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Graded Encoding Schemes from Obfuscation [chapter]

Pooya Farshim, Julia Hesse, Dennis Hofheinz, Enrique Larraia
2018 Lecture Notes in Computer Science  
We construct a graded encoding scheme (GES), an approximate form of graded multilinear maps.  ...  Technically, our scheme extends a previous, non-graded approximate multilinear map scheme due to Albrecht et al. (TCC 2016-A).  ...  We now define graded encoding schemes by introducing explicit algorithms for manipulating encodings of a graded encoding system. κ-graded encoding scheme. Let (R, S) be a κ-graded encoding system.  ... 
doi:10.1007/978-3-319-76581-5_13 fatcat:bz4uctwmh5cb5lehkhvw7if63a

Indistinguishability Obfuscation from Constant-Degree Graded Encoding Schemes [chapter]

Huijia Lin
2016 Lecture Notes in Computer Science  
We construct a general-purpose indistinguishability obfuscation (IO) scheme for all polynomialsize circuits from constant-degree graded encoding schemes in the plain model, assuming the existence of a  ...  In comparison, previous IO schemes rely on graded encodings with degree polynomial in the size of the obfuscated circuit.  ...  from constant-degree graded encoding schemes.  ... 
doi:10.1007/978-3-662-49890-3_2 fatcat:4l3fpbr4ungbpbt26dxlqwbljm

On Virtual Grey Box Obfuscation for General Circuits [chapter]

Nir Bitansky, Ran Canetti, Yael Tauman Kalai, Omer Paneth
2014 Lecture Notes in Computer Science  
Finally, we formulate a slightly stronger variant of the semantic security property of graded encoding schemes [Pass-Seth-Telang Crypto 14], and show that existing obfuscators such as the obfuscator of  ...  Barak et. al [Eurocrypt 14] are SIO for all circuits in NC 1 , assuming that the underlying graded encoding scheme satisfies our variant of semantic security.  ...  From Semantically-Secure Graded Encodings to Strong IO for NC 1 In this section we show that any semantically-secure graded encoding scheme, together with any ideal graded encoding obfuscation (i.e., any  ... 
doi:10.1007/978-3-662-44381-1_7 fatcat:lmmgxkneknd5ng7vskabfmgyvy

Indistinguishability Obfuscation from Semantically-Secure Multilinear Encodings [chapter]

Rafael Pass, Karn Seth, Sidharth Telang
2014 Lecture Notes in Computer Science  
We define a notion of semantic security of multilinear (a.k.a. graded) encoding schemes, which stipulates security of a class of algebraic "decisional" assumptions: roughly speaking, we require that for  ...  of m0, z are computationally indistinguishable from encodings of m1, z.  ...  We are especially gratefeul to Shai for pointing out the connection between semantical security for multilinear encodings and the "uber" assumption for bilinear maps of [BBG05] , and for several very  ... 
doi:10.1007/978-3-662-44371-2_28 fatcat:5phi5na4ajctvidwol6uqllofe

On Virtual Grey Box Obfuscation for General Circuits

Nir Bitansky, Ran Canetti, Yael Tauman Kalai, Omer Paneth
2016 Algorithmica  
The difficulty appears to be in capturing the security properties required from the graded encodings schemes [GGH13a, CLT13], which is a central component in the construction.  ...  Finally, we formulate a slightly stronger variant of the semantic security property of graded encoding schemes [Pass-Seth-Telang Crypto 14], and show that existing obfuscators, such as the obfuscator of  ...  Definition 6.4 (Ideal graded encoding obfuscation). Let E be a graded encoding scheme.  ... 
doi:10.1007/s00453-016-0218-8 fatcat:ytmngd6szjec7d4jkk5cdix36a

Virtual Black-Box Obfuscation for All Circuits via Generic Graded Encoding [chapter]

Zvika Brakerski, Guy N. Rothblum
2014 Lecture Notes in Computer Science  
(FOCS 2013) used graded encoding schemes to present a candidate obfuscator for indistinguishability obfuscation.  ...  We present a new general-purpose obfuscator for all polynomial-size circuits. The obfuscator uses graded encoding schemes, a generalization of multilinear maps.  ...  The Generic Graded Encoding Scheme Model. We prove that our construction is a blackbox obfuscator in the generic graded encoding scheme model.  ... 
doi:10.1007/978-3-642-54242-8_1 fatcat:cp3ksb2qvndsvlma4rrayrl7bu

On Secure and Usable Program Obfuscation: A Survey [article]

Hui Xu, Yangfan Zhou, Yu Kang, Michael R. Lyu
2017 arXiv   pre-print
Recently in 2013, Garg et al. have achieved a breakthrough in secure program obfuscation with a graded encoding mechanism and they have shown that it can fulfill a compelling security property, i.e., indistinguishability  ...  Besides, it focuses on obfuscating computation models (e.g., circuits) rather than real codes. In this paper, we aim to explore secure and usable obfuscation approaches from the literature.  ...  Note that the graded encoding schemes for program obfuscation are slightly different from their original versions for multiparty key exchange.  ... 
arXiv:1710.01139v1 fatcat:tef5esco7rggthw2sjybnze4dy

On Removing Graded Encodings from Functional Encryption [chapter]

