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Multilinear Maps from Obfuscation [chapter]

Martin R. Albrecht, Pooya Farshim, Dennis Hofheinz, Enrique Larraia, Kenneth G. Paterson
2015 Lecture Notes in Computer Science  
This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction.  ...  We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs.  ...  The relationship between IO and multilinear maps is a very natural question to study, given the rich diversity of cryptographic constructions that have been obtained from both multilinear maps and obfuscation  ... 
doi:10.1007/978-3-662-49096-9_19 fatcat:ebd4hoi75vdtrhnkgz2flqf6ua

Multilinear Maps from Obfuscation

Martin R. Albrecht, Pooya Farshim, Shuai Han, Dennis Hofheinz, Enrique Larraia, Kenneth G. Paterson
2020 Journal of Cryptology  
This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction.  ...  We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs.  ...  Multilinear Maps from Obfuscation Game 5 : A s G a m e 4 (bottom).]  ... 
doi:10.1007/s00145-019-09340-0 fatcat:7bcpzd5knjcchch4ddhaojewum

Obfuscation from Low Noise Multilinear Maps [chapter]

Nico Döttling, Sanjam Garg, Divya Gupta, Peihan Miao, Pratyay Mukherjee
2018 CSR und Social Enterprise  
Finally, we investigate the security of the considered composite order variants of GGH13 multilinear maps from a cryptanalytic standpoint.  ...  Our constructions are obtained by instantiating a modification of the Lin's [EUROCRYPT 2016] obfuscation construction with composite order variants of the GGH13 multilinear maps.  ...  Self-fortification from constant-degree multilinear maps.  ... 
doi:10.1007/978-3-030-05378-9_18 dblp:conf/indocrypt/DottlingG0MM18 fatcat:bew6pldtojdebldkhci3cdneie

Projective Arithmetic Functional Encryption and Indistinguishability Obfuscation from Degree-5 Multilinear Maps [chapter]

Prabhanjan Ananth, Amit Sahai
2017 Lecture Notes in Computer Science  
. iO from degree-5 multilinear maps.  ...  We give a degree-preserving construction of PAFE from multilinear maps. That is, we show how to achieve PAFE for arithmetic circuits of degree d using only degree-d multilinear maps.  ...  multilinear maps. iO from degree-5 multilinear maps.  ... 
doi:10.1007/978-3-319-56620-7_6 fatcat:57btx65zkvcadfnleohwevgovq

Cryptanalyses of Branching Program Obfuscations over GGH13 Multilinear Map from the NTRU Problem [chapter]

Jung Hee Cheon, Minki Hhan, Jiseung Kim, Changmin Lee
2018 Lecture Notes in Computer Science  
In this paper, we propose cryptanalyses of all existing indistinguishability obfuscation (iO) candidates based on branching programs (BP) over GGH13 multilinear map for all recommended parameter settings  ...  More precisely, the underlying lattice dimension of GGH13 should be set to n =Θ(κ 2 λ) to rule out attacks from the subfield algorithm for NTRU where κ is the multilinearity level and λ the security parameter  ...  attacks on BP obfuscations over GGH13 multilinear map [24] .  ... 
doi:10.1007/978-3-319-96878-0_7 fatcat:e5hxxkrxizd2zdi2rpnfbgzcwi

How to Obfuscate Programs Directly [chapter]

Joe Zimmerman
2015 Lecture Notes in Computer Science  
From "clean" multilinear maps, on the other hand (whose existence is still open), we present the first approach that would achieve obfuscation for P/poly directly, without FHE.  ...  We propose a new way to obfuscate programs, using composite-order multilinear maps.  ...  [GLSW14] constructs indistinguishability obfuscation (iO) from composite-order multilinear maps.  ... 
doi:10.1007/978-3-662-46803-6_15 fatcat:6wnoonhj6feblo65oi4xwkxlpu

Quantum Attacks Against Indistinguishablility Obfuscators Proved Secure in the Weak Multilinear Map Model [chapter]

Alice Pellet-Mary
2018 Lecture Notes in Computer Science  
The main security weakness of these candidate obfuscators stems from the underlying candidate multilinear maps.  ...  In the following, we will instantiate all the obfuscators with the GGH13 [GGH13a] multilinear map, 5 as our attack exploits a weakness of this specific multilinear map.  ...  The DGGMM obfuscator was designed to obtain a candidate iO obfuscator from low noise multilinear maps.  ... 
doi:10.1007/978-3-319-96878-0_6 fatcat:rbkrpz57i5eh7hlkpdqrfdqgqm

Zeroizing Attacks on Indistinguishability Obfuscation over CLT13 [chapter]

Jean-Sébastien Coron, Moon Sung Lee, Tancrède Lepoint, Mehdi Tibouchi
2017 Lecture Notes in Computer Science  
In this work, we describe a new polynomial-time attack on the multilinear maps of Coron, Lepoint, and Tibouchi (CLT13), when used in candidate iO schemes.  ...  More specifically, we show that given the obfuscation of the simple branching program that computes the always zero functionality previously considered by Miles, Sahai and Zhandry (Crypto 2016), one can  ...  Let us describe the obfuscation procedure of the branching program A from Section 3.1, over the CLT13 multilinear map.  ... 
doi:10.1007/978-3-662-54365-8_3 fatcat:vvrmhufa3ffvjjbid7aqapjvsa

