Sz\303\241m\303\255t\303\263g\303\251pes sz\303\241melm\303\251let J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

restart;

# # This routine randomly choose an elliptic "curve" modulo n, # where gcd(n,6)=1. The coordinates x,y are choosen # randomly, the parameter a too, and b is calculated. # The list [x,y,a,b] is given back or a divisor d of n. # ellrand:=proc(n) local x,y,a,b,r,d,f; r:=rand(n); d:=0; while d=0 do x:=r(n); y:=r(n); a:=r(n); b:=y^2-x^3-a*x mod n; d:=4*a^3+27*b^2 mod n; gcd(d,n); od; if %<n and %>1 then return % fi; [x,y,a,b]; end;

Zio2I0kibkc2IjYpSSJ4R0YlSSJ5R0YlSSJhR0YlSSJiR0YlSSJyR0YlSSJkR0YlSSJmR0YlRiVGJUMnPkYrLUklcmFuZEdGJUYjPkYsIiIhPyhGJSIiIkY1RiUvRixGM0MoPkYnLUYrRiM+RihGOT5GKUY5PkYqLUkkbW9kR0YlNiQsKCokKUYoIiIjRjVGNSokKUYnIiIkRjUhIiIqJkYpRjVGJ0Y1RkdGJD5GLC1GPjYkLCYqJiIiJUY1KUYpRkZGNUY1KiYiI0ZGNSlGKkZDRjVGNUYkLUkkZ2NkR0YlNiRGLEYkQCQzMkkiJUdGJUYkMkY1RllPRlk3JkYnRihGKUYqRiVGJUYl

ellrand(97); ellrand(97); ellrand(97); ellrand(97); ellrand(97);

NyYiIiYiI2UiI1YiIzw=

NyYiI1AiI28iI0UiI2E=

NyYiIyYqIiM7IiMqKSIjYQ==

NyYiI0wiIzwiI14iIzk=

NyYiI2IiI1UiIyMpIiNa

# # This brute force procedure calculate the number of points # on an elliptic curve modulo p>3, a prime. The curve # parameters are a, b. # ellcount:=proc(a,b,p) local x,c; c:=1; for x from 0 to p-1 do c:=c+numtheory[jacobi](x^3+a*x+b,p)+1; od; c; end;

Zio2JUkiYUc2IkkiYkdGJUkicEdGJTYkSSJ4R0YlSSJjR0YlRiVGJUMlPkYqIiIiPyhGKSIiIUYtLCZGJ0YtRi0hIiJJJXRydWVHJSpwcm90ZWN0ZWRHPkYqLChGKkYtLSZJKm51bXRoZW9yeUdGJTYjSSdqYWNvYmlHRiU2JCwoKiQpRikiIiRGLUYtKiZGJEYtRilGLUYtRiZGLUYnRi1GLUYtRipGJUYlRiU=

ellrand(97); ellcount(%[3],%[4],97); ellrand(97); ellcount(%[3],%[4],97); ellrand(97); ellcount(%[3],%[4],97); ellrand(97); ellcount(%[3],%[4],97); ellrand(97); ellcount(%[3],%[4],97);

NyYiI2YiIyMqIiM4IiIl

IiMpKQ==

NyYiI1wiI1kiIigiI1I=

IiQ6Ig==

NyYiI1giI1YiIikiIyop

IiQ3Ig==

NyYiI3ciI2UiIzoiI1I=

IiQwIg==

NyYiIiEiI3AiI3ciIik=

IiMoKg==

with(plots);

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

implicitplot(y^2=x^3-10*x+10,x=-5..10,y=-20..20,numpoints=10000);

