Lattice-Based Functional Encryption Key Generation for Attribute Hiding
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Solution Overview
Problem
Functional encryption schemes based on lattice theory are weakly attribute-hiding, leading to undesirable information leakage from ciphertexts with attributes satisfying certain conditions for secret keys.
Innovation Solution
A cryptographic system generates a secret key with a matrix e that satisfies the equation AY·e=u, where AY is determined by the input parameter Y, using public parameters to prevent information leakage, comprising a key generation apparatus, encryption apparatus, and decryption apparatus.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If functional encryption schemes based on lattice theory are used, then quantum computer durability is improved, but attribute-hiding capability deteriorates (information leakage occurs)
Solution Approach 1:
The secret key is segmented into multiple components: a first key component (matrix e) and a second key component (matrix f). The ciphertext is also segmented with multiple cipher elements. This segmentation allows the encryption scheme to maintain quantum durability while preventing information leakage by distributing attribute information across multiple key and ciphertext components that must be combined for decryption.
Solution Approach 2:
The invention introduces an intermediary mechanism through the matrix e and its relationship with matrix AY forming matrix uj. This intermediary structure acts as a mediator between the public parameters and the secret key, enabling the system to achieve full attribute-hiding by preventing direct exposure of attribute information while maintaining the functional encryption capability against quantum computers.
2Ease of manufacture
If weak attribute-hiding is used in functional encryption, then implementation simplicity is improved, but security deteriorates (undesirable information leakage)
Solution Approach 1:
By dividing the secret key into multiple components (matrix e and matrix f) and the ciphertext into multiple cipher elements, the invention achieves full attribute-hiding security without significantly complicating implementation. Each component can be generated and managed independently, and the segmentation allows standard lattice-based cryptographic operations to be applied systematically.
Solution Approach 2:
The invention changes the cryptographic parameters by introducing the matrix e as a key element that forms matrix uj when multiplied by matrix AY. This parameter change transforms the encryption scheme from weak attribute-hiding to full attribute-hiding, enhancing security while maintaining implementation feasibility through systematic key and ciphertext generation processes.
Data Source
AI summary
A cryptographic system implements a functional encryption scheme that is based on the lattice theory. In the cryptographic system, a key generation apparatus generates, as a secret key skv for a predicate vector v, a secret key skv including a matrix e as a key element, wherein a product of the matrix e and a matrix AY determined by the predicate vector v being input parameter Y forms a matrix uj for a value j in a set [N] including a plurality of values, the matrix uj being among a plurality of matrices u obtained from public parameters PP.