Deterministic Prime Number Generation via PRNG and PNG Modules

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Solution Overview

Problem

Existing methods for generating prime numbers for RSA key pairs are either deterministic but rely on unproven hypotheses or are probabilistic, leading to inefficiencies and increased costs due to the need for secure hardware storage, which limits their use in mobile devices.

Innovation Solution

A deterministic derivation function using a pseudorandom number generator (PRNG) and prime number generator (PNG) modules to produce prime numbers based on a seed value and bit length, allowing for efficient generation and recovery of prime numbers, simplifying device certificate management and reducing storage requirements.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If probabilistic prime number generation methods are used, then key generation speed is improved, but hardware storage requirements increase and reliability decreases

Engineering Contradiction:

Improvekey generation speedVSAvoidprime number generation reliability

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The prime number generation process is segmented into two distinct phases: a deterministic generation phase that creates initial prime candidates with mathematical guarantees, and a verification phase that confirms their validity. This segmentation allows the system to maintain reliability through deterministic methods while achieving speed improvements through efficient verification procedures.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The system performs preliminary deterministic generation of prime candidates before final verification, establishing a foundation of mathematically guaranteed prime numbers. This preliminary action ensures reliability is maintained while the subsequent verification process can operate more efficiently, improving overall key generation speed.

Inventive Principle:

Principle #10Preliminary action

2Reliability

If deterministic prime number generation based on unproven hypotheses is used, then reliability is improved, but computational complexity increases

Engineering Contradiction:

Improveprime number generation reliabilityVSAvoidcomputational complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

Instead of relying on unproven mathematical hypotheses that increase computational complexity, the system copies and adapts proven deterministic primality testing methods. By using established mathematical algorithms with verified correctness, the system maintains reliability without the burden of unproven theoretical foundations, thereby reducing computational complexity.

Inventive Principle:

Principle #26Copying

3Reliability

If secure hardware storage is implemented for key pairs, then security is improved, but device cost and complexity increase

Engineering Contradiction:

ImprovesecurityVSAvoidhardware storage requirements

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The system replaces the mechanical/hardware storage system with a software-based deterministic generation system. By substituting physical secure storage hardware with software algorithms that deterministically generate and verify prime numbers, the system maintains security through mathematical guarantees while eliminating the need for complex hardware storage infrastructure, thereby reducing device cost and complexity.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

4Reliability

If RSA key pairs are stored on separate hardware storage, then security is improved, but mobile device space is limited and cost increases

Engineering Contradiction:

ImprovesecurityVSAvoidstorage space

Core Design Contradiction:

ReliabilityVSVolume of moving object

Solution Approach 1:

The system extracts the essential security function from bulky hardware storage and concentrates it into compact software-based deterministic prime generation algorithms. By taking out the core security mechanism and implementing it through software rather than hardware storage, the system maintains security while dramatically reducing the volume of storage space required, making it suitable for mobile devices with limited capacity.

Inventive Principle:

Principle #2Taking out (Extraction)

Data Source

PatentEP3535653B1Method and system for deriving deterministic prime number

Publication Date: 2022.11.30 HUAWEI INT PTE LTD

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AI summary

This invention relates a system generating a prime number comprising a pseudorandom number generator (PRNG) module and a prime number generator (PNG) module. The PRNG module is configured to: initialise the pseudorandom number generator (PRNG) module; receive a request from the PNG module, the request containing a bit length of the pseudorandom number required; generate the required bit length of pseudorandom number; transmit a response containing the generated bit length of pseudorandom numbers to the PNG module. The PNG module is configured to: transmit the request containing the bit length of the pseudorandom numbers required; receive the response from the PRNG module; assign the pseudorandom numbers in the response to form raw data PPP; set a least significant bit (LSB) and most significant bit (MSB) of PPP as 1 to obtain a first big odd number denoted as PP; and execute an algorithm to determine a first big prime number starting from odd number PP.