Nir Bitansky, Huijia Lin, Omer Paneth
2017 Lecture Notes in Computer Science  
That is, we do not know how to move from an FE scheme based on graded encodings to an IO scheme that uses graded encodings in a black-box way.  ...  Since weakly-succinct FE schemes imply IO, we may be lead to think that weakly-succinct black-box constructions of FE from constant-degree graded encodings would already imply IO in the plain model from  ...  The issue is that the transformations removing degree-d graded encoding oracle from IO may blow up the size of the original obfuscation from | C| in the oracle model to roughly | C| 2d in the plain model  ... 
doi:10.1007/978-3-319-56614-6_1 fatcat:t4iv7jrxebazvap2rynuppk3q4

Obfuscating Conjunctions [chapter]

Zvika Brakerski, Guy N. Rothblum
2013 Lecture Notes in Computer Science  
Security follows from multilinear entropic variants of the Diffie-Hellman assumption.  ...  We conjecture that our construction is secure for any conjunction, regardless of the distribution from which it is drawn.  ...  We thank Ryo Nishimaki for pointing us to the zeroing attack on [GGH13] , and the authors of [CLT13] for discussing the applicability of such attack on their scheme.  ... 
doi:10.1007/978-3-642-40084-1_24 fatcat:pmltma7cpvb53f6dzrafjnbyi4

Obfuscating Conjunctions

Zvika Brakerski, Guy N. Rothblum
2015 Journal of Cryptology  
Security follows from multilinear entropic variants of the Diffie-Hellman assumption.  ...  We conjecture that our construction is secure for any conjunction, regardless of the distribution from which it is drawn.  ...  We thank Ryo Nishimaki for pointing us to the zeroing attack on [GGH13] , and the authors of [CLT13] for discussing the applicability of such attack on their scheme.  ... 
doi:10.1007/s00145-015-9221-5 fatcat:s2jt4vvpdvb5xix3er7c2dbweq

Obfuscating Circuits via Composite-Order Graded Encoding [chapter]

Benny Applebaum, Zvika Brakerski
2015 Lecture Notes in Computer Science  
We present a candidate obfuscator based on composite-order Graded Encoding Schemes (GES), which are a generalization of multilinear maps.  ...  Known instantiations of Graded Encoding Schemes allow us to obfuscate circuit classes of polynomial degree, which include for example families of circuits of logarithmic depth.  ...  Generic Graded Encoding Schemes. A Graded Encoding Scheme is parameterized by a ring R and a top level multiset v zt over the universe [τ ] .  ... 
doi:10.1007/978-3-662-46497-7_21 fatcat:gxunscomnvhpjpzajy3hlh4mom

Privacy-preserving Network Functionality Outsourcing [article]

Junjie Shi, Yuan Zhang, Sheng Zhong
2015 arXiv   pre-print
In contrast to the infeasibility in efficiency if a naive approach is adopted, we devise practical schemes that can outsource the middlebox as a blackbox after obfuscating it such that the cloud provider  ...  Both theoretical analysis and experiments on real-world firewall rules demonstrate that our schemes are secure, accurate, and practical.  ...  (κ−Graded Encoding System [11]) A κ-Graded Encoding System consists of a ring R and a system of sets S = {S (α) v ∈ {0, 1} * : v ∈ N, α ∈ R}, α 1 , α 2 ∈ R, every index i ≤ κ, and every u 1 ∈ S (α1) i  ... 
arXiv:1502.00389v1 fatcat:653sgm3mdjg2pafpc4twrpt6la

Virtual Grey-Boxes Beyond Obfuscation: A Statistical Security Notion for Cryptographic Agents [chapter]

Shashank Agrawal, Manoj Prabhakaran, Ching-Hua Yu
2016 Lecture Notes in Computer Science  
of NC 1 circuits to graded encoding schemas (Barak et al., 2014) and the assumption that there exists an Γ * -s-IND-PRE secure scheme for the graded encoding schema (Pass et al. 2014) .  ...  Our characterization also shows that the semantic security for graded encoding schemes (Pass et al. 2014) , is in fact an instance of this same definition.  ...  and to strong-sampler semantic security for graded encoding schemes and on the composition theorem for Γ *s-IND-PRE (as well as the existence of a statistical reduction from obfuscation for NC 1 to graded  ... 
doi:10.1007/978-3-662-53644-5_11 fatcat:q3nhpwux7nblnoykzwiz45i244

Black-box obfuscation for d-CNFs

Zvika Brakerski, Guy N. Rothblum
2014 Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14  
The family of functions we obfuscate is considerably richer than previous works that consider black-box obfuscation. 1 As one application, we show how to achieve obfuscated functional point testing: namely  ...  We show how to securely obfuscate a new class of functions: conjunctions of N C 0 d circuits.  ...  of a τ -Graded Encoding Scheme.  ... 
doi:10.1145/2554797.2554820 dblp:conf/innovations/BrakerskiR14 fatcat:2kej2lejavalpdsmjwnafxobku

Impossibility of VBB Obfuscation with Ideal Constant-Degree Graded Encodings [chapter]

Rafael Pass, Abhi Shelat
2015 Lecture Notes in Computer Science  
In contrast, Brakerski-Rothblum (TCC'15) and show that in idealized graded encoding models, generalpurpose VBB obfuscation indeed is possible; these construction require graded encoding schemes that enable  ...  We show a complementary impossibility of general-purpose VBB obfuscation in idealized graded encoding models that enable only evaluation of constant-degree polynomials (assuming trapdoor permutations).  ...  Remark (extension to rings) We note that our proof directly generalizes to any graded encoding scheme that operates on elements in a ring (as opposed to F p ) as long as a) there exists an efficient method  ... 
doi:10.1007/978-3-662-49096-9_1 fatcat:xpxktfdxfrch5nqoiiy3yjqcy4
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