We apply our framework and our prime-order group constructions to create more efficient versions of cryptosystems that originally required composite-order groups. Specifically, we consider the Boneh-Goh-Nissim encryption scheme, the Boneh-Sahai-Waters traitor tracing system, and the Katz-Sahai-Waters attribute-based encryption scheme. We give a security theorem for the prime-order group instantiation of each system, using assumptions of comparable complexity to those used in the composite-order setting. Our conversion of the last two systems to prime-order groups answers a problem posed by Groth and Sahai.
Category / Keywords: public-key cryptography / pairing-based cryptography, composite-order groups, cryptographic hardness assumptions Date: received 5 Nov 2009, last revised 5 Nov 2009 Contact author: dfreeman at cs stanford edu Available format(s): PDF | BibTeX Citation Version: 20091108:042526 (All versions of this report) Discussion forum: Show discussion | Start new discussion