6$-I'CURVESG6$%*protectedGI(_syslibG6"6ggl7$7$$!3C)************\$!#<$!3*R(G9dGkW9F.7$$!3nPSR)QkT_$F.$!3;/++++++7F.7$F17$$!3UItivUwHNF.$!39<rK)fG17"F.7$7$$!3@A*>>d&Q_NF.$!3iU++++++!)!#=F77$F=7$$!3XUge&f^!fNF.$!3e*>sVy!HDkFB7$7$$!3w_a.#G=$pNF.$!3KT++++++SFBFD7$FJ7$$!30q>]"fG?d$F.$!3Sau%*fvBz?FB7$7$$!3wH1u=D'\d$F.$!3?zI6">Dy5%!#KFP7$FV7$$!3Zh^1+TCsNF.$"3su42N$4l#>FB7$7$FK$"3;f************RFBFgn7$F]o7$$!3-<#)\FqGiNF.$"3OdC&**R()4m&FB7$7$F>$"3Ce************zFBFao7$Fgo7$$!3#fm<!e.4WNF.$"3)Q4r/)Guv"*FB7$7$$!3cQSR)QkT_$F.$"3'f************>"F.F[p7$Fap7$$!3$>NG&4l7>NF.$"3&)R*3a-/5D"F.7$7$F,$"3btG9dGkW9F.Fgp7$7$$!3J)***********\LF.$!3P3+++D"yU#F.7$$!3#[(>rc'RdN$F.$!3O/++++++CF.7$7$Fgq$!3#R++++++S#F.7$$!3Q#f$Gu9ugLF.$!3p'3x&ogNrBF.7$7$$!3c)3Qf&yeDMF.$!3+/++++++?F.F_r7$Fer7$$!3Vr2@:46sMF.$!3[v7x#*3Pu;F.7$7$$!3IOwd#QOF[$F.$!33/++++++;F.F[s7$FasF+7$F]q7$$!3(ow%GaEo'[$F.$"3/7F4yq[k:F.7$7$$!3>Pwd#QOF[$F.$"33'************f"F.Fhs7$F^t7$$!3<ypt=o6YMF.$"3QU>j;:Jc=F.7$7$$!3X*3Qf&yeDMF.$"3+'*************>F.Fdt7$Fjt7$$!3y")*)))fFd,MF.$"3Z^Rqft_P@F.7$7$$!3rv>rc'RdN$F.$"3#f************R#F.F`u7$Ffu7$$!3vsw.UAq`LF.$"3([zLaks)4CF.7$7$Fbq$"3.2+++D"yU#F.F\v7$7$$!3S)************>$F.$!3O0+++++KIF.7$$!3I&)H]p@viKF.$!3#Q++++++!GF.7$7$$!3v&)H]p@viKF.F^w7$$!3(y***********\LF.Fdq7$Fbv7$$!39#)[)f!HJ'H$F.$"3%[offTMol#F.7$7$$!3_()H]p@viKF.$"3%e************z#F.Fhw7$F^x7$$!3Eg$[=\ckB$F.$"37Ecf6t@(*GF.7$7$Fgv$"3O0+++++KIF.Fdx7$7$$!30)***********\IF.$!3'z#)eq9bvZ$F.7$$!3Ee98&yyx9$F.$!3s.++++++KF.7$FcyFfv7$Fjx7$$!3E?%*Q"yY9<$F.$"3U?^q$3eQ7$F.7$7$$!3#4YJ^yyx9$F.$"3s&************>$F.Fjy7$F`z7$$!3rug$yE;/5$F.$"3H*>'*3QVWL$F.7$7$F_y$"3TG)eq9bvZ$F.Ffz7$7$$!3e)*************GF.$!3#eE0@%oB<QF.7$$!3#*p@%478(**HF.$!33/++++++OF.7$Fe[lF^y7$F\[l7$$!3%eNFGq)*f-$F.$"3Y\H(3a'*f`$F.7$7$$!3[t@%478(**HF.$"3k&************f$F.F\\l7$Fb\l7$$!3#RjltoM[%HF.$"3qc$3j;f&>PF.7$7$Fa[l$"3Em_5UoB<QF.Fh\l7$7$$!3B)***********\FF.$!3aeG9d`q$3%F.7$$!3l$ph-E7/!GF.$!3c.++++++SF.7$7$$!3@$ph-E7/!GF.Fj]lF`[l7$7$Fa[l$"3qm_5UoB<QF.7$$!3/#*))\"y-%fGF.