Elliptic-curve discrete logarithms
Compute discrete logarithms in elliptic-curve groups; distinguish ordinary cryptographic curves from anomalous or other exceptional families.
5 variants · 5 entries. Compare bounds only within the same variant.
COMPARISON VARIANTREGIME / INSTANCEENTRIESBEST c
ECDLPAnomalous prime-field curvesClassical · ProvableTrace one; p-adic lift techniquescurves E/F_p with #E(F_p)=p1— ECDLPBinary fields · quantum resource boundsQuantum · Provable circuit analysisLogical Toffoli count and logical qubits; scalar-multiplication variant specifiedelliptic curves over F_{2^n}1— ECDLPGeneric prime-order groups · classical low storageClassical randomized · Heuristic random-walk modelGroup order r; rho and negation-map variants; no anomalous-curve promiseprime-order elliptic-curve subgroups10.5 ECDLPGeneric prime-order groups · classical square-root storageClassical · source-dependent average-case analysisGroup order r; baby-step/giant-step variants; O(sqrt(r)) group-element storageprime-order elliptic-curve subgroups10.5 ECDLPPrime fields · quantum resource boundsQuantum · Provable circuit analysisLogical Toffoli count and logical qubits; no physical error-correction overheadelliptic curves over prime fields1—