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Lower Bounds on Assumptions Behind Indistinguishability Obfuscation [chapter]

Mohammad Mahmoody, Ameer Mohammed, Soheil Nematihaji, Rafael Pass, Abhi Shelat
2015 Lecture Notes in Computer Science  
In this work we prove lower bounds on the assumptions that imply iO in a black-box way, based on computational assumptions.  ...  Note that any lower bound for iO needs to somehow rely on computational assumptions, because if P = NP then statistically secure iO does exist. Our results are twofold: 1.  ...  To the best of our knowledge, no lower-bounds on the complexity of the assumptions behind iO are proved yet.  ... 
doi:10.1007/978-3-662-49096-9_3 fatcat:zmdkbhfxardzxboktbgrs2lv7q

On Virtual Grey Box Obfuscation for General Circuits [chapter]

Nir Bitansky, Ran Canetti, Yael Tauman Kalai, Omer Paneth
2014 Lecture Notes in Computer Science  
VGB obfuscation is often significantly more meaningful than indistinguishability obfuscation (IO).  ...  Put together, we obtain VGB obfuscation for all NC 1 circuits under assumptions that are almost the same as those used by Pass et. al to obtain IO for NC 1 circuits.  ...  SAT lower bounds.  ... 
doi:10.1007/978-3-662-44381-1_7 fatcat:lmmgxkneknd5ng7vskabfmgyvy

Indistinguishability Obfuscation from Functional Encryption

Nir Bitansky, Vinod Vaikuntanathan
2015 2015 IEEE 56th Annual Symposium on Foundations of Computer Science  
We also show that, under the Learning with Errors assumption, our techniques imply that any indistinguishability obfuscator can be converted into one where the size of obfuscated circuits is twice that  ...  applications of indistinguishability obfuscation.  ...  It is rather tempting to be pessimistic and to interpret our result as a lower-bound showing that improving functional encryption based on standard assumptions may be very hard, or perhaps straight out  ... 
doi:10.1109/focs.2015.20 dblp:conf/focs/BitanskyV15 fatcat:q6p3gz4pmrbltkanym7xhyit5q

One-Way Functions and (Im)Perfect Obfuscation

Ilan Komargodski, Tal Moran, Moni Naor, Rafael Pass, Alon Rosen, Eylon Yogev
2014 2014 IEEE 55th Annual Symposium on Foundations of Computer Science  
Most of them explicitly rely on additional hardness assumptions, such as one-way functions. Our goal is to get rid of this extra assumption.  ...  We cannot argue that indistinguishability obfuscation of all polynomial-time circuits implies the existence of one-way functions, since if P = NP, then program obfuscation (under the indistinguishability  ...  Intuitively, the proof of the lower bound goes as follows.  ... 
doi:10.1109/focs.2014.47 dblp:conf/focs/KomargodskiMNPRY14 fatcat:rwk52styv5foddpph3cq3fzfhi

Indistinguishability Obfuscation: From Approximate to Exact [chapter]

Nir Bitansky, Vinod Vaikuntanathan
2015 Lecture Notes in Computer Science  
on a certain samplable distribution, into exact indistinguishability obfuscation where the obfuscated circuit and the original circuit agree on all inputs.  ...  This is achieved based on various types of secure computation protocols that can be obtained from different standard assumptions.  ...  Indistinguishability: as in Definition 3.1. The intuition behind the proof is outlined in the introduction. We now turn to the actual proof. Proof.  ... 
doi:10.1007/978-3-662-49096-9_4 fatcat:kwblzro4bnhdbdwb6zvrhp4cye

Incremental Program Obfuscation [chapter]

Sanjam Garg, Omkant Pandey
2017 Lecture Notes in Computer Science  
We first give a construction achieving the weaker security notion based on the existence of general purpose indistinguishability obfuscation.  ...  We then turn to the indistinguishabilitybased notions, and present two security definitions of varying strength -namely, a weak one and a strong one.  ...  Positive results for indistinguishability obfuscation. Our lower bound motivates us to look more deeply into the definitions for incremental indistinguishability obfuscation, or IIO.  ... 
doi:10.1007/978-3-319-63715-0_7 fatcat:sgo2yetklnayhg6knq3e3cbf4u

Indistinguishability Obfuscation and UCEs: The Case of Computationally Unpredictable Sources [chapter]

Christina Brzuska, Pooya Farshim, Arno Mittelbach
2014 Lecture Notes in Computer Science  
We extend our attack to show that indistinguishability obfuscation is sufficient to also break the UCE security of any hash function against bounded parallel sources.  ...  We show that the existence of indistinguishability obfuscation (iO) implies (non-black-box) attacks on all the definitions that BHK proposed within their UCE framework in the original version of their  ...  We discuss the revised UCE assumptions introduced in [BHK13c], namely those for bounded parallel sources and split sources, in Sections 4 and 5, respectively. Indistinguishability obfuscation.  ... 
doi:10.1007/978-3-662-44371-2_11 fatcat:r3cxk4frozaodgqx3mkw4r7lsy

