Public Key Retrieval via Relationship Matrices in Memory-Constrained Systems
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Solution Overview
Problem
Existing cryptographic systems face challenges in managing memory constraints for storing and updating public cryptographic keys, particularly in vehicles, due to the large memory requirements and cumbersome update processes.
Innovation Solution
A method and system that generate and store public and private cryptographic keys in a memory-constrained system by characterizing them into first and second cryptographic components, creating a relationship matrix based on predetermined rules, and using this matrix to retrieve public keys from private keys, thereby reducing memory requirements and simplifying updates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If public cryptographic keys are stored in the system, then security verification is enabled, but memory space consumption increases significantly
Solution Approach 1:
The patent extracts only the necessary components for key retrieval. Instead of storing complete public keys, it stores a relationship matrix containing only the mapping relationships between private key components and public key components. When verification is needed, the public key is regenerated on-demand using the stored matrix and the private key components, thus extracting only the essential data needed for security verification while eliminating redundant storage.
Solution Approach 2:
The patent creates a simplified copy or representation of the key relationship through the relationship matrix. Rather than storing the actual public keys, it stores a matrix that enables reconstruction of public keys when needed. This copying approach maintains the functional capability for security verification while using minimal storage space, as the matrix is much smaller than storing complete key pairs.
2Reliability
If public cryptographic keys are updated frequently to prevent key expiration, then security is maintained, but update complexity and cost increase
Solution Approach 1:
The patent segments the key management process into two independent parts: the relationship matrix (which remains stable) and the public key generation function (which can be updated). When key updates are needed, only the public key generation logic needs to be updated, not the entire key storage system. This segmentation reduces update complexity as the stable matrix structure can be reused while only the generation algorithm needs modification.
Solution Approach 2:
The patent performs preliminary action by pre-computing and storing the relationship matrix that captures the mathematical relationships between key components. This preliminary setup enables rapid key generation and updates later without requiring complex real-time computations. The matrix is prepared in advance, so when updates are needed, the system can quickly adapt by using the pre-established relationships rather than computing everything from scratch.
3Measurement precision
If complete key pairs are stored for verification, then verification accuracy is ensured, but memory requirements become unfeasible
Solution Approach 1:
The patent transitions from storing keys in one dimension (direct storage of complete key pairs) to another dimension (mathematical relationships in a matrix structure). Instead of storing keys as flat data, it organizes them into a relationship matrix that captures the mathematical relationships between components. This dimensional transformation allows the system to maintain verification accuracy through mathematical relationships while dramatically reducing the storage footprint.
Solution Approach 2:
The patent changes the parameters of key storage from storing complete key values to storing relationship parameters in a matrix. Rather than storing the actual public key values which are large, it stores the mathematical relationships (parameters) that define how to derive public keys from private keys. This parameter change maintains verification accuracy because the relationships are preserved, while reducing memory requirements by storing only the essential relationship data.
Data Source
AI summary
Retrieving public keys in a memory constrained system is performed by generating a plurality of public cryptographic keys and private cryptographic keys using a cryptographic technique and characterizing each of the plurality of public cryptographic keys and corresponding private cryptographic keys into an associated first cryptographic component and a second cryptographic component. At least one relationship matrix, including the first cryptographic component of each of the plurality of public cryptographic keys and corresponding private cryptographic keys, is created based on predetermined rules. Subsequently, a first cryptographic component and a second cryptographic component of a private cryptographic key are received when a public cryptographic key is required, and the public cryptographic key is retrieved based on the first cryptographic component and the second cryptographic component of the private cryptographic key using the relationship matrix and the predetermined rules.