On the Hardness of Average-case k-SUM

Noah Stephens-Davidowitz
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Abstract:

In this work, we show the first worst-case to average-case reduction for the classical \$k\$-SUM problem. A \$k\$-SUM instance is a collection of \$m\$ integers, and the goal of the \$k\$-SUM problem is to find a subset of \$k\$ elements that sums to \$0\$. In the average-case version, the \$m\$ elements are chosen uniformly at random from some inter...More

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