We introduce a new cryptographic primitive named threshold trapdoor functions (TTDFs), from which we give generic constructions of threshold and revocation encryptions under adaptive corruption model. Then, we show TTDFs can be instantiated under the decisional Diffie-Hellman (DDH) assumption and the learning with errors (LWE) assumption. By combining the instantiations of TTDFs with the generic constructions, we obtain threshold and revocation encryptions which compare favorably over existing schemes. The experimental results show that our proposed schemes are practical.

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