Two matrices are said to be principal minor equivalent if they have equal
corresponding principal minors of all orders. We give a characterization of
principal minor equivalence and a deterministic polynomial time algorithm to
check if two given matrices are principal minor equivalent. Earlier such
results were known for ... more >>>

We show that every NP relation that can be verified by a bounded-depth polynomial-sized circuit, or a bounded-space polynomial-time algorithm, has a computational zero-knowledge proof (with statistical soundness) with communication that is only additively larger than the witness length. Our construction relies only on the minimal assumption that one-way functions ... more >>>

The classical Reed-Muller codes over a finite field $\mathbb{F}_q$ are based on evaluations of $m$-variate polynomials of degree at most $d$ over a product set $U^m$, for some $d$ less than $|U|$. Because of their good distance properties, as well as the ubiquity and expressive power of polynomials, these codes ... more >>>