ON OBFUSCATION WITH RANDOM ORACLES RAN CANETTI YAEL
ON OBFUSCATION WITH RANDOM ORACLES RAN CANETTI, YAEL KALAI, OMER PANETH
![[Lynn-Prabhakaran-Sahai 04]: Can simulation based obfuscation be constructed with a Random Oracle? Today: Impossible](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-2.jpg "[Lynn-Prabhakaran-Sahai 04]: Can simulation based obfuscation be constructed with a Random Oracle? Today: Impossible")
[Lynn-Prabhakaran-Sahai 04]: Can simulation based obfuscation be constructed with a Random Oracle? Today: Impossible in general!
![A Candidate Obfuscator [Garg-Gentry-Halevi-Raykova-Sahai-Waters 13] Multilinear Maps Barrington's theorem Kilian’s randomization](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-3.jpg "A Candidate Obfuscator [Garg-Gentry-Halevi-Raykova-Sahai-Waters 13] Multilinear Maps Barrington's theorem Kilian’s randomization")
A Candidate Obfuscator [Garg-Gentry-Halevi-Raykova-Sahai-Waters 13] Multilinear Maps Barrington's theorem Kilian’s randomization
What is the security of the candidate obfuscator? Other candidate obfuscators: [Brakerski-Rothblum 13, Barak-Garg-Kalai-P-Sahai 13, Pass. Seth-Telang 13, Ananth-Gupta-Ishai-Sahai 14, Gentry-Lewko. Sahai-Waters 14, Zimmerman 14, Applebaum-Brakerski 15, Badrinarayanan-Miles-Sahai-Zhandry 15]
![Virtual-Black-Box Obfuscation (VBB) [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01]](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-5.jpg "Virtual-Black-Box Obfuscation (VBB) [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01]")
Virtual-Black-Box Obfuscation (VBB) [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01]
What is the security of the candidate obfuscators?
![Indistinguishability obfuscation [BGIRSVY 01] Virtual-black-box obfuscation Impossible PC differing-inputs obfuscation [BGIRSVY 01] [Ishai-Pandey-Sahai 14]](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-7.jpg "Indistinguishability obfuscation [BGIRSVY 01] Virtual-black-box obfuscation Impossible PC differing-inputs obfuscation [BGIRSVY 01] [Ishai-Pandey-Sahai 14]")
Indistinguishability obfuscation [BGIRSVY 01] Virtual-black-box obfuscation Impossible PC differing-inputs obfuscation [BGIRSVY 01] [Ishai-Pandey-Sahai 14] Plausible Virtual-grey-box obfuscation [Bitansky-Canetti 10] Ideal model security Provable [BR 14, BGKPS 14]
The Ideal Multilinear-Map Model • Add Subtract • Multiply (multilinear only)
![Security [Brakerski-Rothblum 14, Barak-Garg-Kalai-P-Sahai 14] Ideal MMap Oracle The [BGIRSVI 01] does not extend!](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-9.jpg "Security [Brakerski-Rothblum 14, Barak-Garg-Kalai-P-Sahai 14] Ideal MMap Oracle The [BGIRSVI 01] does not extend!")
Security [Brakerski-Rothblum 14, Barak-Garg-Kalai-P-Sahai 14] Ideal MMap Oracle The [BGIRSVI 01] does not extend!
![Unobfuscatable Functions [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01] Oracle](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-10.jpg "Unobfuscatable Functions [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01] Oracle")
Unobfuscatable Functions [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01] Oracle
![[Miles-Sahai-Weiss 14, Pass-Seth-Telang 13, Bitansky-Canetti-Kalai-P 14] Indistinguishability obfuscation Reduction Virtual-black-box obfuscation Heuristic PC differing-inputs](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-11.jpg "[Miles-Sahai-Weiss 14, Pass-Seth-Telang 13, Bitansky-Canetti-Kalai-P 14] Indistinguishability obfuscation Reduction Virtual-black-box obfuscation Heuristic PC differing-inputs")
[Miles-Sahai-Weiss 14, Pass-Seth-Telang 13, Bitansky-Canetti-Kalai-P 14] Indistinguishability obfuscation Reduction Virtual-black-box obfuscation Heuristic PC differing-inputs Obfuscation in the ideal mmap model Virtual-grey-box obfuscation Mmap construction
Can we get obfuscation in other ideal models? Ideal Multilinear Map Generic group model? Random oracle model? Plain Model
Constructions in Other Ideal Models • Obfuscation with secure hardware [Goyal-Ishai-Sahai-Venkatesan-Wadia 10, Bitansky-Canetti-Goldwasser-Halevi-Kalai-Rothblum 11, …] • Ideal pseudo-free groups [Canetti-Vaikuntanathan 13] • Multilinear maps with relaxed security [Miles-Sahai-Weiss 14]
A Different Motivation What is the best security we can hope for? VBB Obfuscation Plausible Impossible
A Different Motivation Indistinguishability obfuscation PC differing-inputs obfuscation Virtual-grey-box obfuscation Virtual-black-box obfuscation Impossible Ideal model security
A Different Motivation What structures are needed? Ideal Multilinear Map Generic group model? Random oracle model? Plain Model
Motivation – Summary 1. Alternative heuristic obfuscators in the plain model 2. Understand the structures needed for general purpose obfuscation
The Result First negative result with respect to a non-trivial oracle! Ideal Multilinear Map Generic group model? Random oracle model Plain Model
Main Lemma Any function that can be obfuscated with a random oracle, can also be VBB obfuscated in the plain model with approximate correctness.
![Proof Outline Main Lemma + Theorem [Bitansky-P 13]: Assuming trapdoor permutations, there exist “robust”](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-20.jpg "Proof Outline Main Lemma + Theorem [Bitansky-P 13]: Assuming trapdoor permutations, there exist “robust”")
Proof Outline Main Lemma + Theorem [Bitansky-P 13]: Assuming trapdoor permutations, there exist “robust” unobfuscatable functions that cannot be obfuscated (in the plain model) even with approximate correctness.
![Proof Outline Main Lemma + [Bitansky-P 13] Robust unobfuscatable functions cannot be obfuscated with](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-21.jpg "Proof Outline Main Lemma + [Bitansky-P 13] Robust unobfuscatable functions cannot be obfuscated with")
Proof Outline Main Lemma + [Bitansky-P 13] Robust unobfuscatable functions cannot be obfuscated with random oracles
Main Lemma Random oracle Approximately correct
Naïve Attempt Perfect correctness No security
Approximate Correctness
Approximate Correctness
![Comparison with [Impagliazzo-Rrudich 95] Information theoretic key agreement with random oracle [IR 95] Information](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-27.jpg "Comparison with [Impagliazzo-Rrudich 95] Information theoretic key agreement with random oracle [IR 95] Information")
Comparison with [Impagliazzo-Rrudich 95] Information theoretic key agreement with random oracle [IR 95] Information theoretic key agreement In the plain model Obfuscation with random oracle Today Approximately correct obfuscation in the plain model
![Robust Unobfuscatable Functions [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01]](http://slidetodoc.com/presentation_image/57e96867989f72eb05a9ccd78a26f43f/image-28.jpg "Robust Unobfuscatable Functions [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01]")
Robust Unobfuscatable Functions [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01]
approximately correct
A Taste of the Construction
Getting Robustness
Robust Unobfuscatable Functions
Thank You! Ideal Multilinear Map Generic group model? Random oracle model Plain Model
- Slides: 38