$"3g6Pm]2u"*QF.7$7$$!3a)ph-E7/!GF.$"3c&*************RF.Fd^l7$Fj^l7$$!3Fu9j@XMpFF.$"37ks,"R&e^SF.7$7$$!3n)***********\FF.$"3VfG9d`q$3%F.F`_l7$7$Fg_l$!3VfG9d`q$3%F.7$$!3j&H<kXbco#F.$!3*z(Qb\aerTF.7$7$$!3w)************f#F.$!3/I9dG9d)G%F.F_`l7$7$$!36************\FF.Fi_l7$$!3Dnb$pZi:n#F.$"35z"G=FL3>%F.7$7$Ff`l$"3/I9dG9d)G%F.F^al7$7$$!3S)***********\CF.$!3mdp3E.;ZWF.7$$!3G\rz'*)3v\#F.$!3#R++++++S%F.7$F]blFe`l7$Fdal7$$!3\MQGSjJqDF.$"3CC-4uN%3K%F.7$7$$!3Gdrz'*)3v\#F.$"3#f************R%F.Fdbl7$Fjbl7$$!3U")*R_p()GY#F.$"3R;mI(=nVV%F.7$7$$!3%))***********\CF.$"3mdp3E.;ZWF.F`cl7$Fhal7$$!3;NmHzhNDCF.$!3Lu*3_&orlWF.7$7$$!3%*)************H#F.$!3eu@l&p3,c%F.F\dl7$7$Fgcl$"3xcp3E.;ZWF.7$$!3.W`D?,#oM#F.$"35]U,aO&[_%F.7$7$Fcdl$"3pt@l&p3,c%F.F[el7$Fbdl7$$!3(e1y))eO^A#F.$!3UD=*HwN'*f%F.7$7$$!3-************\@F.$!36"R<_12$RYF.Feel7$Fael7$$!3CZ^#*f&3\A#F.$"3)3R+)fhv*f%F.7$7$F\fl$"3+#R<_12$RYF.Fafl7$F[fl7$$!33gn(=,C"[?F.$!3-v>m,$p;n%F.7$7$$!37**************>F.$!3YI"R<_cpo%F.F[gl7$Fgfl7$$!3sn=%)HW:'4#F.$"3&ek6H"=TcYF.7$7$Fbgl$"3YI"R<_cpo%F.Fggl7$Fagl7$$!30D#GZpJs)=F.$!3LNZs![:2q%F.7$7$$!3?************\=F.$!3>8R<_"e_q%F.Fahl7$F]hl7$$!3P%z!))4MYf>F.$"3i$y[jU->p%F.7$7$Fhhl$"3>8R<_"e_q%F.F]il7$Fghl7$$!3pw*=!>Z+Q<F.$!3akgh#3a')p%F.7$7$$!3G*************p"F.$!3sg#yM/8kp%F.Fgil7$Fcil7$$!3GE'>]ToO"=F.$"3xocQtd6.ZF.7$7$$!3_*************p"F.$"3gh#yM/8kp%F.Fcjl7$F]jl7$$!3S=1F!o.vf"F.$!3a`$y#>NKtYF.7$7$$!3Q************\:F.$!3P&p3EGAEm%F.F_[m7$7$F^jl$"3sg#yM/8kp%F.7$$!3$>gMeeqvl"F.$"3vN*eb*[&oo%F.7$7$Ff[m$"3P&p3EGAEm%F.F^\m7$7$Ff[m$!3\%p3EGAEm%F.7$$!3s<A^*Q7PY"F.$!3M)3MYH+,j%F.7$7$$!3Y*************R"F.$!3hQ<_cp31YF.F[]m7$Fd\m7$$!3l;uEgN+!\"F.$"3.Uk/%\4+k%F.7$7$Fb]m$"3hQ<_cp31YF.Fg]m7$Fa]m7$$!3I=%))e[._L"F.$!3(Rb(H/2zsXF.7$7$$!3c************\7F.$!3i8R<_"3!HXF.Fa^m7$7$Fb]m$"3\R<_cp31YF.7$$!3d27*p_D*48F.$"3l$))4`S,)fXF.7$7$Fh^m$"3i8R<_"3!HXF.F`_m7$Fg^m7$$!3A#=To&)R4@"F.$!3&)\ov"QgT]%F.7$7$$!3))*************4"F.$!3<R<_cpeLWF.Fj_m7$7$Fh^m$"3t7R<_"3!HXF.7$$!3LHu(z,Tl6"F.