We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in two models: Exact counting algorithms, which require reading the entire graph, and streaming algorithms, where the edges are given in a stream and the memory is limited. In this work ... more >>>

A one-way function is $d$-local if each of its outputs depends on at most $d$ input bits. In (Applebaum, Ishai, and Kushilevitz, FOCS 2004) it was shown that, under relatively mild assumptions, there exist $4$-local one-way functions (OWFs). This result is not far from optimal as it is not hard ... more >>>

Alice receives a tuple $(a_1,\ldots,a_t)$ of $t$ elements
from the group $G = \text{SL}(2,q)$. Bob similarly
receives a tuple $(b_1,\ldots,b_t)$. They are promised
that the interleaved product $\prod_{i \le t} a_i b_i$
equals to either $g$ and $h$, for two fixed elements $g,h
\in G$. Their task is to decide ... more >>>