CP-ABE for threshold cryptography

Question

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.

Answer 1

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.