Prime Integer Verification via Linked Lists for Lower-Cost Encryption
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Solution Overview
Problem
Cryptographic systems using fixed prime integers are vulnerable to attacks due to high computational cost ratio, increasing motivation for attackers and risk over time, and improvements in computing power may compromise security by making discrete logarithms easier to compute.
Innovation Solution
A device verifies new prime integers using a linked list of potential primes, iteratively applying Pocklington's primality test or lookup operations to ensure the integer is suitable for cryptographic protocols, conserving computing resources and enhancing security by frequent updates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If fixed prime integers are used in cryptographic systems, then security is maintained, but computational cost increases and security becomes vulnerable over time
Solution Approach 1:
The patent applies dynamics by transitioning from static fixed prime integers to dynamic randomly generated prime integers. The system now generates new primes frequently using probabilistic algorithms (Miller-Rabin, Solovay-Strassen) and maintains them in a cache, making the cryptographic parameters changeable and adaptive rather than fixed, thereby reducing computational cost while maintaining security
Solution Approach 2:
The patent implements preliminary action by pre-generating and caching random prime integers before they are needed for cryptographic operations. The system generates primes in advance, stores them in a cache with metadata including generation algorithms and parameters, and retrieves them during protocol execution, avoiding costly on-demand prime generation
2Device complexity
If fixed prime integers are used in cryptographic systems, then system simplicity is maintained, but security risk increases due to attacker motivation
Solution Approach 1:
The system becomes dynamic by frequently updating prime integers used in cryptographic protocols. Instead of relying on fixed, well-known primes that attackers can target, the system generates new random primes and uses them temporarily, then discards them. This dynamic approach increases security against targeted attacks while maintaining manageable complexity through automated cache management
Solution Approach 2:
The patent introduces an intermediary mechanism - a prime cache system with metadata structures that store generation algorithms and parameters. This intermediary layer manages the complexity of random prime generation and validation, shielding the core cryptographic protocols from direct interaction with complex prime generation logic while providing secure, varied primes
3Reliability
If random prime integers are generated and used frequently, then security is enhanced, but computational overhead increases
Solution Approach 1:
The patent reduces computational overhead through preliminary action by generating and caching random prime integers in advance before they are needed for cryptographic operations. The cache stores primes along with their generation metadata, allowing efficient retrieval and validation during protocol execution without repeating expensive generation and validation processes
Solution Approach 2:
The system implements self-service through automated cache management where the prime cache automatically tracks which primes have been used, validates them against security policies, and manages their lifecycle. The metadata stored with each prime includes generation algorithm information and parameters, enabling automated verification and management without external intervention
Data Source
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AI summary
A device may receive a set of cryptographic parameters associated with an integer, wherein the set of cryptographic parameters includes a linked list of potential prime integers, in an order, used to generate the integer. The device may determine, iteratively and in the order, whether each potential prime integer included in the linked list of potential prime integers is a prime integer using a primality test or a lookup operation based on a set of proven prime integers. The device may determine whether the integer is a proven prime integer based on determining whether each potential prime integer included in the linked list of potential prime integers is a prime integer. The device may authorize, when the integer is a proven prime integer, the integer for use in a cryptographic protocol.