Multi-Compartment Threshold Secret Sharing via Lagrange Interpolation
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Solution Overview
Problem
Existing threshold secret sharing methods, such as Shamir's and Blakely's, have limitations in creating multiple compartments and allowing arbitrary access structures, particularly in conjunctive hierarchical secret sharing, where only one compartment can be created per level and only conjunctive secret reconstruction is possible, making them inflexible and complex to implement.
Innovation Solution
The method employs Lagrange interpolation using a polynomial to create and reconstruct secret shares across multiple compartments, enabling the creation of multiple compartments in one level and defining arbitrary access structures, including conjunctive secret reconstruction conditions, by using external shares to encrypt and decrypt secret values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Tassa's conjunctive hierarchical secret sharing method is used, then conjunctive secret reconstruction is possible, but only one compartment can be created per level and the implementation becomes complex
Solution Approach 1:
The patent segments the secret sharing system into multiple compartments at each hierarchical level, allowing independent creation of multiple compartments rather than a single compartment per level. This segmentation enables flexible access structures where different compartments can have different threshold requirements and access policies, directly resolving the limitation of Tassa's method while maintaining manageable complexity through modular design
Solution Approach 2:
The patent creates a universal secret sharing framework that can handle both conjunctive and non-conjunctive access structures within the same system. The method allows arbitrary access structures to be defined by specifying which compartments and shares are required for reconstruction, making the system adaptable to various security scenarios without requiring separate implementations for different access patterns
2Reliability
If derivatives of polynomial are used for conjunctive hierarchical secret sharing, then secret reconstruction is possible, but Birkhoff interpolation is required which is more complicated than Lagrange interpolation
Solution Approach 1:
The patent substitutes the complex Birkhoff interpolation mechanism with the simpler Lagrange interpolation method. By using Lagrange interpolation, the system maintains the ability to reconstruct secrets from qualified shares while eliminating the mathematical complexity of Birkhoff interpolation, making the implementation more straightforward and easier to verify without sacrificing reconstruction reliability
Solution Approach 2:
The patent changes the mathematical parameters of the interpolation approach by using standard polynomial interpolation with Lagrange basis polynomials instead of derivative-based Birkhoff interpolation. This parameter change simplifies the computational requirements and mathematical operations needed for secret reconstruction while maintaining the hierarchical and multi-compartment structure
3Reliability
If shares are assigned to distributed participants in traditional secret sharing, then secrecy is increased, but arbitrary access structures cannot be specified
Solution Approach 1:
The patent introduces dynamic access structure specification where the required shares and compartments for reconstruction can be arbitrarily defined based on security policies. The system allows flexible configuration of which participants and compartments must contribute shares, enabling adaptive access control that can respond to different security scenarios while maintaining the distributed secrecy benefits of traditional secret sharing
Data Source
AI summary
Provided is a method for threshold secret sharing and reconstruction for multi-compartment, and more particularly, to a method for creating a share and reconstructing a secret in a system constituted by a plurality of compartments. The method for threshold secret sharing for multi-compartments may include: an operation of creating, when at least one second compartment is related toward a first compartment in one direction, an encrypted secret value by using an external share which does not belong to the first compartment, but belongs to the at least one second compartment; an operation of creating a first polynomial for defining the first compartment by using the encrypted secret value; and an operation of creating an internal share of the first compartment by using the first polynomial.