Cryptography relies on the computational hardness of structured problems. While one-way functions, the most basic cryptographic object, do not seem to require much structure, as we advance up the ranks into public-key cryptography and beyond, we seem to require that certain structured problems are hard. For example, factoring, quadratic residuosity, ... more >>>

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

Let $\tau \in (0,\infty), \delta \in (0,1), \epsilon \in (0,1)$ be arbitrary constants. Assume sub-exponential security of the following assumptions, where $\lambda$ is a security parameter, and the parameters $\ell,k,n$ below ... more >>>

We present an elementary, self-contained proof of the result of Goldwasser and Rothblum [GR07] that the existence of a (perfect) statistically secure obfuscator implies a collapse of the polynomial hierarchy. In fact, we show that an existence of a weaker object implies a somewhat stronger statement. In addition, we extend ... more >>>

The range avoidance problem (denoted by Avoid) asks to find a string outside of the range of a given circuit $C:\{0,1\}^n\to\{0,1\}^m$, where $m>n$. Although at least half of the strings of length $m$ are correct answers, it is not clear how to deterministically find one. Recent results of Korten (FOCS'21) ... more >>>

We study close connections between Indistinguishability Obfuscation ($IO$) and the Minimum Circuit Size Problem ($MCSP$), and argue that algorithms for one of $MCSP$ or $IO$ would empower the other one. Some of our main results are:

\begin{itemize}
\item If there exists a perfect (imperfect) $IO$ that is computationally secure ... more >>>