  In this paper, we present a new identity-based encryption (IBE) scheme using
bilinear pairings. Our IBE scheme enjoys the same \textsf{Key Extraction} and
\textsf{Decryption} algorithms with the famous IBE scheme of Boneh and Franklin
(BF-IBE for short), while differs from the latter in that it has modified
\textsf{Setup} and \textsf{Encryption} algorithms.
  Compared with BF-IBE, we show that ours are more practical in a multiple
private key generator (PKG) environment, mainly due to that the session secret
$g_{ID}$ could be pre-computed \emph{before} any interaction, and the sender
could encrypt a message using $g_{ID}$ prior to negotiating with the intended
recipient(s). As an application of our IBE scheme, we also derive an escrowed
ElGamal scheme which possesses certain good properties in practice.
