LSA Asymmetric Encryption Using Gauss Wilson Theorem
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Solution Overview
Problem
Existing encryption algorithms fail to effectively address the prime factorization problem and do not utilize Gauss's Generalization of Wilson's Theorem, which limits their security and computational efficiency, especially in the context of quantum computing.
Innovation Solution
The Lucente Stabile Atkins (LSA) algorithm employs a novel asymmetric encryption method using multiplicative and additive groups, specifically generating an encryption key and calculating properties to ensure the cyclic group U(n) is used for secure data sharing, incorporating Gauss's Generalization of Wilson's Theorem for enhanced security and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing encryption algorithms (RSA, Diffie-Hellman, ElGamal) are used, then key exchange and encryption can be performed, but they are susceptible to the prime factorization problem and vulnerable to quantum computing attacks
Solution Approach 1:
The patent changes the mathematical foundation from prime factorization-based security to a security model based on Gauss's Generalization of Wilson's Theorem applied to multiplicative groups U(n). This parameter change in the underlying mathematical problem provides resistance to both classical prime factorization attacks and quantum computing threats while maintaining algorithmic structure.
Solution Approach 2:
The patent extracts and removes the dependency on prime factorization problems from the encryption scheme. By using Gauss's Generalization of Wilson's Theorem instead, it takes out the vulnerable mathematical foundation while retaining the essential cryptographic functionality of key exchange and encryption.
2Reliability
If traditional asymmetric encryption algorithms are used, then secure communication can be established, but computational intensity is high
Solution Approach 1:
The patent changes the computational parameters by using Gauss's Generalization of Wilson's Theorem which provides a more efficient computational path for key generation and encryption compared to traditional algorithms. This reduces the computational energy required while maintaining security through the mathematical properties of multiplicative groups.
3Reliability
If existing algorithms are used, then encryption can be performed, but they do not utilize Gauss's Generalization of Wilson's Theorem limiting their security
Solution Approach 1:
The patent fundamentally changes the mathematical parameter basis from standard prime factorization to Gauss's Generalization of Wilson's Theorem. This provides enhanced security by utilizing properties of multiplicative groups U(n) where the product of elements has specific congruence properties, making the system resistant to traditional factorization attacks.
Data Source
AI summary
A method of asymmetrical encryption and transferring encrypted data is provided that incorporates the Lucente Stabile Atkins Cryptosystem (“LSA” algorithm). This algorithm uses certain properties of mathematical objects called “groups”. Groups are sets of elements that are equipped with an operator and have the closure, associativity, identity, and invertibility properties. The LSA algorithm uses groups to encrypt and decrypt (secret sharing) any kind of symbolic information between two or more parties.