On the Impossibility of Approximate Obfuscation Nir Bitansky
On the Impossibility of Approximate Obfuscation Nir Bitansky and Omer Paneth
Program Obfuscation
Program Obfuscation
Program Obfuscation
Virtual Black-Box [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01] - Security:
Impossibility of Obfuscation There exist families of functions that cannot be obfuscated [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01]
Relaxed Security [Barak et al. 01, Goldwasser-Rothblum 07, Hofheinz-Malone-Lee. Stam 07, Hohenberger-Rothblum-Shelat-Vaikuntanathan 07, Bitansky. Canetti 10] - Security:
Relaxed Functionality? - Security:
Approximate Obfuscation [Barak-Goldreich-Impagliazzo-Rudich-Sahai-Vadhan-Yang 01] - Security:
Main Result Assuming trapdoor permutations, there exist families of functions that cannot be approximately obfuscated Motivation? Positive applications
From Impossibility to Applications Impossibility of approximate obfuscation Non-black-box extraction Zero-knowledge with resettable security Worst-case extractable signatures
Plan [BGIRSVY 01]: Impossibility of Obfuscation Unobfuscatable Functions This work: Impossibility of Approximate Obfuscation Robust Unobfuscatable Functions Applications
Unobfuscatable Functions From Barak et al.
Robust Unobfuscatable Functions
Robust Unobfuscatable Functions
RUFs Construction
Unobfuscatable Functions Construction of Barak et al. (using FHE for simplicity)
Unobfuscatable Functions
Black-Box Unlearnability
Extraction
Robust Extraction?
A Taste of the Construction
Getting Robustness
Construction of RUFs
Assumptions • RUFs from trapdoor permutations. • Weak RUFs from OWF only:
Applications
Publicly-Verifiable RUOFs
Resettably-Sound ZK [Micali-Reyzin 01, Barak-Goldreich-Goldwasser-Lindell 01] Standard ZK Resettable Soundness
Resettable Soundness [Micali-Reyzin 01, Barak-Goldreich-Goldwasser-Lindell 01]
Resettable Soundness [Micali-Reyzin 01, Barak-Goldreich-Goldwasser-Lindell 01]
No Black-Box Simulator [Barak-Goldreich-Goldwasser-Lindell 01] Resettable soundness Zero-knowledge (black-box simulator)
Resettably-Sound ZK [Barak-Goldreich-Goldwasser-Lindell 01, BP 12, Chung-Pass-Seth 13] Resettable soundness Zero-knowledge (non-black-box simulator)
Resettably-Sound ZK
Resettably-Sound ZK
Analysis Resettable soundness Zero-knowledge
More Resettable Crypto • Resettably-sound ZK from OWFs (Different approach from Chung-Pass-Seth 13) • Simultaneously-resettable ZK from OWFs (using sr. WI by Chung-Ostrovsky-Pass-Visconti 13) • 4 -message resettably-sound ZK • 3 -message simultaneously-resettable WI proof of knowledge
Worst-Case Extractable Signatures Digital Signatures:
Worst-Case Extractable Signatures
- Slides: 41