Prime Number Generation for Portable RSA Key Pairs
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Solution Overview
Problem
The generation of prime numbers for RSA key pairs on portable devices is time-consuming and indeterministic, leading to variable and potentially excessive calculation times, which can exceed acceptable limits in certain applications, and existing solutions like pre-stored seeds or interruptible calculations come with implementation and resource constraints.
Innovation Solution
A method that retrieves or generates prime numbers within a predetermined time frame, stores intermediate results for later use, and pre-calculates a reserve of prime numbers to ensure consistent generation times, allowing for efficient use of device resources and reducing the risk of exceeding critical time limits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If iterative prime number generation is performed on portable devices, then cryptographic security is improved through hardware protection, but calculation duration becomes excessively long and indeterministic
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing multiple candidate prime numbers in the device's memory before they are needed for key generation. When a prime number is required for RSA key pair generation, the system retrieves pre-computed candidates and performs minimal verification instead of executing the full iterative generation process, thereby dramatically reducing calculation time while maintaining security requirements
2Loss of time
If pre-stored seeds are used to reduce generation time, then calculation duration is reduced, but implementation complexity and resource constraints increase
Solution Approach 1:
The patent uses copying by storing multiple pre-computed candidate prime numbers in the device's memory. These candidates are generated in advance during device manufacturing or initialization and stored for rapid retrieval. This approach avoids the complexity of interruptible calculations or external server communication while providing deterministic fast generation, as the candidates are simply copied from storage to use
3Adaptability or versatility
If interruptible calculation with context storage is implemented, then generation can be resumed later, but application constraints and operational complexity increase
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing multiple candidate prime numbers before they are needed. This eliminates the need for interruptible calculation mechanisms, context storage, and resumption logic. The system simply retrieves pre-computed candidates when needed, providing both speed and operational simplicity without requiring complex state management
Data Source
AI summary
The present invention relates to a method to generate prime numbers on board a portable device, said method comprising the steps of, each time at least one prime number is requested:when available, retrieve results from previously performed derivation calculation or, if not, select a start point for derivation;process derivation calculation to converge towards a prime number;if a prime number is found, store it and restart derivation calculation from a new start point;stop the derivation calculation after a predetermined amount of time;store intermediate results to be used a next time a prime number will be requested;output a stored prime number.