  We present a framework for fully-simulatable $h$-out-of-$n$ oblivious
transfer ($OT^{n}_{h}$) with security against non-adaptive malicious
adversaries. The framework costs six communication rounds and costs at most
$40n$ public-key operations in computational overhead. Compared with the known
protocols for fully-simulatable oblivious transfer that works in the plain mode
(where there is no trusted common reference string available) and proven to be
secure under standard model (where there is no random oracle available), the
instantiation based on the decisional Diffie-Hellman assumption of the
framework is the most efficient one, no matter seen from communication rounds
or computational overhead.
  Our framework uses three abstract tools, i.e., perfectly binding commitment,
perfectly hiding commitment and our new smooth projective hash. This allows a
simple and intuitive understanding of its security.
  We instantiate the new smooth projective hash under the lattice assumption,
the decisional Diffie-Hellman assumption, the decisional $N$-th residuosity
assumption, the decisional quadratic residuosity assumption. This indeed shows
that the folklore that it is technically difficult to instantiate the
projective hash framework under the lattice assumption is not true. What's
more, by using this lattice-based hash and lattice-based commitment scheme, we
gain a concrete protocol for $OT^{n}_{h}$ which is secure against quantum
algorithms.
