidcomputation time

Core Design Contradiction:

Adaptability or versatilityVSLoss of time

Solution Approach 1:

The patent replaces traditional binary logic-based mechanical/electronic computation with a wave-based computational system. The wave computer uses continuous wave signals and their interactions (superposition, interference, phase relationships) to perform computations, fundamentally substituting the discrete binary logic mechanism with a continuous wave phenomenon-based mechanism. This allows certain computations like prime factorization to occur in constant time by exploiting wave properties rather than sequential logic operations.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Productivity

If prime factorization is performed on large integers using traditional methods, then the computation can be completed, but the time required increases significantly with input size

Engineering Contradiction:

Improvefactorization capabilityVSAvoidfactorization time

Core Design Contradiction:

ProductivityVSLoss of time

Solution Approach 1:

The wave computer utilizes oscillating wave signals with specific frequencies representing integers and their factors. By generating waves at frequencies corresponding to potential factors and observing their interaction with the dividend wave, the system performs factorization through vibrational resonance principles. When a wave frequency matches a factor of the dividend, constructive interference patterns emerge that can be detected, enabling factorization in constant time independent of the dividend's magnitude.

Inventive Principle:

Principle #18Mechanical vibration

3Loss of time

If wave-based computation is used, then prime factorization can be performed in constant time, but the device complexity increases

Engineering Contradiction:

Improvecomputation timeVSAvoidsystem complexity

Core Design Contradiction:

Loss of timeVSDevice complexity

Solution Approach 1:

The wave computer employs a universal wave generation and detection mechanism that can handle multiple computational tasks. The same core components (wave generators, transmission medium, detectors) serve both prime factorization and other computational functions by adjusting wave frequencies and detection parameters. This multi-functionality reduces the need for specialized hardware for each computation type, managing device complexity while maintaining constant-time performance for factorization.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

Enables prime factorization in constant time, improving computational efficiency and potentially breaking current cryptographic protocols by reducing the time required for large integer factorization.

Implementation Method 1

a plurality of prime oscillators, each of the prime oscillators configured to generate a corresponding one of the prime waves having a frequency corresponding to a prime number, and a dividend oscillator configured to be tuned to generate the dividend wave to have a frequency that corresponds to the dividend

Methodology Applied

Scientific EffectElectromagnetic oscillation:

Implementation Method 2

detect zero-crossings of each of the prime waves and the dividend wave, and determine prime factors of the dividend based on the detected zero-crossings

Methodology Applied

Scientific EffectWave zero-crossing detection:

Data Source

PatentUS20240126510A1Method and system for wave-based computation

Publication Date: 2024.04.18 CALECTIVE LLC

AI summary

Methods and systems for wave-based computation are provided. In one aspect, a wave-based computer includes an input circuit configured to receive a dividend and generate a plurality of prime waves and a dividend wave based on the received dividend, and a transmission circuit configured to receive the prime waves and the dividend wave from the input circuit. The wave-based computer further includes an output circuit configured to receive the prime waves and the dividend wave from the transmission circuit, detect zero-crossings of each of the prime waves and the dividend wave, and determine prime factors of the dividend based on the detected zero-crossings.