The low-degree method postulates that no efficient algorithm outperforms low-degree polynomials in certain hypothesis-testing tasks. It has been used to understand computational indistinguishability in high-dimensional statistics.

We explore the use of the low-degree method in the context of cryptography. To this end, we apply it in the design and analysis ... more >>>

The celebrated $\mathbf{IP}=\mathbf{PSPACE}$ Theorem gives an efficient interactive proof for any bounded-space algorithm. In this work we study interactive proofs for non-deterministic bounded space computations. While Savitch's Theorem shows that nondeterministic bounded-space algorithms can be simulated by deterministic bounded-space algorithms, this simulation has a quadratic overhead. We give interactive protocols ... more >>>

We prove the first polynomial separation between randomized and deterministic time-space tradeoffs of multi-output functions. In particular, we present a total function that on the input of $n$ elements in $[n]$, outputs $O(n)$ elements, such that:

- There exists a randomized oblivious algorithm with space $O(\log n)$, time $O(n\log n)$ ... more >>>