Implementation of a secret sharing scheme with an arbitrary access structure

This work explores secret sharing schemes with arbitrary access structures, including formal definitions of access structures, minimal authorized, and maximal unauthorized coalitions. Particular attention is given to the Ito–Saito–Nishizeki scheme, which efficiently supports any monotonic access structure and is notable for its perfect secrecy. The paper presents algorithms for secret distribution and reconstruction, along with an analysis of their computational complexity. Practical implementation aspects are discussed, including efficient access structure representation and handling of minimal authorized coalitions. The results are applicable to secure distributed systems with flexible access control policies.