Abstract
The Boneh-Franklin identity-based encryption (BF-IBE) scheme [6] is well-known as a fully functional identity-based encryption (IBE) scheme. Recently, Galindo [13] pointed out a flaw in the original proof of the security of the BF-IBE scheme. He claims that its security can be fixed without changing both the scheme and the underlying assumption if the efficiency of the security reduction is sacrificed. This result would be bad news for many cryptographic schemes [1,7,10,15] that are based on the BF-IBE scheme because an inefficient security reduction would imply either the lower security level or the use of larger key sizes to attain a given security level. In this paper, we give a new proof of the security of the BF-IBE scheme, showing that it has a tighter security reduction than had been previously believed.
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