Identity based encryption (IBE) has received great attention since Boneh and Franklin\'s breakthrough work on bilinear group based IBE . Till now, many IBE schemes relying on bilinear groups with dierent properties have been proposed [5, 25, 29, 14]. However, one part of the user\'s private key in all these IBE schemes is constructed as y = f(msk), where msk is the master key and y is an element in the underlying bilinear group G. In this paper, we propose a new IBE: one part of the private key is y = f(msk), where msk is the master key and y is an element in Zp . Here p is the underlying bilinear group\'s prime order. By using some novel techniques, we prove this new IBE is semantic secure under the selective identity chosen plaintext attacks (IND-sID-CPA) in the standard model. Based on this IBE scheme, we construct
an IND-ID-CCA secure identity based proxy re-encryption (IBPRE) scheme
which is master secret secure and ecient for the proxy compared with
other IND-ID-CCA (IBPRE) schemes.