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Conjunctive hierarchical secret sharing by finite geometry.

Máté Gyarmati¹, Péter Ligeti^1,2, Peter Sziklai^3,4

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.

Keywords:

Finite geometry Secret sharing Threshold schemes

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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.