  We introduce a 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 TTDF can be
instantiated under the decisional Diffie-Hellman (DDH) assumption and the
learning with errors (LWE) assumption. By combining the instantiations of TTDF
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.
