Multilevel threshold secret sharing based on the Chinese Remainder Theorem

Abstract The ( t , n ) threshold secret sharing schemes (SSs) were introduced by Shamir and Blakley separately in 1979. Multilevel threshold secret sharing (MTSS) is a generalization of classical threshold SS, and it has been studied extensively in the literature. In an MTSS, shareholders are classified into different security subsets. The threshold value of a higher-level subset is smaller than the threshold value of a lower-level subset. Shareholders in each subset can recover the secret if the number of shares available is equal to or more than a threshold value. Furthermore, the share of a shareholder in a higher-level subset can be used as a share in the lower-level subset to recover the secret. Chinese Remainder Theorem (CRT) is one of popular tools used for designing SSs. For example, the Mignotte's scheme and Asmuth–Bloom's scheme are two classical ( t , n ) threshold SSs based on the CRT. So far, there was no CRT-based MTSS in the literature. In this paper, we propose the first MTSS based on the CRT. In our proposed scheme, one unique feature is that each shareholder needs to keep only one private share. Our proposed scheme is based on the Asmuth–Bloom's SS which is unconditionally secure.

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