On the Impossibility of Approximate Obfuscation Nir Bitansky

On the Impossibility of Approximate Obfuscation Nir Bitansky and Omer Paneth

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

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]

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

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