$"3.UJF"Q4TW%F.7$7$$!3k*************4"F.$"3HQ<_cpeLWF.Fi`m7$7$F`am$!3HQ<_cpeLWF.7$$!3g8&)*fl^,4"F.$!3&Rjq1DiiU%F.7$7$$!3XK:'o1T[0"F.F`blFham7$F^bm7$$!3?xUk7$>`u*FB$!3C'>Gm^"eMVF.7$7$$!37&************\*FB$!3x8dG9#)f9VF.Fbbm7$7$$!3A'************\*FB$"3x8dG9#)f9VF.7$$!3,A:'o1T[0"F.F]cl7$FccmF_am7$Fhbm7$$!3]\'['p&y>i)FB$!3,'p$4[!RTB%F.7$7$$!3+'*************zFB$!3:cG9dG9xTF.Fhcm7$F^cm7$$!3!)o'Qnxs?,*FB$"3Fvpztg))pUF.7$7$F_dm$"3:cG9dG9xTF.Fddm7$F^dm7$$!3XJeBfu:<vFB$!39Z/(3,e(GTF.7$7$$!3!e************\'FB$!3)p&G9d.$o-%F.F^em7$Fjdm7$$!3$G9&QAO=hmFB$"39,FI*H#)H/%F.7$7$Feem$"3)p&G9d.$o-%F.Fjem7$Fdem7$$!3b[hWO-BGkFB$!3"GO9OgQ">SF.7$7$$!3<U;?uGl\iFBFj]lFdfm7$Fjfm7$$!3(\:yC_jVQ&FB$!3_%\s11.v*QF.7$7$$!3c&*************\FB$!3mD0@%ot>&QF.F^gm7$7$Fegm$"3mD0@%ot>&QF.7$$!37r:?uGl\iFBF]_l7$F]hm7$$!3o%************\'FB$"34cG9d.$o-%F.7$Fdgm7$$!3vzoT"pMcN%FB$!3v+b&*[2$=x$F.7$7$$!3M&************\$FB$!3pD0@%=6am$F.Fghm7$7$Fegm$"35E0@%ot>&QF.7$$!3B;=5FzpfRFB$"369Q*Q6'eAPF.7$7$F^im$"3DD0@%=6am$F.Ffim7$F]im7$$!3i]eNv,[MLFB$!3!*3^!*>'QTk$F.7$7$$!3s)y*)*></"*HFB$!3?.++++++OF.F`jm7$Ffjm7$$!3R<DKUI%pM#FB$!3Pk1Qb=[2NF.7$7$$!37&*************>FB$!3&)GN#)eqkdMF.F\[n7$7$$!3S&*************>FB$"3&)GN#)eqkdMF.7$$!3+J(*)*></"*HFB$"3?&************f$F.7$7$F^\nFe\lF\jm7$7$Fi[nFe[n7$$!3X'>3?*o3w8FB$!3&o"yzGoPmLF.7$7$$!3[a************\!#>$!310Zw6p@QKF.Ff\n7$7$$!3o&*************>FBF[\n7$$!3HOBF\?pu")F_]n$"3")eska%eYG$F.7$7$F]]n$"3h/Zw6p@QKF.Ff]n7$F\]n7$$!3/nm'pPFg2%F_]n$!3!zbZ*p#RYA$F.7$7$$!3W,igu%*H*R#F_]nFfyF`^n7$Ff^n7$$"3)eX&zd.CL_F_]n$!3t97a4k)G2$F.7$7$$"3]/++++++5FB$!3;**********\$*HF.Fj^n7$7$Fa_n$"3;**********\$*HF.7$$!3c.dgu%*H*R#F_]nFcz7$7$$!3#Rq0YZ*H*R#F_]nFczF\^n7$F`_n7$$"3b/H&QG>#[9FB$!34x2OU^_>HF.7$7$$"3oK8C/7Vs@FBF^wFa`n7$Fg`n7$$"36y"f`=JNO#FB$!3R$y&4;$3Ow#F.7$7$$"3W/++++++DFB$!3F"p2B>?wt#F.F[an7$7$Fban$"3s"p2B>?wt#F.7$$"3Ew8C/7Vs@FBFax7$7$F[bn$"3Q&************z#F.Ff_n7$Faan7$$"3Q_L(e-tcC$FB$!3%o*GBSh%))f#F.7$7$$"37/++++++SFB$!3"y`h%Q:YeCF.Fbbn7$Fgan7$$"3^\E8z'=VF$FB$"3+dz*)=]^$f#F.7$7$$"3o/++++++SFB$"3OP:YQ:YeCF.F^cn7$7$Fecn$!3DQ:YQ:YeCF.7$$"3vh45rR7JTFB$!3Y#f$H#Rm\V#F.7$7$$"3h%)3pvxEEVFBF]rF]dn7$Fcdn7$$"3H5Ol\P[!)