text_combined: harleyargotech robert harley dozen jokes thanks guys girls plus antifrench abuse usual suspect well brain doesnt hurt much well worth ive got even faster method ellipticcurve point counting pratically asymptotically lifts curve field degree n time on212eps on2eps precomputation best methods took on3eps without precomputation on212eps precomputation done per field per curve takes time on3eps eps arbitrarily small number hiding logarithmic factors lifting compute norm time on213eps get number points curve heres example 1009bit field without precomputation using 1 ghz pentium iii ecpc4 1009 j 0x123 info info ecpc elliptic curve point counting made easy info v400 c argotech 2001 rights reserved info info picked field polynomial 1x55x1009 info starting ecpc j 0x123 info done 13833 seconds info checking ok ok ok ok ok ok ok ok ok ok curve 5486124068793688683255936251187209270074392635932332070112001988456197381759672947165175699536362793613284725337872111744958183862744647903224103718245568925556758419805069056847065147709058947190200192542277555125346128173135573355537502225974504428432790108988791795746287271944131683364548299056172016 info 1 curve processed info bye l8r rob robertharleyargotech software development _ argotech httpargotech httpxentcommailmanlistinfofork wed 24 jul 2002 200613 0200 cest brain hurts