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Let's assume that we're talking about monotonic access structures (without negated attributes in the policy). A Threshold policy was introduced in Sahai, Amit, and Brent Waters. "Fuzzy identity-based encryption." Advances in Cryptology–EUROCRYPT 2005. Springer Berlin Heidelberg, 2005. 457-473. (link) It means that a user secret key and the ciphertext are ...

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