  The concept of proxy re-encryption (PRE) dates back to the work of Blaze,
Bleumer, and Strauss in 1998. PRE offers delegation of decryption rights, i.e.,
it securely enables the re-encryption of ciphertexts from one key to another,
without relying on trusted parties. PRE allows a semi-trusted third party
termed as a ``proxy" to securely divert encrypted files of user A (delegator)
to user B (delegatee) without revealing any information about the underlying
files to the proxy. To eliminate the necessity of having a costly certificate
verification process, Green and Ateniese introduced an identity-based PRE
(IB-PRE). The potential applicability of IB-PRE sprung up a long line of
intensive research from its first instantiation. Unfortunately, till today,
there is no collusion-Resistant unidirectional IB-PRE secure in the standard
model, which can withstand quantum attack. In this paper, we present the first
concrete constructions of collusion-Resistant unidirectional IB-PRE, for both
selective and adaptive identity, which are secure in standard model based on
the hardness of learning with error problem.