Output-Compressing Randomized Encodings and Applications [chapter]

Huijia Lin, Rafael Pass, Karn Seth, Sidharth Telang
2015 Lecture Notes in Computer Science  
most one input x * and their outputs on input x * are indistinguishable.  ...  their outputs and run-time are the same on all inputs,) O(Π 0 ) is indistinguishable from O(Π 1 ). iO for Turing machines [BGI + 01, BCP14, ABG + 13] additionally requires that the size of the obfuscated  ...  hash functions; this results was the inspiration behind our main impossibility result.  ... 
doi:10.1007/978-3-662-49096-9_5 fatcat:ouieihstoragrhmssu5zycbkmq

Succinct Randomized Encodings and their Applications

Nir Bitansky, Sanjam Garg, Huijia Lin, Rafael Pass, Sidharth Telang
2015 Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15  
assumptions on multi-linear maps.  ...  The scheme guarantees computational privacy of (Π, x), and is based on indistinguishability obfuscation for a relatively simple circuit class, for which there exist instantiations based on polynomial hardness  ...  adversaries, no lower bounds or barriers are known.  ... 
doi:10.1145/2746539.2746574 dblp:conf/stoc/BitanskyGLPT15 fatcat:xh456jdiz5aivdovp56tnb4ugq

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

Takashi Yamakawa, Shota Yamada, Goichiro Hanaoka, Noboru Kunihiro
2016 Algorithmica  
In this paper, we introduce a self-bilinear map with auxiliary information which is a weaker variant of a self-bilinear map, construct it based on indistinguishability obfuscation and prove that a useful  ...  Besides direct applications of our self-bilinear map, we show that our technique can also be used for constructing somewhat homomorphic encryption based on indistinguishability obfuscation and the Φ-hiding  ...  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  
In this paper, we introduce a self-bilinear map with auxiliary information which is a weaker variant of a self-bilinear map, construct it based on indistinguishability obfuscation and prove that a useful  ...  Besides direct applications of our self-bilinear map, we show that our technique can also be used for constructing somewhat homomorphic encryption based on indistinguishability obfuscation and the Φ-hiding  ...  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

On Virtual Grey Box Obfuscation for General Circuits

Nir Bitansky, Ran Canetti, Yael Tauman Kalai, Omer Paneth
2016 Algorithmica  
VGB obfuscation is often significantly more meaningful than indistinguishability obfuscation (IO).  ...  Put together, we obtain VGB obfuscation for all NC 1 circuits under assumptions that are almost the same as those used by Pass et al. to obtain IO for NC 1 circuits.  ...  To show this lower bound, we rely on a result by Wee [Wee05] that shows a similar lower from any point function obfuscation. Efficiency limitations via a generic attack.  ... 
doi:10.1007/s00453-016-0218-8 fatcat:ytmngd6szjec7d4jkk5cdix36a

The Magic of ELFs [chapter]

Mark Zhandry
2016 Lecture Notes in Computer Science  
The only known positive example [CCR16] relies on extremely strong cryptographic assumptions such as general-purpose program obfuscation.  ...  Similar weaknesses have been shown for other strong assumptions that can be cast as families of assumptions or as knowledge/extracting assumptions, such as extractable one-way functions (eOWFs) [BCPR14  ...  Let δ be an inverse polynomial that lower bounds infinitely often.  ... 
doi:10.1007/978-3-662-53018-4_18 fatcat:xaay2rqylvdalagbnibfol76va

The Magic of ELFs

Mark Zhandry
2018 Journal of Cryptology  
The only known positive example [CCR16] relies on extremely strong cryptographic assumptions such as general-purpose program obfuscation.  ...  Similar weaknesses have been shown for other strong assumptions that can be cast as families of assumptions or as knowledge/extracting assumptions, such as extractable one-way functions (eOWFs) [BCPR14  ...  Let δ be an inverse polynomial that lower bounds infinitely often.  ... 
doi:10.1007/s00145-018-9289-9 fatcat:aox3v4ow5nhf3mohas7dhotopa

Lower Bounds on Obfuscation from All-or-Nothing Encryption Primitives [chapter]

Sanjam Garg, Mohammad Mahmoody, Ameer Mohammed
2017 Lecture Notes in Computer Science  
Hence, tremendous research effort has been put towards basing obfuscation on better-understood computational assumptions.  ...  Indistinguishability obfuscation (IO) enables many heretofore out-of-reach applications in cryptography.  ...  Now we describe previous work on the complexity of assumptions behind IO and previous works on generalizing the black-box framework of [47, 62] . Previous Lower Bounds on Complexity of IO.  ... 
doi:10.1007/978-3-319-63688-7_22 fatcat:bgqet5sbynfmfotz74oxd3pykq
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