Decrypting Data Without Private Key via Inverse Decimal Search
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Solution Overview
Problem
Existing public key encryption systems, such as RSA, face challenges in decrypting data when the private key is lost or unavailable, leading to inaccessible encrypted information and potential ransom scenarios.
Innovation Solution
A computing device calculates the private key by obtaining an encrypted message with a public key, determining its inverse, and searching for prime factors within a designated range using a 'jump' calculation and geometric factorization to derive the private key for decryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If RSA encryption with large prime numbers is used, then security is improved, but the difficulty of factoring increases making decryption impossible without the private key
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing the decimal period of the inverse of the public key before the factoring operation. This pre-computed decimal period serves as a prepared resource that enables the subsequent factorization process to proceed efficiently by providing a structured search space, rather than attempting to factor the large quasi-prime number directly without any preparatory work.
Solution Approach 2:
The patent applies segmentation by dividing the large quasi-prime number into smaller manageable components through its decimal period representation. By segmenting the factorization problem into searching for prime factors within the constrained decimal period rather than attempting to factor the entire large number at once, the complex task becomes broken down into smaller, more tractable sub-problems that can be solved systematically.
2Reliability
If the private key is stored securely in a computing device, then security is improved, but access to encrypted data is lost if the device is lost or destroyed
Solution Approach 1:
The patent applies the intermediary principle by introducing the decimal period of the inverse of the public key as a mediating mathematical structure between the public key and the private key. Instead of directly storing or relying on the private key, the system uses this intermediate decimal period representation that can be computed from the public key alone, serving as a bridge that enables private key recovery without requiring the original private key storage.
3Reliability
If a hacker encrypts data with a public key, then security is improved, but the data becomes inaccessible if the private key is unavailable
Solution Approach 1:
The patent applies mechanics substitution by replacing the mechanical/physical storage mechanism (private key stored in a device) with a mathematical computation mechanism (decimal period calculation and factorization algorithm). Instead of relying on physical possession of the private key, the system substitutes a mathematical process that can derive the necessary information from the public key through decimal period analysis and systematic factorization.
Data Source
AI summary
A method for decrypting encrypted data/message whereby a computing device derives the prime numbers that are used to make up a public key by searching the decimals of the inverse of the quasi-prime number that is the public key. The computing devices designates a search range around a jump point of the decimals of the inverse of the public key and searches within the search range for prime numbers by testing them against the quasi-prime. When the prime numbers are found, the computing device then uses them to derive the private key and decrypt the data.