Multilevel Threshold Secret and Function Sharing based on the Chinese Remainder Theorem
This work addresses security and functionality issues in cryptographic secret sharing for applications like secure data storage and access control, representing an incremental improvement over prior methods.
The authors identified security flaws and functional limitations in a previous multilevel threshold secret sharing scheme based on the Chinese Remainder Theorem, and proposed a secure scheme that works for all threshold settings, also extending it to multilevel conjunctive threshold secret sharing and function sharing applications.
A recent work of Harn and Fuyou presents the first multilevel (disjunctive) threshold secret sharing scheme based on the Chinese Remainder Theorem. In this work, we first show that the proposed method is not secure and also fails to work with a certain natural setting of the threshold values on compartments. We then propose a secure scheme that works for all threshold settings. In this scheme, we employ a refined version of Asmuth-Bloom secret sharing with a special and generic Asmuth-Bloom sequence called the {\it anchor sequence}. Based on this idea, we also propose the first multilevel conjunctive threshold secret sharing scheme based on the Chinese Remainder Theorem. Lastly, we discuss how the proposed schemes can be used for multilevel threshold function sharing by employing it in a threshold RSA cryptosystem as an example.