### TCS+ talk: Wednesday, October 21 — Aayush Jain, UCLA

The next TCS+ talk will take place this coming Wednesday, October 21th at 1:00 PM Eastern Time (10:00 AM Pacific Time, 19:00 Central European Time, 17:00 UTC). Aayush Jain from UCLA will speak about “Indistinguishability Obfuscation from Well-Founded Assumptions” (abstract below).

You can reserve a spot as an individual or a group to join us live by signing up on the online form. Due to security concerns, registration is required to attend the interactive talk. (The link to the YouTube livestream will also be posted on our website on the day of the talk, so people who did not sign up will still be able to watch the talk live.) As usual, for more information about the TCS+ online seminar series and the upcoming talks, or to suggest a possible topic or speaker, please see the website.

Abstract: We present a construction of an indistinguishability obfuscation scheme, whose security rests on the subexponential hardness of four well-founded assumptions. We show the existence of an indistinguishability Obfuscation scheme for all circuits assuming sub-exponential security of the following assumptions:

• The Learning with Errors (LWE) assumption with arbitrarily small subexponential modulus-to-noise ratio,
• The SXDH assumption with respect to bilinear groups of prime order $p$,
• Existence of a Boolean Pseudorandom Generator (PRG) in $\mathsf{NC}^0$ with arbitrary polynomial stretch, that is, mapping $n$ bits to $n^{1+\tau}$ bits, for any constant \tau>0.
• The Learning Parity with Noise (LPN) assumption over $\mathbb{Z}_p$ with error-rate $\ell^{-\delta}$, where $\ell$ is the dimension of the secret and $\delta>0$ is an arbitrarily small constant.
Further, assuming only polynomial security of these assumptions, there exists a compact public-key functional encryption scheme for all circuits.

The main technical novelty is the introduction and construction of a cryptographic pseudorandom generator that we call a Structured-Seed PRG (sPRG), assuming LPN over $\mathbb{Z}_p$ and PRGs in $\mathsf{NC}^0$. During the talk, I will discuss how structured seed PRGs have evolved from different notions of novel pseudorandom generators proposed in the past few years, and how an interplay between different areas of theoretical computer science played a major role in providing valuable insights leading to this work. Time permitting, I will go into the details of how to construct sPRGs.

Joint work with Huijia (Rachel) Lin and Amit Sahai