Generic Transforms to Acquire CCA-Security for Identity Based Encryption: The Cases of FOpkc and REACT

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Fujisaki-Okamoto (FOpkc) conversion [13] and REACT[17] are widely known to be able to generically convert a weak public key encryption scheme to a strong encryption scheme. In this paper, we discuss applications of FOpkc conversion and REACT to Identity Based Encryptions (IBE). It has not been formally verified yet that whether these conversions are generic in the IBE setting.

Our results show that both conversions are effective in the IBE case: plain REACT already achieves a good security reduction while the plain FOpkc conversion results in bad running time of the simulator. We further propose a simple modification to the plain FOpkc that solves this problem. Finally, we choose some concrete parameters to explain (visually) the effect of how the modified FOpkc substantially improves reduction cost regarding the plain conversion.