All reports by Author Sagnik Saha:

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TR23-060
| 17th April 2023
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Sagnik Saha, Nikolaj Schwartzbach, Prashant Nalini Vasudevan#### The Planted $k$-SUM Problem: Algorithms, Lower Bounds, Hardness Amplification, and Cryptography

Revisions: 1

Sagnik Saha, Nikolaj Schwartzbach, Prashant Nalini Vasudevan

In the average-case $k$-SUM problem, given $r$ integers chosen uniformly at random from $\{0,\ldots,M-1\}$, the objective is to find a set of $k$ numbers that sum to $0$ modulo $M$ (this set is called a ``solution''). In the related $k$-XOR problem, given $k$ uniformly random Boolean vectors of length $\log{M}$, ... more >>>