We show that the bipartite matching problem is in NC. We extend the result to weighted bipartite matching and the computation of the noncommutative rank of a symbolic matrix. In particular, this implies that the decision version of linear matroid intersection is in NC as well. The techniques are based ... more >>>

We prove that level-$\ell$ Kikuchi graphs of random $2r$-uniform hypergraphs spectrally approximate Kikuchi graph of the complete $2r$-uniform hypergraph at a sampling rate that is sharp up to a logarithmic factor, in the regime $r\leq \ell \leq n/2$. Our proof is based on the matrix Bernstein inequality, but, unlike prior ... more >>>

Modern cryptography relies on the intractability of computational problems. We present an approach to build cryptography from a new source of hardness: proving mathematical theorems.

Our main result is a construction of succinct non-interactive arguments (SNARGs) for NP under standard derandomization (prBPP = prP) and cryptographic assumptions (LWE and SXDH), ... more >>>