Public Key Retrieval with Relationship Matrices for Memory-Constrained Systems
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Solution Overview
Problem
Existing cryptographic systems face challenges in storing and updating public keys due to memory constraints, especially in memory-constrained environments like Electronic Control Units (ECUs) in vehicles, which is costly and cumbersome.
Innovation Solution
A method and system that generates a relationship matrix between public and private cryptographic keys, allowing retrieval of public keys using only partial components of private keys, reducing memory requirements and simplifying key updates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If public cryptographic keys are stored in a memory constrained system, then security verification is enabled, but memory space consumption increases significantly
Solution Approach 1:
The public key is segmented into two components: a first component (e.g., high-order bytes) and a second component (e.g., low-order bytes). The system stores only the first component in memory, while the second component is derived on-demand using a hash function. This segmentation reduces the stored data size while maintaining the ability to reconstruct the full public key for security verification operations.
Solution Approach 2:
A hash function serves as an intermediary mechanism that enables reconstruction of the second component of the public key from the first component. This intermediary allows the system to store minimal data (first component) while still accessing the complete public key information when needed for verification, thus resolving the contradiction between storage efficiency and security functionality.
2Reliability
If public cryptographic keys are updated frequently to prevent key expiration, then security is maintained, but operational complexity and cost increase
Solution Approach 1:
By segmenting the public key into storable and derivable components, the system simplifies key update operations. Only the first component needs to be updated and stored, while the second component can be regenerated through hashing. This reduces the complexity of key management during updates compared to storing and replacing entire key pairs.
Solution Approach 2:
The system changes the representation parameters of the public key from storing the complete key to storing only a compressed form (first component). This parameter change enables more efficient key updates, as the system only needs to update the stored first component rather than managing complete key pairs, thereby reducing operational complexity while maintaining security.
3Ease of operation
If complete public and private key pairs are stored, then cryptographic operations are straightforward, but storage requirements become prohibitive in constrained systems
Solution Approach 1:
The system extracts only the essential first component of the public key for storage, removing the need to store the complete public key or private key pair. The extracted first component contains sufficient information to reconstruct the full public key when needed, thereby simplifying storage requirements while preserving cryptographic functionality.
Solution Approach 2:
Instead of storing the actual complete public key, the system stores a compressed representation (first component) that can be copied and stored efficiently. When needed, the full public key is reconstructed by combining the stored first component with the derived second component, effectively creating a functional copy without the storage overhead of the original complete key.
Data Source
Figure 1a
Figure 1b~1c
Figure 1d
AI summary
Present invention discloses a method and a system for retrieving public keys in a memory constrained system. The method comprising 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. Thereafter, the method comprising creating at least one relationship matrix comprising the first cryptographic component of each of the plurality of public cryptographic keys and corresponding private cryptographic keys based on predetermined rules. Subsequently, the method comprising receiving a first cryptographic component and a second cryptographic component of a private cryptographic key when a public cryptographic key is required and retrieving the public cryptographic key based on the first cryptographic component and the second cryptographic component of the private cryptographic key using the relationship matrix and the predetermined rules.