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According to the MOV reduction theory, the identity-based encryption (IBE) scheme basing on the bilinear map will lose the high efficiency of elliptic curve. So it is meaningful to build the provably secure identity-based encryption scheme, but which is without the bilinear map. In this paper, based on this existing result and our new research, an improved IBE scheme will be proposed. But it is different from previous scheme that the new scheme is without symmetric encryption, and at the same time having strong provable security. At last, we will analyze the performance of this new scheme.