In 1998, at Eurocrypt, a novel primitive, called Proxy Re-Encryption (PRE) was introduced by Blaze, Bleumer and Strauss [1]. In the given concept, a delegator computes re-encryption key and gives it to the semi trusted proxy. Then proxy can convert a message, enciphered with Alice's public key into a message, enciphered with Bob's public key without knowing the message. Upto best our knowledge, we have proposed the first unidirectional PRE scheme, which is noninteractive and based on lattice based identity based cryptosystem. In this scheme a trapdoor function is used for lattices, which is proposed by Micciancio and Peikert [2]. It is simple, efficient, strong and easy to implement compared to [3]. In 2013, Wang et al.[4, 5] introduced a new primitive: PRE+, which is similar to the conventional PRE except that, in PRE+ scheme encryptor computes re-encryption keys. Here encryptor is the delegator. We have also constructed a lattice identity based unidirectional PRE+ scheme. © 2020 Elsevier Ltd