2 Part Seminar, Aayush Jain, Huijia (Rachel) Lin and Amit Sahai: Indistinguishability Obfuscation from Well-Founded Assumptions

Speaker: Aayush Jain, Huijia (Rachel) Lin and Amit Sahai

Date: Friday, December 04, 2020

Time: 1:00 PM to 4:00 PM Note: all times are in the Eastern Time Zone

Public: Yes

Location: Please email dlehto@mit.edu for Zoom Link

Event Type: Seminar

Room Description:

Host: Vinod Vaikuntanathan

Contact: Deborah Goodwin, dlehto@csail.mit.edu

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Reminders to: seminars@csail.mit.edu, cis-seminars@csail.mit.edu, crypto@lists.csail.mit.edu, theory-seminars@csail.mit.edu

Reminder Subject: TALK: 2 Part Seminar, Aayush Jain, Huijia (Rachel) Lin and Amit Sahai: Indistinguishability Obfuscation from Well-Founded Assumptions

Abstract:

Indistinguishability obfuscation, introduced by [Barak et. al. Crypto’2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions.

In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove:

Theorem (Informal) Let p be a prime of magnitude \Theta(2^n), where n is the security parameter. Assume sub-exponential security of the following assumptions:

the Learning With Errors (LWE) assumption over Z_p with subexponential modulus-to-noise ratio,

the Learning Parity with Noise (LPN) assumption over Z_p with polynomially many LPN samples and inverse polynomial error rate,

the existence of a Boolean Pseudo-Random Generator (PRG) in NC0 with polynomial stretch,

the Symmetric eXternal Diffie-Hellman (SXDH) assumption on asymmetric bilinear groups of order p.

Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists.

Further, assuming only polynomial security of the aforementioned assumptions, there exists collusion resistant public-key functional encryption for all polynomial-size circuits.

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See other events that are part of the Cryptography and Information Security (CIS) Seminar 2020.

Created by Deborah Goodwin at Thursday, December 03, 2020 at 9:40 AM.