\FB$!3Nl4CLBYhAF.7$7$$"3)[++++++]&FB$!3oijjj)[9:#F.Fgdn7$7$F^en$"3oijjj)[9:#F.7$$"3eC4pvxEEVFBFiu7$7$$"3-C4pvxEEVFBFiu7$FibnFgcn7$F]en7$$"3yXzk^!yT#eFB$!3ga%R/[Zk3#F.7$7$$"3alR')>JJbiFBFhrF_fn7$Fefn7$$"3)pV-!y3PVmFB$!3]_1!3!*)*[!>F.7$7$$"350++++++qFB$!3,**********\<=F.Fifn7$7$$"3+/++++++qFB$"3y)*********\<=F.7$$"3=-S')>JJbiFBF]u7$Fjgn7$F^en$"3Bijjj)[9:#F.7$7$FfgnFbgn7$$"31iM\kI2SuFB$!3Ff#)><GN<<F.7$7$$"3Dk$*Q7AvbzFBFdsFchn7$Fihn7$$"3:x]sDEE:#)FB$!3!**oEN.qS_"F.7$7$$"3K0++++++&)FB$!32F9dG*e2W"F.F]in7$7$Fdin$"32F9dG*e2W"F.7$$"3M&R*Q7AvbzFBFat7$F\jn7$F`gn$"3,**********\<=F.7$Fcin7$$"34gpC#35E&*)FB$!3WDD$>-'p?8F.7$7$$"3[V\Pmog2%*FBF4Fdjn7$Fjjn7$$"3vk.TK\>b'*FB$!36+h(>)>036F.7$7$$"3W+++++++5F.$!3S&)***********z*FBF^[o7$7$Fe[o$"3%)z***********z*FB7$$"37q\Pmog2%*FBFdp7$F]\oFiin7$Fd[o7$$"3Q^e())*>NI5F.$!3Z-%*oOmQ4))FB7$7$$"3i>L.$G^^0"F.F@Fb\o7$Fh\o7$$"38$f!fAJN'3"F.$!3T$=\d$*\FI'FB7$7$$"3TZx2FjoG6F.FMF\]o7$Fb]o7$$"3QNtb<+oJ6F.$!3L3B'[8n9^$FB7$7$$"3O++++++]6F.$!3p&*)******\(=_F_]nFf]o7$7$F]^o$"3I[#******\(=_F_]n7$$"3I[x2FjoG6F.F^o7$Fe^o7$$"3*y#)H8L*=36F.$"36$*y`k6&\6&FB7$7$$"3i@L.$G^^0"F.$"3Of************zFBFi^o7$7$F`_oFho7$Fe[o$"33#)***********z*FB7$7$F]^o$!33(*)******\(=_F_]n7$$"3#z*Q#*oD=`6F.$!3%f0JPY]o[)!#?7$7$$"3(**eKsj+Q:"F.FYF]`o7$Fd`oFb^o7$7$$"3c*************\#F.$!3#)\*********\(yFB7$$"31Agi:e>RCF.FM7$F^ao7$$"3nRLzb-MHCF.$!3H3"*[a,u:@FB7$7$$"3?+RtXRF=CF.FYFbao7$Fhao7$$"3Vn=r3xFGCF.$"3`],NMWf7>FB7$7$$"3<@gi:e>RCF.F^oF\bo7$Fbbo7$$"3Z'H\*zH8dCF.$"3cs`oM07V^FB7$7$Fj`o$"3C%)*********\(yFBFfbo7$7$$"3Z************\EF.$!3P%G9dy^"R9F.7$$"3_g#pi-WBe#F.F47$Feco7$$"39QcpqkG.DF.$!3p3/b=#Rw3)FB7$7$$"3_:eAMb^,DF.$!3_T++++++!)FBFico7$F_doFi`o7$F\co7$$"3t#QGnDX6]#F.$"366kd?)f%pzFB7$7$$"3>9eAMb^,DF.Fb_oFfdo7$7$$"3u8eAMb^,DF.Fb_o7$$"3H&=+e()4Nb#F.$"3Lnh'y*pId5F.7$7$$"3ue#pi-WBe#F.