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intelligence_src_e53adb99e40ae66258
observed · 2026-10-13 04:25:05 UTC
ePrint Report: Rapid mixing in superspecial isogeny graphs Maria Corte-Real Santos, Harun Kır, Olivier Taïbi, Benjamin Wesolowski We prove expansion properties of superspecial isogeny graphs in dimension $g \geq 2$, including arbitrary level structure. In particular, we provide explicit bounds for the spectral gap, and a fine characterization of obstructions created by level structures (disconnectedness and periodicity). Without the level structure (the only case which was previously studied), our bounds dramatically improve the state of the art. These isogenies in dimension greater than one have become increasingly important in isogeny-based cryptography, and previous works have already conjectured consequences of their expansion properties. We present several applications of our result: we transform conjectural predecessors into rigorous algorithms, and we give the first algorithm for computing endomorphism rings of superspecial principally polarized abelian varieties in arbitrary dimension, with complexity $\tilde O(p^{g-1})$.
Fingerprint: 170a045b4786fed3575aa0aee8616a6e2962340b6773041dff36b6976b05a223
intelligence_src_e53adb99e40ae66258
observed · 2026-10-12 16:25:03 UTC
available
Fingerprint: 366cb966e32414edc1db353849a1ee8d6b8462b83786e04001881ba6594765ad