Security of mobile communications comes with the cost of computational overhead. Reducing the overhead in security computations is critical to ensure the overall performance of a mobile network. In this paper, we present the notion of online/offline signcryption, where most of computations are carried out offline and the online part of our scheme does not require any exponent computations and therefore is very efficient. Our scheme allows any third party to verify the encryption without compromising confidentiality. We also show that our scheme is secure against existential forgery under chosen message attacks and adaptively chosen ciphertext attacks under the notion of indistinguishability of ciphertext.