The Exact Security of Pairing Based Encryption and Signature Schemes
David Galindo · 2004
Bilinear pairings have been intensively used in the design of cryptographic protocols during the last few years. For instance, short sig- natures and non-interactive key exchange protocols have been designed with them, and they appear as a key component for identity-based cryp- tography. Focusing on encryption and signature schemes built on bilinear pairings, we look at the security reductions of some known constructions. For any pair scheme/security reduction, we deduce key sizes to securely implement the schemes. It turns out that some important protocols in the literature appear to be not as efficient as one would wish, due to the lack of tightness of their security reductions. Finally, we summarize current trends to obtain tight security reductions and suggest some open problems.