Predicate Encryption Key Derivation in Semi-Ordered Structures

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Solution Overview

Problem

Existing hierarchical cryptography systems cannot derive a key for a common child node from keys of parent nodes in general semi-ordered structures other than tree structures.

Innovation Solution

An information generation apparatus and method that employs predicate encryption to implement key derivation in general semi-ordered structures, using basis vectors and random numbers to generate and derive information corresponding to indices, allowing key derivation in structures with parent and child nodes.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If tree structure is used for hierarchical cryptography, then key derivation is possible, but the system cannot handle general semi-ordered structures

Engineering Contradiction:

Improvestructure compatibilityVSAvoidsystem complexity

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent extends hierarchical cryptography from tree structures to general semi-ordered structures by introducing a universal key derivation mechanism that works for any semi-ordered structure. The system uses a master key and a set of basis vectors to derive child keys from parent keys, making the system applicable to various hierarchical configurations including organizations, file systems, and access control models beyond traditional trees.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Solution Approach 2:

The patent segments the key derivation process into discrete mathematical operations using basis vectors. Each child node's key is derived by applying a specific basis vector to the parent node's key through a deterministic function, allowing modular and scalable key management in complex semi-ordered structures without requiring complete re-encryption.

Inventive Principle:

Principle #1Segmentation

2Ease of operation

If key derivation is enabled for common child nodes from multiple parent nodes, then flexibility is improved, but security complexity increases

Engineering Contradiction:

Improvekey derivation flexibilityVSAvoidsecurity strength

Core Design Contradiction:

Ease of operationVSReliability

Solution Approach 1:

The patent introduces basis vectors as intermediary mathematical objects that mediate between parent keys and child keys. The basis vectors act as a standardized transformation layer that enables flexible key derivation while maintaining security through cryptographic hardness assumptions. The master key combined with basis vectors generates all child keys in a controlled manner, preventing unauthorized key derivation.

Inventive Principle:

Principle #24Intermediary (Mediator)

Data Source

PatentEP2424155B1Information generating device, information generating method, and information generating program and storage medium thereof

Publication Date: 2014.09.03 NIPPON TELEGRAPH & TELEPHONE CORP

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AI summary

Hierarchical cryptography expressed in a general semiordered structure other than a tree structure is implemented. In information generation, random numbers σv and (σvj)j∈w(v) ∈ Zq are generated; main information kv = σvΣ i ∈ {1, ..., N - 1} \ w(v)vibi* + bN* is calculated; and derivation information kvj = σvjΣ i ∈ {1, ..., N - 1} \ w(v)vibi* + bj* is calculated for each j ∈ w(v). In information derivation, random numbers σu and (σuj)j∈w(u) ∈ Zq are generated; main information ku = σuΣ i ∈ w(v)= \ w(u)uikvi + kv is calculated; and derivation information kuj = σujΣ i ∈ w(v) \ w(u)uikvi + kvj is calculated for each j ∈ w(v).