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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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What you're looking for is called packed secret sharing. It was introduced by Franklin & Yung in: Franklin, M. and Yung, M., Communication complexity of secure computation.. STOC 1992. If you have a polynomial of degree $< d$, with at most $t$ corrupt parties, then you can use a single polynomial to hide $d - t$ secrets. It's not hard to see that ...



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