Ideal and Perfect Hierarchical Secret Sharing Schemes based on MDS codes

An ideal conjunctive hierarchical secret sharing scheme, constructed based on the Maximum Distance Separable (MDS) codes, is proposed in this paper. The scheme, what we call, is computationally perfect. By computationally perfect, we mean, an authorized set can always reconstruct the secret in polynomial time whereas for an unauthorized set this is computationally hard. Also, in our scheme, the size of the ground field is independent of the parameters of the access structure. Further, it is efficient and requires $O(n^3)$, where $n$ is the number of participants. Keywords: Computationally perfect, Ideal, Secret sharing scheme, Conjunctive hierarchical access structure, Disjunctive hierarchical access structure, MDS code

FlexHi: A Flexible Hierarchical Threshold

Threshold signature schemes have gained prominence in enhancing the security and flexibility of digital signatures, allowing a group of participants to collaboratively create signatures while maintaining a predefined threshold of participants for validity. However, conventional threshold signatures treat all participants equally, lacking the capability to accommodate hierarchical structures often seen in real-world applications. Hierarchical Threshold Signature Schemes (HTSS) naturally extend the concept of simple threshold signatures, offering a solution that aligns with hierarchical organizational structures. Our paper introduces a novel, efficient, and flexible HTSS that employs independent polynomials at each hierarchical level, removing limitations on threshold values. This adaptability enables us to tailor the scheme to diverse requirements, whether signing requires only top-level nodes or lower-level participants\u27 involvement. Based on our analysis, our FlexHi integrated into the FROST scheme outperforms Tassa\u27s hierarchical scheme on FROST and operates approximately 30% to 40% faster, depending on the number of participants and the chosen threshold values. This demonstrates that, in addition to flexibility, our scheme has practical benefits through improved performance