Lightweight devices such as smart cards and RFID tags have a very limited hardware resource, which could be too weak to cope with asymmetric-key cryptography. It would be desirable if the cryptographic algorithm could be optimized in order to better use hardware resources. In this paper, we demonstrate how identity-based encryption algorithms from bilinear pairing can be optimized so that hardware resources can be saved. We notice that the identity-based encryption algorithms from bilinear pairing in the literature must perform both elliptic curve group operations and multiplicative group operations, which consume a lot of hardware resources. We manage to eliminate the need of multiplicative group operations for encryption. This is a significant discovery since the hardware structure can be simplified for implementing pairing-based cryptography. Our experimental results show that our encryption algorithm saves up to 47 percent memory (27,239 RAM bits) in FPGA implementation.