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Improvements on Security Proofs of Some Identity Based Encryption Schemes

  • Rui Zhang
  • Hideki Imai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3822)

Abstract

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.

Keywords

IBE tight security reductions BDH assumption 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Rui Zhang
    • 1
  • Hideki Imai
    • 1
  1. 1.Institute of Industrial ScienceThe University of Tokyo 

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