$"3s&************>"F.Fceo7$7$FjeoFdp7$$"3e_e>(QO9h#F.$"3&R063IOGI"F.7$7$Faco$"3:%G9dy^"R9F.F`fo7$7$$"3Q*************z#F.$!39kmmmmm')>F.7$$"3MH3hB!omo#F.Fds7$F_goF`co7$Fffo7$$"3"3]%pfZ!Gn#F.$"3:D8[2t=R:F.7$7$$"3dF3hB!omo#F.FatFdgo7$7$F[ho$"3K'************f"F.7$$"3j*QxU_(QOFF.$"3!=i$foKjp<F.7$7$F[go$"3Pkmmmmm')>F.Faho7$7$$"3%))***********\HF.$!3S#Q:Y)GIzCF.7$$"3+Op9I:9AHF.F]r7$F`io7$$"3T/BQC%Rc"GF.$!3J]hoJ^qT?F.7$7$$"3xF1\&pUK!GF.FhrFdio7$Fjio7$$"3%*)************z#F.F]go7$7$F[go$"39kmmmmm')>F.7$$"3r"ow:,n>!GF.$"3G4bzNYv%*>F.7$7$$"3bD1\&pUK!GF.F]uFejo7$F[[p7$$"3KS+$QGM"oGF.$"3m?KXw&3$=AF.7$7$$"3MLp9I:9AHF.FiuF_[p7$Fe[p7$$"3(G-$**zghNHF.$"3R*f=+7d$QCF.7$7$$"3H************\HF.$"3S#Q:Y)GIzCF.Fi[p7$7$$"3?*************4$F.$!3C(*********\eHF.7$$"3v0Z0Y[_XIF.F^w7$Fj\p7$F`\pF^io7$7$F`\p$"3'>Q:Y)GIzCF.7$$"3k(H7$\wB.IF.$"3j*>n^$H.eEF.7$7$$"33.Z0Y[_XIF.FaxFc]p7$Fi]p7$$"3`mv%)zedrIF.$"3b:)RPl(zvGF.7$7$Ff\p$"3C(*********\eHF.F]^p7$7$$"36************\KF.$!3VWw6%zZNV$F.7$$"34:bm!Rk:<$F.Ffy7$F\_pFe\p7$Fc^p7$$"3^E9qq^(*RJF.$"3G*='zW&*R$4$F.7$7$$"3K8bm!Rk:<$F.FczFa_p7$7$$"3(G^l1Rk:<$F.Fcz7$$"3apf+D>i3KF.$"3L2uJL:M5LF.7$7$Fh^p$"3VWw6%zZNV$F.F^`p7$7$$"3Y*************R$F.$!3pv:j_5U3RF.7$$"3AQOT9c%))H$F.$!3k.++++++OF.7$F]ap7$Fh^p$!3*Rk<TzZNV$F.7$Fd`p7$$"35DA&RI-uF$F.$"3OE2Y*=Fp_$F.7$7$$"3cNOT9c%))H$F.F`\nFgap7$7$$"37NOT9c%))H$F.F`\n7$$"3"za*\![RgM$F.$"3$['ym=Z*Qu$F.7$7$Fi`p$"38w:j_5U3RF.Fdbp7$7$$"3$*)***********\NF.$!35`G9d.e&Q%F.7$$"3W^npt>`EMF.Fj]l7$Fccp7$Fi`p$!38w:j_5U3RF.7$7$$"3-*************R$F.F[cp7$$"3W#Rz,,o\T$F.$"3.z#)=1`3gRF.7$7$$"3y[npt>`EMF.F]_lF^dp7$Fddp7$$"3Fky$y,,M[$F.$"3+)oldG(fxTF.7$7$$"3\)***********\NF.$"3*R&G9d.e&Q%F.Fhdp7$7$$"3%))************p$F.$!3S'*********Hh[F.7$$"3s*o2X9p"zOF.$!3G/++++++[F.7$Fiep7$$"3>#es1&)[Zd$F.$!3*G*o7Np*fY%F.7$7$$"3>nV"z/;Tb$F.F`blF_fp7$FefpF^cp7$7$F_cpFaep7$$"3PgctzqL_NF.$"3![crtynPR%F.7$7$$"3(\O9z/;Tb$F.F]clF[gp7$Fagp7$$"3[J)4hHU/i$F.$"3AU//xQ:7YF.7$7$$"31(o2X9p"zOF.$"3G'************z%F.Fegp7$F[hp7$$"3o$Gpu%>2*o$F.