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Conjunctive hierarchical secret sharing by finite geometry.
Máté Gyarmati1, Péter Ligeti1,2, Peter Sziklai3,4
1Department of Computeralgebra, Eötvös Loránd University, Budapest, Hungary.
Designs, Codes, and Cryptography
|February 20, 2025
Summary
We introduce conjunctive hierarchical secret sharing, a new method for secure data distribution. This approach improves efficiency by using finite geometry over existing polynomial-based techniques.
Area of Science:
- Cryptography
- Information Security
- Computer Science
Background:
- Secret sharing distributes data securely among participants.
- Threshold secret sharing requires a minimum number of participants to access data.
- Existing methods often rely on polynomial constructions.
Purpose of the Study:
- To propose a novel generalized threshold secret sharing scheme.
- To introduce conjunctive hierarchical secret sharing for structured access control.
- To improve the efficiency of secret sharing schemes.
Main Methods:
- Developed a new construction for conjunctive hierarchical secret sharing.
- Utilized finite geometry arguments for the scheme's design.
- Ensured arbitrary parameter support for the construction.
Main Results:
- The proposed scheme supports hierarchical structures with multiple thresholds.
- It is the first construction for arbitrary parameters based on finite geometry.
- Achieved a smaller underlying finite field size compared to polynomial-based methods.
Conclusions:
- Conjunctive hierarchical secret sharing offers an efficient alternative for secure data distribution.
- Finite geometry provides a powerful tool for designing advanced secret sharing schemes.
- The new method enhances security and efficiency in hierarchical systems.
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