Journal of Mathematical Cryptology (Dec 2018)
Better path-finding algorithms in LPS Ramanujan graphs
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.
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