Obfuscating Re-encryption Algorithm With Flexible and Controllable Multi-Hop on Untrusted Outsourcing Server

Mingwu Zhang, Yan Jiang, Yi Mu, Willy Susilo
2017 IEEE Access  
INDEX TERMS Average-case virtual black-box, controllable multi-hop, multilinear map, obfuscation, re-encryption.  ...  We also present a flexible and controllable construction of re-encryption scheme, functionality model and its obfuscation version in leveled multilinear groups, and exemplify some scenarios to deploy in  ...  Compared with leveled multilinear maps in this work that encoding is deterministic, the encoding of candidate multilinear maps proposed by Garg et al.  ... 
doi:10.1109/access.2017.2771335 fatcat:i2berlgkmvfjlf4nuzujyec2ji

5Gen

Kevin Lewi, Mariana Raykova, Alex J. Malozemoff, Daniel Apon, Brent Carmer, Adam Foltzer, Daniel Wagner, David W. Archer, Dan Boneh, Jonathan Katz
2016 Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security - CCS'16  
Roughly speaking, an obfuscator takes as input a program and 1 The name 5Gen comes from the fact that multilinear maps can be considered the "fifth generation" of cryptography, where the prior four are  ...  Secure multilinear maps (mmaps) have been shown to have remarkable applications in cryptography, such as multi-input functional encryption (MIFE) and program obfuscation.  ...  Multilinear maps.  ... 
doi:10.1145/2976749.2978314 dblp:conf/ccs/LewiMACFWABK016 fatcat:q424asoc7be47msxbdwoojqkre

Indistinguishability Obfuscation from the Multilinear Subgroup Elimination Assumption

Craig Gentry, Allison Bishop Lewko, Amit Sahai, Brent Waters
2015 2015 IEEE 56th Annual Symposium on Foundations of Computer Science  
We revisit the question of constructing secure general-purpose indistinguishability obfuscation (iO), with a security reduction based on explicit computational assumptions over multilinear maps.  ...  In our work, we provide the first construction of general-purpose indistinguishability obfuscation proven secure via a reduction to a natural computational assumption over multilinear maps, namely, the  ...  Our work provides a natural security reduction mapping indistinguishability obfuscation to a natural assumption over multilinear maps.  ... 
doi:10.1109/focs.2015.19 dblp:conf/focs/GentryLSW15 fatcat:tbth5tc7pvcdrihmc5awoejjei

Protecting Obfuscation against Algebraic Attacks [chapter]

Boaz Barak, Sanjam Garg, Yael Tauman Kalai, Omer Paneth, Amit Sahai
2014 Lecture Notes in Computer Science  
We describe a simplified variant of this compiler, and prove that it is a virtual black box obfuscator in a generic multilinear map model.  ...  security guarantees on candidate instantiations of multilinear maps.  ...  Matrix multiplication is an algebraic (and in fact multilinear) operation, that can be done in a group supporting multilinear maps.  ... 
doi:10.1007/978-3-642-55220-5_13 fatcat:gcv4kioqrrculi6iwu3mjcgm3a

Self-Bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications

Takashi Yamakawa, Shota Yamada, Goichiro Hanaoka, Noboru Kunihiro
2016 Algorithmica  
From our construction, we obtain a multilinear map with interesting properties: the level of multilinearity is not bounded in the setup phase, and representations of group elements are compact, i.e., their  ...  This is the first construction of a multilinear map with these properties. Note, however, that to evaluate the multilinear map, auxiliary information is required.  ...  Especially, we would like to thank Satsuya Ohata for his instructive comment on self-bilinear maps, and Takahiro Matsuda and Jacob Schuldt for their detailed proofreading.  ... 
doi:10.1007/s00453-016-0250-8 fatcat:iboxtbx6hbefjcvpxkoozvqeby

Self-bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications [chapter]

Takashi Yamakawa, Shota Yamada, Goichiro Hanaoka, Noboru Kunihiro
2014 Lecture Notes in Computer Science  
From our construction, we obtain a multilinear map with interesting properties: the level of multilinearity is not bounded in the setup phase, and representations of group elements are compact, i.e., their  ...  This is the first construction of a multilinear map with these properties. Note, however, that to evaluate the multilinear map, auxiliary information is required.  ...  Especially, we would like to thank Satsuya Ohata for his instructive comment on self-bilinear maps, and Takahiro Matsuda and Jacob Schuldt for their detailed proofreading.  ... 
doi:10.1007/978-3-662-44381-1_6 fatcat:uezb2kjetfabdnqb7pwtyn2cou

How to Avoid Obfuscation Using Witness PRFs [chapter]

Mark Zhandry
2015 Lecture Notes in Computer Science  
Current candidate obfuscators are far from practical and typically rely on unnatural hardness assumptions about multilinear maps.  ...  We give a construction of witness PRFs from multilinear maps that is simpler and much more efficient than current obfuscation candidates, thus bringing several applications of obfuscation closer to practice  ...  A simple instantiation from multilinear maps. We now construct subset-sum encodings from asymmetric multilinear maps. Construction 5.3.  ... 
doi:10.1007/978-3-662-49099-0_16 fatcat:axsywzqmjngujl7gplqn2chfs4
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