Key Generation Using Pre-calculated Subkey Groups
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Solution Overview
Problem
Existing ID-based cryptography schemes, such as TDL-IBC, require significant resources and time to generate private keys for users, leading to high costs as the number of users increases, due to the complexity of the discrete logarithm problem involved.
Innovation Solution
A key generation apparatus and method that identifies symbols from user identity information, derives permutations, and uses pre-calculated keys stored in subkey groups to efficiently generate cryptographic keys by applying mathematical transformations, reducing the computational burden and time required for key generation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If TDL-IBC scheme is used to generate private keys, then cryptographic security is improved, but key generation time and computational resources increase significantly
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing discrete logarithm values for all possible symbol permutations in a lookup table during system initialization. When a private key needs to be generated, the system simply queries the pre-computed table using the user ID as an index, avoiding time-consuming real-time discrete logarithm calculations while maintaining cryptographic security.
Solution Approach 2:
The patent applies preliminary action by organizing and storing pre-computed keys in subkey groups arranged in a tree structure during system initialization. This allows the system to quickly navigate to the required pre-computed key by traversing the tree structure based on the user ID, significantly reducing key generation time while maintaining cryptographic security.
2Reliability
If TDL-IBC scheme is used to generate private keys, then cryptographic security is improved, but computational resources and cost increase
Solution Approach 1:
The patent applies preliminary action by performing computationally intensive discrete logarithm calculations during system initialization and storing the results in a lookup table. This shifts the computational burden from individual key generation operations to the initial system setup, making subsequent key generations resource-efficient while maintaining cryptographic security.
Solution Approach 2:
The patent applies copying by creating and storing multiple pre-computed key pairs in the lookup table, each corresponding to different symbol permutations. Instead of performing new calculations for each user, the system copies and returns the appropriate pre-computed key from the table, dramatically reducing computational resource usage while maintaining security.
3Productivity
If pre-calculated keys are stored in subkey groups, then key generation speed is improved, but storage requirements increase
Solution Approach 1:
The patent applies segmentation by dividing the pre-computed keys into multiple subkey groups organized in a tree structure. Each node in the tree contains a subset of keys, and the system navigates through the tree structure to locate the required key. This segmentation reduces the search space at each step, improving key generation speed while distributing storage requirements across the tree structure.
Data Source
AI summary
Provided are an apparatus and method for generating a key. The apparatus includes: an input analyzer configured to identify a plurality of symbols from user identity (ID) information, and to derive at least one permutation from the plurality of symbols; and a key generator configured to obtain a plurality of pre-calculated keys including a plurality of first pre-calculated keys and at least one second pre-calculated key, and to generate, from the plurality of pre-calculated keys, a cryptographic key corresponding to the user ID information, the plurality of first pre-calculated keys respectively corresponding to the plurality of symbols, the at least one second pre-calculated key respectively corresponding to the at least one permutation.