$"3"eB:MZT"H[F.7$7$Feep$"3S'*********Hh[F.Fahp7$7$$"3v)***********\QF.$!3jimmmTNT`F.7$$"3Q.j")ohR.QF.$!3g/++++++_F.7$F`ip7$Feep$!3H(*********Hh[F.7$Fghp7$$"3_g(**H,(*pv$F.$"3zlRLlz+[]F.7$7$$"3s+j")ohR.QF.$"3i'************>&F.Fjip7$7$$"3F+j")ohR.QF.Fcjp7$$"3_t\C;+?DQF.$"39)R8+HLhE&F.7$7$F\ip$"3jimmmTNT`F.Fijp7$7$$"3C)*************RF.$!30[l*o?'eFeF.7$$"3MX\LBr6FRF.$!3'\++++++g&F.7$7$$"3*[%\LBr6FRF.F[\qF[ip7$F_[q7$$"3%)\g=H,'H*QF.$"3[gQ]b'Ra[&F.7$7$$"3nU\LBr6FRF.$"3)p************f&F.Fb\q7$Fh\q7$$"3Vj!4&[%)ogRF.$"3)R#e(R!3$[q&F.7$7$Fd[q$"3;Zl*o?'eFeF.F^]q7$7$$"3e)***********\TF.$!3$4$>unMV?jF.7$$"3#*=)eR'GA]SF.$!3K0++++++gF.7$F]^q7$$"3o)*************RF.Ff[q7$Fd]q7$$"3q;&)o?iEGSF.$"3+#G(\6MiCfF.7$7$$"3E;)eR'GA]SF.$"3M(*************fF.Fg^q7$7$$"39<)eR'GA]SF.$"3C)*************fF.7$$"33Rx(4W([&4%F.$"3'oNfS#oOXhF.7$7$Fi]q$"3$4$>unMV?jF.Fh_q7$7$$"3%*)************H%F.$!3oC9dG92>oF.7$$"3;RAhr,(QH%F.$!3/1++++++oF.7$Fg`q7$$"3XyFKZE0oUF.$!3'*=u_fq![r'F.7$7$$"3l7BQ$4^E<%F.$!3o0++++++kF.F]aq7$Fcaq7$Fi]q$!3#=$>unMV?jF.7$7$Fi]q$"3#=$>unMV?jF.7$$"3<=-hfh(G;%F.$"3KYFPuNmljF.7$7$$"3**4BQ$4^E<%F.$"3o(************R'F.F`bq7$Ffbq7$$"38$48Dho&HUF.$"3G7%)HLq"ye'F.7$7$$"3]OAhr,(QH%F.$"3/)************z'F.F\cq7$Fbcq7$$"3k-!p^D*p'H%F.$"3(y)f@')>!)3oF.7$7$Fc`q$"3oC9dG92>oF.Fhcq7$7$$"3H************\WF.$!30#y$y$GY.K(F.7$$"3IkXE6`W7WF.$!3G2++++++sF.7$7$$"3TjXE6`W7WF.$!3S1++++++sF.Fb`q7$F^dq7$$"3r,[/6#=HO%F.$"3/C0)Q5=A.(F.7$7$$"3jhXE6`W7WF.$"3S)************>(F.Fceq7$7$$"3ugXE6`W7WF.F\fq7$$"3$=%o)RO-&HWF.$"3__<qi.masF.7$7$Fcdq$"30#y$y$GY.K(F.Fbfq7$7$$"3k*************f%F.$!3xo2Bp2BHyF.7$$"3JH]$y(>ZIXF.$!3w1++++++wF.7$7$$"3UG]$y(>ZIXF.Fdgq7$Fcdq$!3;"y$y$GY.K(F.7$7$Fcdq$"3%Hy$y$GY.K(F.7$$"3]!pTcfKb\%F.$"3<*[b\uz&yuF.7$7$$"3vD]$y(>ZIXF.$"3w)************f(F.Fahq7$7$Fhhq$"3k*************f(F.7$$"3?dTz>=chXF.$"3?VA)Q"=]-xF.7$7$F]gq$"3+n2Bp2BHyF.F`iq7$7$$"3+++++++]ZF.$!3sl`eOg%eM)F.7$$"3aw$*4zt$zk%F.$!372++++++!)F.7$F_jqF\gq7$7$F]gq$"3)ywI#p2BHyF.7$$"3[x^vj^TFYF.