Multilinear Maps from Obfuscation. / Albrecht, Martin; Farshim, Pooya; Hofheinz, Dennis; Larraia de Vega, Enrique; Paterson, Kenneth.

Theory of Cryptography. ed. / Eyal Kushilevitz; Tal Malkin. Vol. 9562 Springer, 2015. p. 446-473 (Lecture Notes in Computer Science; Vol. 9562).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Published

Standard

Multilinear Maps from Obfuscation. / Albrecht, Martin; Farshim, Pooya; Hofheinz, Dennis; Larraia de Vega, Enrique; Paterson, Kenneth.

Theory of Cryptography. ed. / Eyal Kushilevitz; Tal Malkin. Vol. 9562 Springer, 2015. p. 446-473 (Lecture Notes in Computer Science; Vol. 9562).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Harvard

Albrecht, M, Farshim, P, Hofheinz, D, Larraia de Vega, E & Paterson, K 2015, Multilinear Maps from Obfuscation. in E Kushilevitz & T Malkin (eds), Theory of Cryptography. vol. 9562, Lecture Notes in Computer Science, vol. 9562, Springer, pp. 446-473. https://doi.org/10.1007/978-3-662-49096-9_19

APA

Albrecht, M., Farshim, P., Hofheinz, D., Larraia de Vega, E., & Paterson, K. (2015). Multilinear Maps from Obfuscation. In E. Kushilevitz, & T. Malkin (Eds.), Theory of Cryptography (Vol. 9562, pp. 446-473). (Lecture Notes in Computer Science; Vol. 9562). Springer. https://doi.org/10.1007/978-3-662-49096-9_19

Vancouver

Albrecht M, Farshim P, Hofheinz D, Larraia de Vega E, Paterson K. Multilinear Maps from Obfuscation. In Kushilevitz E, Malkin T, editors, Theory of Cryptography. Vol. 9562. Springer. 2015. p. 446-473. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-662-49096-9_19

Author

Albrecht, Martin ; Farshim, Pooya ; Hofheinz, Dennis ; Larraia de Vega, Enrique ; Paterson, Kenneth. / Multilinear Maps from Obfuscation. Theory of Cryptography. editor / Eyal Kushilevitz ; Tal Malkin. Vol. 9562 Springer, 2015. pp. 446-473 (Lecture Notes in Computer Science).

BibTeX

@inproceedings{0478719c052f492db60a86bd0e096d0e,
title = "Multilinear Maps from Obfuscation",
abstract = "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 DDHDDH assumption hold for them. Our first construction is symmetric and comes with a κκ-linear map e:Gκ⟶GTe:Gκ⟶GTfor prime-order groups GG and GTGT. To establish the hardness of the κκ-linear DDHDDH problem, we rely on the existence of a base group for which the (κ−1)(κ−1)-strong DDHDDH assumption holds. Our second construction is for the asymmetric setting, where e:G1×⋯×Gκ⟶GTe:G1×⋯×Gκ⟶GT for a collection of κ+1κ+1 prime-order groups GiGi and GTGT, and relies only on the standard DDHDDH assumption in its base group. In both constructions the linearity κκ 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+NZN+. At a high level, we enable “bootstrapping” multilinear assumptions from their simpler counterparts in standard cryptographic groups, and show the equivalence of IO and multilinear maps under the existence of the aforementioned primitives.",
author = "Martin Albrecht and Pooya Farshim and Dennis Hofheinz and {Larraia de Vega}, Enrique and Kenneth Paterson",
year = "2015",
month = dec,
day = "19",
doi = "10.1007/978-3-662-49096-9_19",
language = "English",
isbn = "978-3-662-49095-2",
volume = "9562",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "446--473",
editor = "Eyal Kushilevitz and Malkin, {Tal }",
booktitle = "Theory of Cryptography",

}

RIS

TY - GEN

T1 - Multilinear Maps from Obfuscation

AU - Albrecht, Martin

AU - Farshim, Pooya

AU - Hofheinz, Dennis

AU - Larraia de Vega, Enrique

AU - Paterson, Kenneth

PY - 2015/12/19

Y1 - 2015/12/19

N2 - 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 DDHDDH assumption hold for them. Our first construction is symmetric and comes with a κκ-linear map e:Gκ⟶GTe:Gκ⟶GTfor prime-order groups GG and GTGT. To establish the hardness of the κκ-linear DDHDDH problem, we rely on the existence of a base group for which the (κ−1)(κ−1)-strong DDHDDH assumption holds. Our second construction is for the asymmetric setting, where e:G1×⋯×Gκ⟶GTe:G1×⋯×Gκ⟶GT for a collection of κ+1κ+1 prime-order groups GiGi and GTGT, and relies only on the standard DDHDDH assumption in its base group. In both constructions the linearity κκ 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+NZN+. At a high level, we enable “bootstrapping” multilinear assumptions from their simpler counterparts in standard cryptographic groups, and show the equivalence of IO and multilinear maps under the existence of the aforementioned primitives.

AB - 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 DDHDDH assumption hold for them. Our first construction is symmetric and comes with a κκ-linear map e:Gκ⟶GTe:Gκ⟶GTfor prime-order groups GG and GTGT. To establish the hardness of the κκ-linear DDHDDH problem, we rely on the existence of a base group for which the (κ−1)(κ−1)-strong DDHDDH assumption holds. Our second construction is for the asymmetric setting, where e:G1×⋯×Gκ⟶GTe:G1×⋯×Gκ⟶GT for a collection of κ+1κ+1 prime-order groups GiGi and GTGT, and relies only on the standard DDHDDH assumption in its base group. In both constructions the linearity κκ 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+NZN+. At a high level, we enable “bootstrapping” multilinear assumptions from their simpler counterparts in standard cryptographic groups, and show the equivalence of IO and multilinear maps under the existence of the aforementioned primitives.

UR - http://eprint.iacr.org/2015/780

U2 - 10.1007/978-3-662-49096-9_19

DO - 10.1007/978-3-662-49096-9_19

M3 - Conference contribution

SN - 978-3-662-49095-2

VL - 9562

T3 - Lecture Notes in Computer Science

SP - 446

EP - 473

BT - Theory of Cryptography

A2 - Kushilevitz, Eyal

A2 - Malkin, Tal

PB - Springer

ER -