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Indistinguishability Obfuscation Without Multilinear Maps: iO from LWE, Bilinear Maps, and Weak Pseudorandomness [article]

Prabhanjan Ananth, Aayush Jain, Dakshita Khurana, Amit Sahai
2018 IACR Cryptology ePrint Archive  
The existence of secure indistinguishability obfuscators (iO) has far-reaching implications, significantly expanding the scope of problems amenable to cryptographic study.  ...  Informally, a ∆RG maps n integers to m integers, and has the property that for any sufficiently short vector a ∈ Z m , all efficient adversaries must fail to distinguish the distributions ∆RG(s) and (∆  ...  We thank Boaz Barak, Sam Hopkins and Pravesh Kothari for insights and extremely helpful suggestions about how attacks based on the Sum of Squares paradigm could impact our new assumptions on perturbation-resilient  ... 
dblp:journals/iacr/AnanthJKS18 fatcat:jxtfji2surgm3kw4trdbmsuue4

New Methods for Indistinguishability Obfuscation: Bootstrapping and Instantiation [article]

Shweta Agrawal
2018 IACR Cryptology ePrint Archive  
Constructing indistinguishability obfuscation (iO) [BGI + 01] is a central open question in cryptography. We provide new methods to make progress towards this goal.  ...  Bootstrapping.  ...  We thank Chris Peikert for telling us about the NTRU learning problem as well as for spending time thinking about our new problem of RLWE with structured noise.  ... 
dblp:journals/iacr/Agrawal18 fatcat:mmzzfqcisbdkvim2f6lmzhld7i

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.  ...  At a high level, we enable "bootstrapping" multilinear assumptions from their simpler counterparts in standard cryptographic groups and show the equivalence of PIO and multilinear maps under the existence  ...  This is not trivial since the new method should not lead to an exponential blowup in κ.  ... 
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  
For example, noise in GGH13 multilinear maps grows with the number of levels that need to be supported and must remain below the maximal noise supported by the multilinear map for correctness.  ...  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.  ...  All existing candidates of indistinguishability obfuscation (iO for short) for all circuits (i.e., P/Poly) rely on "bootstrapping" iO for weaker class of circuits.  ... 
doi:10.1007/978-3-030-05378-9_18 dblp:conf/indocrypt/DottlingG0MM18 fatcat:bew6pldtojdebldkhci3cdneie

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

Alice Pellet-Mary
2018 Lecture Notes in Computer Science  
Some others can be instantiated with either GGH13 or CLT13 multilinear map. For those, we only consider the GGH13 instantiation. 2 MSW14].  ...  They showed that iO for the class of polynomial-size branching programs 2 could be bootstrapped to iO for all polynomial-size circuits, 3 and they then described a candidate iO obfuscator for polynomial-size  ...  The author is grateful to Damien Stehlé for helpful discussions and comments on the draft. The author was supported by an ERC Starting Grant ERC-2013-StG-335086-LATTAC.  ... 
doi:10.1007/978-3-319-96878-0_6 fatcat:rbkrpz57i5eh7hlkpdqrfdqgqm

Indistinguishability Obfuscation from Trilinear Maps and Block-Wise Local PRGs [chapter]

Huijia Lin, Stefano Tessaro
2017 Lecture Notes in Computer Science  
We show that the existence of PRGs with block-wise locality is plausible for any L ≥ 3, and also provide: • A construction of a general-purpose indistinguishability obfuscator from L-linear maps and a  ...  All our constructions are based on the SXDH assumption on L-linear maps and subexponential Learning With Errors (LWE) assumption, and follow by instantiating our new generic bootstrapping theorems with  ...  Acknowledgements The authors thank Benny Applebaum and Vinod Vaikuntanathan for many helpful discussions and insights.  ... 
doi:10.1007/978-3-319-63688-7_21 fatcat:occcx3vwdjgvpben7w2px4ca2e

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

Prabhanjan Ananth, Amit Sahai
2017 Lecture Notes in Computer Science  
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.  ...  Recently, the works of Lin [Eurocrypt 2016] and Lin-Vaikuntanathan [FOCS 2016] showed how to build iO from constant-degree multilinear maps.  ...  encodings using prime order multilinear maps without increasing the degree.  ... 
doi:10.1007/978-3-319-56620-7_6 fatcat:57btx65zkvcadfnleohwevgovq

Obfuscation without the Vulnerabilities of Multilinear Maps [article]

Sanjam Garg, Pratyay Mukherjee, Akshayaram Srinivasan
2016 IACR Cryptology ePrint Archive  
Building on a modification of the Garg, Gentry and Halevi [EUROCRYPT 2013] multilinear maps (GGH for short), we present a new obfuscation candidate that is resilient to these vulnerabilities.  ...  Indistinguishability obfuscation is a central primitive in cryptography. Security of existing multilinear maps constructions on which current obfuscation candidates are based is poorly understood.  ...  Realizing this intuition involves building a new obfuscation construction and a corresponding multilinear maps that support it. Modifying GGH Maps and realizing our construction.  ... 
dblp:journals/iacr/GargMS16 fatcat:fc25rweksvautk37p2fvkbc6l4

Indistinguishability Obfuscation from SXDH on 5-Linear Maps and Locality-5 PRGs [chapter]

