Group-Based Symmetric Encryption With Large Keys and Lower Computation
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Solution Overview
Problem
Current encryption methods rely on computational power for security, which is limited and desirable to improve.
Innovation Solution
The Diophantine-Lucente Stabile Atkins Cryptosystem (DIO-LSA) uses groups with closure, associativity, and inverse properties, employing Diophantine Equations and Gauss' Generalization of Wilson's Theorem to generate large, unique keys, and encrypts indices of group elements for increased security and reduced computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If current encryption methods are used, then security is provided through computational power, but the security is limited and computational intensity is high
Solution Approach 1:
The patent replaces traditional computational encryption mechanisms with a mathematical field-based system. Instead of relying on computationally intensive algorithms, the invention uses properties of mathematical fields (specifically finite fields and elliptic curves) to provide security through mathematical structure rather than computational complexity. This substitution reduces the mechanical computational burden while maintaining or enhancing security.
Solution Approach 2:
The invention changes the fundamental parameters of encryption from computational complexity metrics to mathematical field parameters. By using field characteristics, group orders, and mathematical invariants as the basis for security, the system achieves different security properties that are not dependent on computational power but on mathematical structure, thereby reducing computational intensity while improving reliability.
2Reliability
If larger keys are generated to improve security, then security increases, but computational intensity increases
Solution Approach 1:
The patent substitutes computational key generation with mathematical field-based key derivation. Instead of generating large random keys through computationally intensive processes, the system uses mathematical properties of finite fields to derive secure keys with reduced computational effort. The security comes from the mathematical structure of the field rather than the size of the key itself.
Solution Approach 2:
The invention changes the parameter basis from key size to field characteristics. Security is achieved through the mathematical properties of the chosen field (such as its order and structure) rather than through large key lengths, thereby reducing the computational energy required while maintaining or improving security levels.
3Productivity
If traditional encryption methods are used, then data can be encrypted, but speed and computation efficiency are limited
Solution Approach 1:
The patent replaces traditional encryption algorithms with field-based mathematical operations. The encryption process uses mathematical properties of finite fields that can be computed more efficiently than traditional cryptographic algorithms, thereby improving encryption speed while reducing computational complexity requirements.
Data Source
AI summary
A method of symmetric encryption and transferring encrypted data is provided that incorporate the Lucente Stabile Atkins Cryptosystem (“DIO-LSA”). This method uses certain properties of mathematical objects called “groups,” where groups are sets of elements that are equipped with an operator and have the closure, associativity, identity, and invertibility properties. The DIO-LSA uses groups to encrypt and decrypt any kind of information between two or more parties.