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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 ...


I suggest, you look into the code how that works. Basically, you start with a secret that you want to share according to some tree. You share the secret with a Threshold Secret Sharing Scheme like Shamir's Secret Sharing and put the resulting shares into the children of that node (in the beginning this is the root node). Then you can re-share each of the ...


Short refresher on KP-ABE: The Master Secret Key (MSK) and the Public Parameters (PP) are created during Setup and both enable the attribute authority to create Secret Keys (SK) for users using the Keygen algorithm. Some user who possesses PP can Encrypt some data with a set of attributes $\gamma$. The encryption works by generating a new random secret ...


It means exactly what is written, the advantage of the adversary is a quantity which is defined as the difference between the probability that $b = b'$ and $1/2$. For example if the probability that $b = b'$ is $3/4$, then the advantage of the adversary is $3/4-1/2 = 1/4$.

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