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A recent work of Harn and Fuyou presents the first multilevel (disjunctive)threshold secret sharing scheme based on the Chinese Remainder Theorem. In thiswork, we first show that the proposed method is not secure and also fails towork with a certain natural setting of the threshold values on compartments. Wethen propose a secure scheme that works for all threshold settings. In thisscheme, we employ a refined version of Asmuth-Bloom secret sharing with aspecial and generic Asmuth-Bloom sequence called the {\it anchor sequence}.Based on this idea, we also propose the first multilevel conjunctive thresholdsecret sharing scheme based on the Chinese Remainder Theorem. Lastly, wediscuss how the proposed schemes can be used for multilevel threshold functionsharing by employing it in a threshold RSA cryptosystem as an example.

Multilevel Threshold Secret and Function Sharing based on the Chinese Remainder Theorem