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Multilinear Maps from Obfuscation [in press]

Albrecht, Martin R.; Farshim, Pooya; Han, Shuai; Hofheinz, Dennis; Larraia, Enrique; Paterson, Kenneth G.

We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs. This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction. We provide two distinct, but closely related constructions and show that multilinear analogues of the DDH assumption hold for them. Our first construction is symmetric and comes with a κ-linear map e : Gκ −→ GT for prime-order groups G and GT . To establish the hardness of the κ-linear DDH problem, we rely on the existence of a base group for which the κ-strong DDH assumption holds. Our second construction is for the asymmetric setting, where e : G1×· · ·×Gκ −→ GT for a collection of κ+1 prime-order groups G and GT , and relies only on the 1-strong DDH assumption in its base group. In both constructions, the linearity κ can be set to any arbitrary but a priori fixed polynomial value in the security parameter. We rely on a number of powerful tools in our constructions: probabilistic indistinguishability obfuscation, dual-mode NIZK proof systems (with perfect soundness, witness-indistinguishability, and zero knowledge), and additively homomorphic encryption for the group Z+N. ... mehr

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Verlagsausgabe §
DOI: 10.5445/IR/1000105369
Veröffentlicht am 21.02.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Theoretische Informatik (ITI)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 0933-2790, 1432-1378
KITopen-ID: 1000105369
Erschienen in Journal of cryptology
Vorab online veröffentlicht am 02.01.2020
Schlagwörter Multilinear map, Indistinguishability obfuscation, Homomorphic encryption, Decisional Diffie–Hellman, Groth–Sahai proofs
Nachgewiesen in Web of Science
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