Improvements on Security Proofs of Some Identity Based Encryption Schemes

Concrete security reduction plays an important role in practice, because it explicitly bounds an adversary’s success probability as a function of their resources. In this paper, we study the security reductions of Boneh-Franklin identity based encryption (IBE) schemes and its variants, focusing on the efficiency of their security reductions:

Improvements on proofs of Boneh-Franklin IBE and variants.

The proof of the Boneh-Franklin IBE (BF-IBE) scheme was long believed to be correct until recently, Galindo pointed out a flawed step in the proof and gave a new proof, however, the new reduction was even looser. We give a new proof of the BF-IBE scheme that essentially improves previously known results. Very interestingly, our result is even better than the original underestimated one. Similar analysis can also be applied to Galindo’s BF-IBE variant, resulting in a tighter reduction.

A new BF-IBE variant with tighter security reductions.

We propose another variant of the BF-IBE that admits better security reduction, however, the scheme relies on a stronger assumption, namely the Gap Bilinear Diffie-Hellman (GBDH) assumption.