IACR News item: 13 June 2014
Gottfried Herold, Julia Hesse, Dennis Hofheinz, Carla Ràfols, Andy Rupp
ePrint ReportIn this work, we present a new framework for composite-to-prime-order conversions. Our framework is in the spirit of Freeman\'s work; however, we develop a different, ``polynomial\'\' view of his approach, and revisit several of his design decisions. This eventually leads to significant efficiency improvements, and enables us to circumvent previous lower bounds. Specifically, we show how to implement Groth-Sahai proofs in a prime-order environment (with a symmetric pairing) almost twice as efficiently as the state of the art.
We also show that our new conversions are optimal in a very broad sense. Besides, our conversions also apply in settings with a multilinear map, and can be instantiated from a variety of computational assumptions (including, e.g., the $k$-linear assumption).
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