Graph-Based Encryption Keys Using Edwards Curves and Node Analysis
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Solution Overview
Problem
Modern cryptographic systems face limitations due to reduced computational capacity in electronic systems, limiting the potential length of encryption keys and relying on factoring or graphical curve equations, which are not sufficiently robust against reverse engineering.
Innovation Solution
The method employs hyperbolic random number generators to generate parabolic graphs, identifies best-connected nodes, and uses Edwards curve equations over a finite field to create a plane curve for encryption keys, reducing time complexity and enhancing encryption strength.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional cryptographic systems use multiplication of random numbers or graphical curve equations for encryption key generation, then encryption can be executed, but the encryption strength is insufficient against reverse engineering and computational capacity is limited
Solution Approach 1:
The patent segments the encryption process into multiple stages: generating parabolic graphs using hyperbolic random numbers, identifying best-connected nodes through depth-first search and topological sorting, extracting strongly-connected components, and creating plane curves over finite fields using Edwards curve equations. This segmentation allows each stage to be computationally efficient while collectively providing strong encryption.
Solution Approach 2:
The patent transitions from traditional one-dimensional number multiplication to two-dimensional parabolic graph representations, then to node connection analysis, and finally to plane curves over finite fields. This dimensional transformation enables stronger encryption by adding geometric and topological layers of complexity that are difficult to reverse engineer.
2Reliability
If encryption key length is increased to improve encryption strength, then security against reverse engineering improves, but computational capacity requirements increase which modern electronic systems cannot meet
Solution Approach 1:
The patent changes the parameters of encryption from traditional large-number multiplication to parabolic graph equations with specific geometric properties. By using vertex-parabolic equations and factored forms with controlled degrees, the system achieves strong encryption with smaller, more manageable numbers that modern computers can process efficiently.
Solution Approach 2:
The patent replaces traditional mechanical number-theoretic operations (multiplication and factoring) with geometric operations on parabolic graphs and plane curves. This substitution allows for stronger encryption mathematics that are easier to compute with modern electronic systems while maintaining security against reverse engineering.
3Ease of manufacture
If graphical curve equations are used for encryption key generation, then encryption can be implemented, but the equations are not sufficiently robust against reverse engineering
Solution Approach 1:
The patent employs asymmetric parabolic equations where the vertex form and factored form are not interchangeable. The depth-first search and topological sorting processes create asymmetric node connections that are easy to compute in one direction but difficult to reverse. The Edwards curve equations further enhance this asymmetry, providing robust encryption that resists reverse engineering attempts.
Solution Approach 2:
The patent introduces intermediate steps including depth-first search traversal, topological sorting, and strongly-connected component extraction between the parabolic graph generation and final plane curve creation. These intermediary processes add layers of computational complexity that make reverse engineering difficult while maintaining the feasibility of implementing the encryption system.
Data Source
AI summary
The present invention is a method for generating encryption using graph analysis to create geometric curves. This method increases the strength of encryption keys while maintaining reduced time complexity.