Lattice-Based Identity Encryption Parameter Flexibility
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Solution Overview
Problem
Existing identity-based encryption methods based on lattices face limitations in parameter flexibility, particularly requiring entire dimensions to be powers of 2 for stability, which restricts security parameter selection and increases calculation time and key generation complexity.
Innovation Solution
The proposed method generates a master secret key and user secret key using a lattice-based encryption system that allows for flexible parameter selection by computing a trapdoor and master public key using a ring with dimensions represented by powers of 2 and integer multiples, enabling efficient key generation and encryption/decryption processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the dimension is restricted to powers of 2 for stability, then system stability is ensured, but parameter flexibility and security level selection are limited
Solution Approach 1:
The patent changes the parameter constraint from 'dimension must be power of 2' to 'dimension can be any integer >= 3'. This allows flexible selection of security parameters (e.g., n=512 for 80-bit security, n=1024 for 192-bit security) while maintaining system stability through the lattice-based cryptographic framework and NTRU polynomial ring structure.
2Reliability
If the dimension is increased to meet higher security requirements, then security level is improved, but calculation amount and key generation time increase sharply
Solution Approach 1:
The patent enables direct correlation between dimension parameter n and security level without requiring dimension doubling. Security level can be adjusted by selecting appropriate n values (e.g., n=512, 1024, 2048) based on required security strength, avoiding unnecessary computational overhead from excessive dimension increases.
Solution Approach 2:
The system allows dynamic adjustment of security parameters based on operational requirements. The dimension n can be flexibly selected to match specific security needs, enabling the system to adapt between security levels without fixed step increases, thus optimizing the balance between security and computational efficiency.
3Reliability
If the dimension is increased to provide higher security, then security level is improved, but the size of public keys and secret keys increases
Solution Approach 1:
The patent optimizes the relationship between dimension n and key size by using efficient polynomial ring representations and NTRU lattice structures. Keys are represented as polynomials with coefficients in Z_q, allowing compact storage. The key size grows linearly with n rather than exponentially, enabling higher security levels with manageable key sizes through parameter optimization.
Data Source
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AI summary
A calculation device is disclosed. The calculation device includes: a memory storing at least one instruction and identity information; and a processor performing the at least one instruction, wherein the processor may randomly sample small elements, generate a function-processed output value by function-processing the stored identity information, and generate an encrypted text for a message by using a master public key computed using a ring having a dimension (d) represented by a power of 2 and an integer multiplication of 3 or more, the sampled small elements and the function-processed output value.