Cryptology ePrint Archive: Report 2018/933

Asymptotically Ideal CRT-based Secret Sharing Schemes for Multilevel and Compartmented Access Structures

Ferucio Laurentiu Tiplea and Constantin Catalin Dragan

Abstract: 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 in 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 paper we propose the first asymptotically ideal CRT-based secret sharing schemes for (disjunctive, conjunctive) multilevel and compartmented access structures. 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, we show that 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.

Category / Keywords: cryptographic protocols / secret sharing

Date: received 30 Sep 2018

Contact author: ferucio tiplea at uaic ro

Available format(s): PDF | BibTeX Citation

Version: 20181002:041217 (All versions of this report)

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