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Polynomial spaces: a new framework for composite to-prime-order transformations

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dc.contributor.author Herold, Gottfried
dc.contributor.author Hesse, Julia
dc.contributor.author Hofheinz, Dennis
dc.contributor.author Ràfols, Carla
dc.contributor.author Rupp, Andy
dc.date.accessioned 2019-08-01T13:54:48Z
dc.date.available 2019-08-01T13:54:48Z
dc.date.issued 2014
dc.identifier.citation Herold G, Hesse J, Hofheinz D, Ràfols C, Rupp A. Polynomial spaces: a new framework for composite to-prime-order transformations. In: Garay JA, Gennaro R, editors. Advances in Cryptology – CRYPTO 2014. 34th Annual Cryptology Conference Proceedings, Part I; 2014 Aug 17-21; Santa Barbara, CA, USA. Berlin: Springer; 2014. p. 261-79. (LNCS; no. 8616). DOI: 10.1007/978-3-662-44371-2_15
dc.identifier.isbn 978-3-662-44370-5
dc.identifier.issn 0302-9743
dc.identifier.uri http://hdl.handle.net/10230/42229
dc.description Comunicació presentada a: CRYPTO 2014. 34th Annual Cryptology Conference, celebrada a Santa Barbara, Califòrnia, Estats Units d'Amèrica, del 17 al 21 d'agost de 2014
dc.description.abstract At Eurocrypt 2010, Freeman presented a framework to convert cryptosystems based on composite-order groups into ones that use prime-order groups. Such a transformation is interesting not only from a conceptual point of view, but also since for relevant parameters, operations in prime-order groups are faster than composite-order operations by an order of magnitude. Since Freeman's work, several other works have shown improvements, but also lower bounds on the efficiency of such conversions. In 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 e ciency improvements, and enables us to circumvent previous lower bounds. Specifically, we show how to verify 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).
dc.description.sponsorship This work has been supported in part by DFG grant GZ HO 4534/4-1. Carla Ràfols was supported by a Sofja Kovalevskaja Award of the Alexander von Humboldt Foundation and the German Federal Ministry for Education and Research.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Springer
dc.relation.ispartof Garay JA, Gennaro R, editors. Advances in Cryptology – CRYPTO 2014. 34th Annual Cryptology Conference Proceedings, Part I; 2014 Aug 17-21; Santa Barbara, CA, USA. Berlin: Springer; 2014. p. 261-79. (LNCS; no. 8616).
dc.rights © International Association for Cryptologic Research 2014 The final publication is available at Springer via https://doi.org/10.1007/978-3-662-44371-2_15
dc.title Polynomial spaces: a new framework for composite to-prime-order transformations
dc.type info:eu-repo/semantics/conferenceObject
dc.identifier.doi https://doi.org/10.1007/978-3-662-44371-2_15
dc.subject.keyword Bilinear maps
dc.subject.keyword Composite-order groups
dc.subject.keyword Groth-Sahai proofs
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.type.version info:eu-repo/semantics/acceptedVersion


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