Huijia Lin
2017 Lecture Notes in Computer Science  
Two recent works [Lin, EUROCRYPT 2016, Lin and Vaikuntanathan, FOCS 2016] showed how to construct Indistinguishability Obfuscation (IO) from constant degree multilinear maps.  ...  In this work, we reduce the degree of multilinear maps needed to 5, by giving a new construction of IO from asymmetric L-linear maps and a pseudo-random generator (PRG) with output locality L and polynomial  ...  The author thanks Benny Applebaum, Nir Bitansky, Stefano Tessaro, and Vinod Vaikuntanathan for many helpful and insightful discussions.  ... 
doi:10.1007/978-3-319-63688-7_20 fatcat:zyatiaqpqrfgffjt6xfff55twi

Lattice-Based SNARGs and Their Application to More Efficient Obfuscation [chapter]

Dan Boneh, Yuval Ishai, Amit Sahai, David J. Wu
2017 Lecture Notes in Computer Science  
We then show a surprising connection between our new lattice-based SNARGs and the concrete efficiency of program obfuscation. All existing obfuscation candidates currently rely on multilinear maps.  ...  Among the constructions that make black-box use of the multilinear map, obfuscating a circuit of even moderate depth (say, 100) requires a multilinear map with multilinearity degree in excess of 2 100  ...  Acknowledgments We thank the anonymous reviewers for helpful feedback on the presentation. D. Boneh  ... 
doi:10.1007/978-3-319-56617-7_9 fatcat:5qejnchovjbzdht444ph35yiry

Protecting Obfuscation against Algebraic Attacks [chapter]

Boaz Barak, Sanjam Garg, Yael Tauman Kalai, Omer Paneth, Amit Sahai
2014 Lecture Notes in Computer Science  
security guarantees on candidate instantiations of multilinear maps.  ...  We describe a simplified variant of this compiler, and prove that it is a virtual black box obfuscator in a generic multilinear map model.  ...  They proved that their construction achieves a notion called indistinguishability obfuscation (see below for further explanation), under a complex new intractability assumption.  ... 
doi:10.1007/978-3-642-55220-5_13 fatcat:gcv4kioqrrculi6iwu3mjcgm3a

Indistinguishability Obfuscation: From Approximate to Exact [chapter]

Nir Bitansky, Vinod Vaikuntanathan
2015 Lecture Notes in Computer Science  
At the core of our techniques is a method for "fooling" the obfuscator into giving us the correct answer, while preserving the indistinguishability-based security.  ...  Put together with the recent results of Canetti, Kalai and Paneth (TCC 2015), Pass and Shelat (TCC 2016), and Mahmoody, Mohammed and Nemathaji (TCC 2016), we show how to convert indistinguishability obfuscation  ...  Acknowledgements We thank Ilan Komargodsky for pointing out [KMN + 14, Appendix B], and the anonymous TCC reviewers for their comments.  ... 
doi:10.1007/978-3-662-49096-9_4 fatcat:kwblzro4bnhdbdwb6zvrhp4cye

Graded Encoding Schemes from Obfuscation [chapter]

Pooya Farshim, Julia Hesse, Dennis Hofheinz, Enrique Larraia
2018 Lecture Notes in Computer Science  
Our construction relies on indistinguishability obfuscation, and a pairing-friendly group in which (a suitable variant of) the strong Diffie-Hellman assumption holds.  ...  We construct a graded encoding scheme (GES), an approximate form of graded multilinear maps.  ...  Acknowledgments We thank the anonymous reviewers for their helpful comments, and Kenny Paterson and Geoffroy Couteau for useful discussions.  ... 
doi:10.1007/978-3-319-76581-5_13 fatcat:bz4uctwmh5cb5lehkhvw7if63a

Factoring and Pairings are not Necessary for iO: Circular-Secure LWE Suffices [article]

Zvika Brakerski, Nico Döttling, Sanjam Garg, Giulio Malavolta
2020 IACR Cryptology ePrint Archive  
We construct indistinguishability obfuscation (iO) solely under circular-security properties of encryption schemes based on the Learning with Errors (LWE) problem.  ...  We show why their transformation inherently falls short of achieving the desired goal, and then rectify this situation by showing that shallow XiO (i.e. one where the obfuscator is depth-bounded) does  ...  In fact, several attacks on multilinear map candidates [CHL + 15,HJ16] and on obfuscation constructions based on multilinear maps [MSZ16, CGH17] were demonstrated.  ... 
dblp:journals/iacr/BrakerskiDGM20a fatcat:wndqqcak3vdi7ea2fhwalkpsry

Functional Encryption Without Obfuscation [chapter]

Sanjam Garg, Craig Gentry, Shai Halevi, Mark Zhandry
2015 Lecture Notes in Computer Science  
In this work, we overcome the above limitations and realize a fully secure functional encryption scheme without using indistinguishability obfuscation.  ...  Specifically the security of our scheme relies only on the polynomial hardness of simple assumptions on a variant of the new CLT composite order multilinear maps.  ...  This new garbling method, denoted by notationĈ, has the additional property that it hides the circuit C in the sense of indistinguishability obfuscation.  ... 
doi:10.1007/978-3-662-49099-0_18 fatcat:axvvtnq4dfaalmp6txlimt2v5u
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