Dynamic Prime Generation for Cryptographic Security
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Solution Overview
Problem
Cryptographic systems based on fixed prime integers are vulnerable to attacks as improvements in computing power reduce the time required to break these systems, compromising security once a successful attack occurs.
Innovation Solution
A method involving a device that generates candidate prime integers using a combination of known prime integers and pseudorandom integers, employing a sieve for initial filtering and Galois registers or linear feedback shift registers to increase entropy and improve primality testing, allowing for the replacement of prime integers over time to enhance security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If fixed prime integers are used in cryptographic systems, then the system is simple to implement, but the security deteriorates over time as computing power improves
Solution Approach 1:
The patent applies dynamics by transitioning from fixed, static prime integers to a dynamic prime generation system that actively creates new primes based on pseudorandom numbers. The system generates candidate primes using the formula P = hR + 1 where h is a pseudorandom integer and R is a product of known primes, allowing the cryptographic parameters to evolve and adapt over time, thereby maintaining security against improving computational capabilities.
Solution Approach 2:
The patent implements parameter changes by varying the prime generation parameters including the pseudorandom integer h, the known prime product R, and the exponent k in the formula P = hR^k + 1. This allows the system to generate diverse prime candidates with different properties, making it computationally difficult to predict or reverse-engineer the prime generation process, thus maintaining security while remaining implementable.
2Reliability
If pseudorandom integers are used to generate candidate primes, then the security increases, but the computing resources required increase
Solution Approach 1:
The patent applies preliminary action by performing sieve testing on candidate primes before conducting full primality tests. The system first checks whether candidate primes pass basic divisibility tests against a sieve of primes, and only proceeds to more computationally intensive primality testing for candidates that pass the sieve. This staged approach filters out obviously composite numbers early, reducing overall computing resource consumption while maintaining high security through thorough testing of promising candidates.
Solution Approach 2:
The patent implements feedback mechanisms by using the results of primality tests to determine whether to continue generating new candidate primes or to accept a found prime. The system feedbacks based on test outcomes to adjust the prime generation process, and also uses feedback from cryptographic applications to determine when prime replacement is necessary, optimizing the balance between security and computational resource usage.
3Reliability
If prime integers are replaced regularly, then the security against computational attacks improves, but the system complexity increases
Solution Approach 1:
The patent applies self-service by implementing an automated prime generation and replacement system that manages its own operations without external intervention. The system automatically generates candidate primes, performs primality testing, validates found primes, and replaces existing primes in cryptographic applications based on predetermined criteria. This self-managing approach handles the complexity internally, maintaining high security through regular prime replacement while presenting a simple interface to external users.
Data Source
AI summary
A device may select a first pseudorandom integer within a range of integers. The device may generate a first candidate prime, based on the first pseudorandom integer, for primality testing. Based on determining that the first candidate prime fails a primality test, the device may select a second pseudorandom integer within the range of integers. The device may generate a second candidate prime, based on the second pseudorandom integer, for primality testing. The device may determine whether the second candidate prime satisfies the primality test. The device may selectively: re-perform, based on the second candidate prime failing the primality test, the selecting the second pseudorandom integer, the generating the second candidate prime, and the determining whether the second candidate prime satisfies the primality test, or using, based on the second candidate prime satisfying the primality test, the second candidate prime as a prime integer in a cryptographic protocol.