Supersingular isogeny search
Construct an explicit isogeny between two supersingular elliptic curves.
5 variants · 8 entries. Compare bounds only within the same variant.
COMPARISON VARIANTREGIME / INSTANCEENTRIESBEST c
SSIPGeneral curves · classical · unconditionalClassical · ProvableAny explicit isogeny between supersingular elliptic curves; unconditional asymptotic analysisSupersingular curves over F_{p^2}30.333333 SSIPGeneral curves · classical · heuristicClassical · HeuristicAny explicit isogeny between two supersingular elliptic curves; p→∞Supersingular curves over F_{p^2}20.333333 SSIPF_p-rational curves · classical · heuristicClassical · HeuristicFind an isogeny between F_p-rational supersingular curves using small-degree isogeniesBoth curves defined over F_p10.25 SSIPF_p-rational curves · quantum · GRHQuantum · Conditional on GRHQuantum isogeny construction between F_p-rational supersingular curvesBoth curves defined over F_p10.866025 SSIPGeneral curves · quantum · GRHQuantum · Conditional on GRHQuantum explicit-isogeny construction under GRHSupersingular curves over F_{p^2}10.25