I would like to know if there is any research work using CP-ABE for threshold cryptography?
I want to know also if applying CP-ABE for threshold cryptography would overcome other techniques.
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$\begingroup$ I removed the "is it interesting" part because it is purely opinion based. If you disagree or can state it in objective terms, feel free to edit again. $\endgroup$ – otus Aug 3 '15 at 8:26
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$\begingroup$ actually, when I ask if it is interesting, I wanted arguments not just an opinion. I wanted to know if CP-ABE could overcome other techniques for threshold cryptography. $\endgroup$ – watou Aug 3 '15 at 9:37
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$\begingroup$ That's fine, it's just better to state those things explicitly. $\endgroup$ – otus Aug 3 '15 at 10:04
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$\begingroup$ "I want to know also if applying CP-ABE for threshold cryptography would overcome other techniques." What techniques are you talking about? $\endgroup$ – Artjom B. Aug 6 '15 at 12:07
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Many ABE schemes support Threshold Cryptography in the sense that the policy that is used to share a random secret supports threshold gates. This is also not limited to Ciphertext-Policy ABE. Key-Policy ABE schemes also support threshold policies.
The threshold policy is usually written with the of operator such as
2 of (attribute1, attribute2, attribute3, attribute4)
or more complex examples such as
2 of (a1, a2, a3, (a4 and a5 and (a6 or a7 or a8)))
The paper you linked to (BSW07) describes a high-level view of the threshold policy in section 4.1 and a more detailed view in the Encrypt and Decrypt paragraphs of section 4.2. The functionality is very similar to Shamir Secret Sharing executed for each gate in the policy.
Access trees are not the only access structures that are used for policies in ABE schemes. LSSS matrices are also very popular. Liu et al. have published an algorithm in "Efficient Generation of Linear Secret Sharing Scheme Matrices from Threshold Access Trees" (2010) to transform boolean threshold formulas into threshold LSSS access structures.
