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6

I assume that your question relates to sharing a secret specifically of this form. Furthermore, you want to guarantee this even if the dealer is not trusted and may try to share a secret of a different form. Otherwise, you could just use any secret sharing (or verifiable secret sharing) scheme. However, note that $s$ as you wrote actually does not have any ...


0

In a multilevel secret sharing scheme there is only one secret $S$ that all levels seek to find. In a compartemnted scheme we can have multiple secrets that correspond to each level that must be found before $S$ can be recovered. In a compartmented scheme a set of compartments must work together to recover the secret, where each compartment contains a number ...


7

This cannot be achieved information-theoretically. This is typically the task that requires multiparty computation protocol to be achieved. In particular, the common method for what you want is called "secure multiplication protocol", and is in general constructed from an additively homomorphic encryption scheme (over the ring $R$), or from oblivious ...


2

I too had to go through this decision some time back and did a comparative study of both schemes. Shamir's scheme is used for the majority of works in the area of threshold secret sharing. This is because of the foremost reason of the number of primes required in both the schemes. Asmuth-Bloom's scheme require $n+1$ ($n$ being the number of shares) prime ...



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