Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups

We develop an abstract framework that encompasses the key properties of bilinear groups of composite order that are required to construct secure pairing-based cryptosystems, and we show how to use prime-order elliptic curve groups to construct bilinear groups with the same properties. In particular, we define a generalized version of the subgroup decision problem and give explicit constructions of bilinear groups in which the generalized subgroup decision assumption follows from the decision DiffieHellman assumption, the decision linear assumption, and/or related assumptions in prime-order groups. 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-GohNissim 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 inst...

• Type: Conference
• Year: 2010
• Where: EUROCRYPT
• Authors: David Mandell Freeman
• Keywords: Bilinear Groups, Cryptology, EUROCRYPT 2010, Prime-order Groups, Subgroup Decision