Better path-finding algorithms in LPS Ramanujan graphs
Carvalho Pinto Eduardo, Petit Christophe
Journal of Mathematical Cryptology · 2018
doi:10.1515/jmc-2017-0051 (opens in a new tab)
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Abstract
We provide a new heuristic polynomial time algorithm that computes short paths between arbitrary pairs of vertices in Lubotzky–Philipps–Sarnak’s Ramanujan graphs. The paths returned by our algorithm are shorter by a factor approximately 16/7 compared to previous work, and they are close to optimal for vertices corresponding to diagonal matrices. Our results also lead to an improved cryptanalysis of the Charles–Goren–Lauter hash function.
Abstract licence: CC BY
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