Identity-Based Public Key Cryptosystem Parameter Generation
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Solution Overview
Problem
Existing public key cryptography methods are computationally intensive and time-consuming, particularly for small-scale devices, and are vulnerable to attacks, making them unsuitable for secure information transmission over insecure networks.
Innovation Solution
A method and system for generating cryptographic parameters using a private_IGTABLE and public_IGTABLE based on an Euler totient function of a composite number, reducing computational time and resources required for key generation, while maintaining security through the use of a master public key, master private key, and identity-based public key cryptography.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional public key cryptography methods are used, then security is maintained, but computational time and resources increase significantly
Solution Approach 1:
The patent segments the key generation process into two distinct tables: a private lookup table containing random numbers and a public lookup table containing modular exponentiations. This segmentation allows the system to pre-compute and store values in an optimized structure, reducing the computational burden during actual key generation operations while maintaining cryptographic security.
Solution Approach 2:
The patent implements preliminary action by pre-computing the private lookup table with random numbers and the public lookup table with modular exponentiations during system initialization. These pre-computed tables are stored for future use, eliminating the need to perform computationally intensive operations during real-time key generation, thus reducing computational time while preserving security.
2Reliability
If traditional public key cryptography methods are used, then security is maintained, but device complexity and resource requirements increase
Solution Approach 1:
The patent divides the cryptographic system into segmented lookup tables (private and public) that organize computational data in a structured manner. This segmentation simplifies the device architecture by replacing complex real-time computation structures with organized data storage structures, reducing overall system complexity while maintaining security through the mathematical properties embedded in the tables.
Solution Approach 2:
The patent creates simplified copies of cryptographic relationships through lookup tables that store pre-computed values. Instead of implementing complex cryptographic algorithms directly in hardware, the system uses tabulated copies of computational results that can be retrieved efficiently, reducing device complexity while preserving the security properties of the original cryptographic methods.
3Reliability
If traditional public key cryptography methods are used, then security is maintained, but scalability to small-scale devices is reduced
Solution Approach 1:
The patent implements scalable cryptographic functionality by copying essential computational relationships into compact lookup tables that can be stored in limited memory resources of small-scale devices. This approach allows resource-constrained devices to perform secure cryptographic operations using simplified table lookups rather than full cryptographic algorithm implementations, enhancing scalability while maintaining security.
Solution Approach 2:
The patent changes the operational parameters of the cryptographic system by transitioning from real-time computation of cryptographic functions to retrieval of pre-computed values from lookup tables. This parameter change reduces the computational resources required, enabling the system to scale to small-scale devices with limited processing power and memory while preserving security through the mathematical foundations embedded in the table structures.
Data Source
AI summary
A method for generating cryptographic parameters comprises generating a private_IGTABLE based on an Euler totient function of a composite number (φ(n)), where the private_IGTABLE includes a plurality of random numbers (x). Further, a public_IGTABLE based on the private_IGTABLE, a composite number (n), and a group generator element (g) is generated, where the public_IGTABLE includes a corresponding modular exponentiation under modulo n for each of the plurality of random numbers with g as base. Further, a public key of a user is computed based on the public_IGTABLE, an identity number (ID) corresponding to the user, and n. Further, a secret key of the user is generated based on the ID, a master private key, the φ(n), and the private_IGTABLE. Thereafter, the cryptographic parameters are provided to the user for performing encryption and decryption, where the cryptographic parameters include at least one of the ID, the public key, and the secret key.