A Note on the Permuted Puzzles Toy Conjecture
Keller Blackwell, Mary Wootters
TL;DR
This paper disproves a simplified version of a conjecture related to permuted puzzles, proposes a new conjecture, and aims to guide future research in the area, while noting similar independent findings.
Contribution
It invalidates a toy version of the conjecture from prior work and introduces a new conjecture to advance understanding in the field.
Findings
Disproved the toy conjecture by Boyle et al. (2017).
Proposed a new, refined conjecture.
Similar results independently obtained by Boyle et al. (2021).
Abstract
In this note, we show that a "Toy Conjecture" made by (Boyle, Ishai, Pass, Wootters, 2017) is false, and propose a new one. Our attack does not falsify the full ("non-toy") conjecture in that work, and it is our hope that this note will help further the analysis of that conjecture. Independently, (Boyle, Holmgren, Ma, Weiss, 2021) have obtained similar results.
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Taxonomy
TopicsCryptography and Data Security · Benford’s Law and Fraud Detection · Complexity and Algorithms in Graphs