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In this paper, we propose a different approach to outsourcing computational tasks. We are not concerned with hiding the job or the data, but our main task is to ensure that the job is computed correctly. We also observe that not all contractors are malicious; rather, majority are rational. Thus, our approach brings together elements from cryptography, as well as game theory and mechanism design. We achieve the following results: (1) We incentivize all the rational contractors to perform the outsourced job correctly, (2) we guarantee high fraction (e.g., 99.9%) of correct results even in the existence of a relatively large fraction (e.g., 33%) of malicious irrational contractors in the system, (3) and we show that our system achieves these while being almost as efficient as running the job locally (e.g., with only 3% overhead). Such a high correctness guarantee was not known to be achieved with such efficiency.
In particular, they have been used to create an ABE system with multi authorities, but limited to the ciphertext-policy instance.
Here, for the first time, we propose two multi-authority key-policy ABE systems.
In our first proposal, the authorities may be set up in any moment and without any coordination.
A party can simply act as an ABE authority by creating its own public parameters and issuing private keys to the users.
A user can thus encrypt data choosing both a set of attributes and a set of trusted authorities, maintaining full control unless all his chosen authorities collude against him.
In our second system, the authorities are allowed to collaborate to achieve shorter keys and parameters, enhancing the efficiency of encryption and decryption.
We prove our systems secure under algebraic assumptions on the bilinear groups: the bilinear Diffie-Hellmann assumption and an original variation of the former.
- We suggest a general new notion of partial garbling which unifies several previous notions from the literature, including standard garbling schemes, secret sharing schemes, and \"conditional disclosure of secrets\". This notion considers garbling schemes in which part of the input is public, in the sense that it can be leaked by F^.
- We present constructions of partial garbling schemes for (boolean and arithmetic) formulas and branching programs which take advantage of the public input to gain better efficiency.
- We demonstrate the usefulness of the new notion by presenting applications to efficient attribute-based encryption, delegation, and secure computation. In each of these applications, we obtain either new schemes for larger classes of functions or efficiency improvements from quadratic to linear. In particular, we obtain the first ABE scheme in bilinear groups for arithmetic formulas, as well as more efficient delegation schemes for boolean and arithmetic branching programs.