Example of the project fnx.Demo.BigInts for Lazarus

Elliptic curve point halving over a GF(P) field with the TGFPEllipticCurve.GetHalves method of the fnx.BigInts.GFPECurves unit.

//////////////////////////////////////////////////////////////////////////////// Random BPSW-prime ----------------- M = 13719165191747829003318256337325870227252942667993160467594045021403 Curve coefficients ------------------ A4 = 10535623683466291052686038561413726083980811147439265038592122765898 A6 = 6846200065576149012739105555501568550650873998075401483137881065570 Curve type = Ordinary Halving a point different from IDENTITY ooooooooooooooooooooooooooooooooooooooo Random point P -------------- X = 6406120790314488090611436867631858524392945283590718644309815814808 Y = 4790835978927033499476552802962358539063617294824179600986751292995 Z = 1 P has 4 halves H0 -- X = 13169915851708673006259180740632455088775109065020165943757290586694 Y = 13056579049696031230029257346249124414115590083319025331175090771997 Z = 1 H1 -- X = 8654096893533257500063979329435419880763896206004103139673045872742 Y = 13686758148979832806264548476381018707337820643889372710361109247841 Z = 1 H2 -- X = 5456829463747570641123164733478985157100826502997608188837802132810 Y = 6239954445882698125080044672357588637301944965045057976868051301964 Z = 1 H3 -- X = 12062806144016280218317679004306444198184892028334157772565169688389 Y = 5343396186857705834438571928711136553753582666339980789489759022158 Z = 1 Check (H0*2 = P) : OK Check (H1*2 = P) : OK Check (H2*2 = P) : OK Check (H3*2 = P) : OK Halving the IDENTITY point oooooooooooooooooooooooooo IDENTITY has 4 halves H0 -- IDENTITY H1 -- X = 6427056110265475635683083200561586867492436999219026428046347572394 Y = 0 Z = 1 H2 -- X = 11474799717698203526248939220924525779665061245331656284373212119256 Y = 0 Z = 1 H3 -- X = 9536474555531978844704490253165627807348387091435638222768530351156 Y = 0 Z = 1 Check (H1*2 = IDENTITY) ......... : OK Check (H2*2 = IDENTITY) ......... : OK Check (H3*2 = IDENTITY) ......... : OK Check ((H1 + H2) = H3) .......... : OK Check ((H1 + H3) = H2) .......... : OK Check ((H2 + H3) = H1) .......... : OK Check ((H1 + H2 + H3) = IDENTITY) : OK Running times (milliseconds) ---------------------------- Creating prime ........ : 1.780 Finding random curve .. : 0.151 Computing curve type .. : 9.558 Finding random point .. : 0.256 Halving ............... : 21.065 Halving IDENTITY ...... : 8.433 ////////////////////////////////////////////////////////////////////////////////