We prove that any non-adaptive algorithm that tests whether an unknown
Boolean function $f\colon \{0, 1\}^n\to\{0, 1\} $ is a $k$-junta or $\epsilon$-far from every $k$-junta must make $\widetilde{\Omega}(k^{3/2} / \epsilon)$ many queries for a wide range of parameters $k$ and $\epsilon$. Our result dramatically improves previous lower ... more >>>

Yao's garbled circuit construction is a central cryptographic tool with numerous applications. In this tutorial, we study garbled circuits from a foundational point of view under the framework of \emph{randomized encoding} (RE) of functions. We review old and new constructions of REs, present some lower bounds, and describe some applications. ... more >>>

In this work, we introduce an online model for communication complexity. Analogous to how online algorithms receive their input piece-by-piece, our model presents one of the players Bob his input piece-by-piece, and has the players Alice and Bob cooperate to compute a result it presents Bob with the next piece. ... more >>>