  Design efficient lattice-based cryptosystem secure against adaptive chosen
ciphertext attack (IND-CCA2) is a challenge problem. To the date, full
CCA2-security of all proposed lattice-based PKE schemes achieved by using a
generic transformations such as either strongly unforgeable one-time signature
schemes (SU-OT-SS), or a message authentication code (MAC) and weak form of
commitment. The drawback of these schemes is that encryption requires "separate
encryption". Therefore, the resulting encryption scheme is not sufficiently
efficient to be used in practice and it is inappropriate for many applications
such as small ubiquitous computing devices with limited resources such as smart
cards, active RFID tags, wireless sensor networks and other embedded devices.
  In this work, for the first time, we introduce an efficient universal random
data padding (URDP) scheme, and show how it can be used to construct a "direct"
CCA2-secure encryption scheme from "any" worst-case hardness problems in
(ideal) lattice in the standard model, resolving a problem that has remained
open till date. This novel approach is a "black-box" construction and leads to
the elimination of separate encryption, as it avoids using general
transformation from CPA-secure scheme to a CCA2-secure one. IND-CCA2 security
of this scheme can be tightly reduced in the standard model to the assumption
that the underlying primitive is an one-way trapdoor function.
