This paper presents the first Distributed Oblivious RAM (DORAM) protocol that achieves sub-logarithmic communication overhead without computational assumptions.
That is, given $n$ $d$-bit memory locations, we present an information-theoretically secure protocol which requires $o(d \cdot \log(n))$ bits of communication per access (when $d = \Omega(\log^2(n)$).

This comes as a surprise, ... more >>>

An $n$-variate polynomial $g$ of degree $d$ is a $(n,d,t)$ design polynomial if the degree of the gcd of every pair of monomials of $g$ is at most $t-1$. The power symmetric polynomial $\mathrm{PSym}_{n,d} := \sum_{i=1}^{n} x^d_i$ and the sum-product polynomial $\mathrm{SP}_{s,d} := \sum_{i=1}^{s}\prod_{j=1}^{d} x_{i,j}$ are instances of design polynomials ... more >>>

A long-standing open problem dating back to the 1960s is whether there exists a search-to-decision reduction for the time-bounded Kolmogorov complexity problem - that is, the problem of determining whether the length of the shortest time-$t$ program generating a given string $x$ is at most $s$.

In this work, we ... more >>>