Inner-Product Predicate Encryption Dimension Mismatch
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Solution Overview
Problem
Inner-product predicate encryption schemes face limitations due to the requirement that the dimensions of the attribute vector and predicate vector must be equivalent, restricting flexibility and efficiency in applications such as genetic data encryption and dynamic attribute category management.
Innovation Solution
A cryptographic system is developed where the encryption device generates ciphertexts with attribute information as coefficients of basis vectors, and the decryption device uses decryption keys generated from predicate information, allowing pairing operations to decrypt ciphertexts without requiring equivalent dimensions between the attribute and predicate vectors, enabling flexible inner-product predicate encryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the dimensions of attribute vector and predicate vector are required to be equivalent, then the cryptographic system maintains mathematical consistency, but the flexibility and adaptability of the system deteriorates
Solution Approach 1:
The attribute vector and predicate vector are segmented into multiple components with different dimensions. The encryption system processes each component separately through pairing operations, allowing the attribute vector to have dimension n and the predicate vector to have dimension m where n ≠ m. This segmentation enables flexible dimension matching while maintaining cryptographic security through the structured composition of multiple smaller operations.
Solution Approach 2:
The patent introduces a new dimensional framework where attribute vectors and predicate vectors operate in different dimensional spaces. Instead of requiring both vectors to reside in the same dimension, the system establishes a cross-dimensional pairing mechanism that operates between an n-dimensional attribute space and an m-dimensional predicate space, enabling operations across incompatible dimensions through mathematical transformation.
2Device complexity
If the dimensions of attribute vector and predicate vector are required to be equivalent, then the pairing operation structure remains simple, but the efficiency in applications like genetic data encryption deteriorates
Solution Approach 1:
The cryptographic system dynamically adapts the dimensions of attribute and predicate vectors based on application requirements. Rather than fixing both vectors to the same dimension, the system allows independent dimension selection for each vector type, enabling dynamic optimization for specific use cases such as genetic data encryption where attribute dimensions may differ from predicate dimensions based on data characteristics.
Solution Approach 2:
The patent changes the parameter of vector dimensions from a fixed equal value to independent variable values. By allowing the attribute vector dimension n and predicate vector dimension m to be independently configured, the system optimizes encryption efficiency for different applications while maintaining a relatively simple pairing operation structure through standardized mathematical procedures that work across different dimensional configurations.
3Stability of the object's composition
If fixed dimension requirements are imposed, then the public parameters remain stable, but the ability to manage dynamic attribute categories deteriorates
Solution Approach 1:
The system performs preliminary dimension allocation by establishing separate dimension spaces for attribute vectors and predicate vectors before actual encryption operations. This preliminary structuring allows public parameters to remain stable with predefined dimension frameworks, while individual attribute categories can dynamically adjust their specific dimension allocations within the established framework, enabling flexible attribute management without compromising overall system stability.
Solution Approach 2:
The cryptographic system achieves universality by creating a dimension-agnostic pairing mechanism that works across different dimensional configurations. The public parameters define a universal framework that supports multiple attribute categories with varying dimensions, allowing the same cryptographic primitive to serve multiple functions across diverse application scenarios without requiring reissuance of public parameters for each new attribute type.
Data Source
AI summary
An inner-product predicate encryption scheme with improved flexibility without a restriction that the dimensions of an attribute vector x→ and a predicate vector v→ should be equivalent. A ciphertext having an element c0 and an element ct for each index t included in a set Ix→ is decrypted with a decryption key having an element k0 and an element kt for each index t included in a set Iv→ by computing a product of pairing operations between corresponding pairs of basis vectors on the element c0 and the element k0 and on the element ct and the element kt.