Asymptotically ideal Chinese remainder theorem ‐based secret sharing schemes for multilevel and compartmented access structures

Multilevel and compartmented access structures are two important classes of access structures where participants are grouped into levels/compartments with different degrees of trust and privileges. The construction of secret sharing schemes for such access structures has been the attention of researchers for a long time. Two main approaches have been taken so far, one of them is based on polynomial interpolation and the other one is based on the Chinese Remainder Theorem (CRT). In this article the first asymptotically ideal CRT-based secret sharing schemes for (disjunctive, conjunctive) multilevel and compartmented access structures are proposed. Our approach is compositional and it is based on a variant of the Asmuth-Bloom secret sharing scheme where some participants may have public shares. Based on this, the proposed secret sharing schemes for multilevel and compartmented access structures are asymptotically ideal if and only if they are based on 1-compact sequences of co-primes. Possible applications for secret image and multi-secret sharing are pointed-out.