Although getting a CPA secure IBE scheme is quite easy, achieving a fully secure IBE scheme against CCA is still a challenging problem nowadays. We get such a IBE scheme. First we propose a fully secure HIBE against CPA based on Waters' IBE [23]. And then, as IBE is a special case of HIBE, we use Boneh's result and technique [6] to construct a fully secure IBE against CCA.
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