Analog Processor for Integer Factorization
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Solution Overview
Problem
Current methods for factoring large integer numbers, particularly biprimes, are inefficient and require substantial computational power, making them unsuitable for secure encryption schemes as they can be decrypted with significant effort, compromising data security over time.
Innovation Solution
A method involving the creation of a factor graph mapped onto an analog processor, where the processor is initialized and evolved to find the prime factors of a number, utilizing quantum devices and classical computing elements to optimize the factorization process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If classical computing methods are used to factor large biprime numbers, then the encryption security is maintained for a certain period, but the computational time required becomes excessively long and the security period is limited
Solution Approach 1:
The patent replaces classical digital computing mechanisms with an analog physical system. The factorization problem is mapped to a physical Hamiltonian system where quantum mechanical evolution naturally performs the factorization computation, substituting sequential digital logic with parallel quantum mechanical processes.
Solution Approach 2:
The patent transforms the computational parameters by mapping integer factorization variables to continuous physical parameters in the Hamiltonian system. The discrete mathematical problem is converted into a continuous physical evolution problem, allowing exploitation of quantum mechanical effects for computation.
2Strength
If larger biprime numbers are used for encryption, then security strength increases, but the difficulty and time required for factoring increases exponentially
Solution Approach 1:
The patent replaces exponentially complex digital factorization algorithms with a polynomial-time quantum mechanical evolution process. The physical system's natural evolution follows the Hamiltonian dynamics, providing a fundamental mechanism change that avoids exponential complexity growth.
Solution Approach 2:
The patent employs dynamic quantum mechanical evolution instead of static algorithmic computation. The system evolves continuously in time according to the Schrödinger equation, allowing the computational process to adapt and explore the solution space dynamically rather than following fixed computational steps.
3Productivity
If more computational resources are allocated to factorization, then the speed of factoring improves, but the cost and complexity of the system increases
Solution Approach 1:
The patent creates a universal analog quantum processor that can solve factorization problems of varying sizes using the same physical system. The Hamiltonian formulation allows the same device architecture to handle different input sizes by adjusting parameters rather than scaling hardware complexity.
Solution Approach 2:
The patent uses quantum mechanical superposition to effectively create multiple computational paths simultaneously. The quantum state represents multiple possible factorization paths in parallel, allowing the system to explore many solutions at once without proportionally increasing physical resources.
Data Source
AI summary
Systems, methods and apparatus for factoring numbers are provided. The factoring may be accomplished by creating a factor graph, mapping the factor graph onto an analog processor, initializing the analog processor to an initial state, evolving the analog processor to a final state, and receiving an output from the analog processor, the output comprising a set of factors of the number.