$"37fGl'*G*o#zF.7$7$$"3xu$*4zt$zk%F.$"3C)*************zF.Fijq7$7$$"3)QP*4zt$zk%F.Fb[r7$$"3g"[Z^x%)Gp%F.$"3()yLFmsI_")F.7$7$F[jq$"3sl`eOg%eM)F.Fh[r7$7$$"3O+++++++\F.$!3vnmmmm;n))F.7$$"3(od9\l)zz[F.$!3#y++++++!))F.7$Fg\r7$$"3(fq@!oW_8[F.$!3,@7R"e)Rp&)F.7$7$$"3#pGh6!)R[w%F.$!3Y2++++++%)F.F]]r7$Fc]rFjiq7$F^\r7$$"3ts7U@UdeZF.$"3^pKa4a8x$)F.7$7$$"3D%Gh6!)R[w%F.$"3e)************R)F.Fj]r7$F`^r7$$"3:.REYB[B[F.$"37"fHm2ZSg)F.7$7$$"3KtX"\l)zz[F.$"3;(************z)F.Ff^r7$7$$"3?uX"\l)zz[F.$"3%*)************z)F.7$$"3.-QBE(*y))[F.$"3QGlPjS*)H))F.7$7$Fc\r$"3vnmmmm;n))F.Fg_r7$7$$"3r++++++]]F.$!3e#)HQ1E-%R*F.7$$"3+f4"GDMK*\F.$!3;3++++++#*F.7$Ff`rFb\r7$7$$"3Y**************[F.F^`r7$$"3$*3P#=PoL&\F.$"3^UM!=M%od!*F.7$7$$"3Yb4"GDMK*\F.$"3G*************>*F.F`ar7$Ffar7$$"3KqY+6E6=]F.$"3q#)3KPI.&G*F.7$7$Fb`r$"3!3)HQ1E-%R*F.F\br7$7$$"31,++++++_F.$!3hRn$=fz*G**F.7$$"31e2?vCG1^F.$!3_3++++++'*F.7$F[cr7$Fb`r$!3!3)HQ1E-%R*F.7$7$Fb`r$"3e#)HQ1E-%R*F.7$$"36$e_C_eD3&F.$"3$*z(fMFxJ^*F.7$7$$"3Sb2?vCG1^F.$"3k*************f*F.Fhcr7$7$$"3Hc2?vCG1^F.Fadr7$$"38m%))y=Tn9&F.$"3/"4k*)\B?u*F.7$7$Fgbr$"3hRn$=fz*G**F.Fgdr7$7$$"3U,+++++]`F.$!3*f2K6tNp/"!#;7$$"3$oI0P8!**H`F.$!3v++++++S5Ffer7$7$Fher$!3#4++++++/"Ffer7$$"3:0T(oTYHF&F.$!3P&4LyP_%>5Ffer7$7$$"39`j"eGV*=_F.$!3)3+++++++"FferF`fr7$Fffr7$Fgbr$!3%ytO=fz*G**F.7$F]er7$$"3oID'elp5@&F.$"3&)>**p<4[q**F.7$7$$"3O^j"eGV*=_F.$"#5""!F`gr7$Ffgr7$$"3'\ufjc$pu_F.$"3%=SPcr"3?5Ffer7$7$$"3</`qL,**H`F.$"3/++++++S5FferF]hr7$Fchr7$$"3,I%z/!3pQ`F.$"3E>)Qly:I/"Ffer7$7$Fber$"3*f2K6tNp/"FferFihr7$7$$"3y,++++++bF.$!3-GFFFF_,6Ffer7$$"3J%)\jFb_RaF.$!3'4++++++3"Ffer7$FhirFaer7$F_ir7$$"3f7L(RH))>S&F.$"3J]/%\XOh1"Ffer7$7$$"3a#)\jFb_RaF.$"32++++++!3"FferF_jr7$Fejr7$$"3qq'))Q"*GaY&F.$"3:bjHc*=#*3"Ffer7$7$Fdir$"3-GFFFF_,6FferF[[s7$7$$"38-+++++]cF.$!3"G%otW"Rp:"Ffer7$$"3oiS?&HI)[bF.$!3*4++++++7"Ffer7$Fj[sFcir7$Fa[s7$$"3%G]jZ2W'GbF.$"3nmI1!ehB6"Ffer7$7$$"3!41/_HI)[bF.$"36++++++?6FferFa\s7$Fg\s7$$"3S%\^qIK:f&F.$"3yoiy%Q"fN6Ffer7$7$Ff[s$"3)H%otW"Rp:"FferF]]s7$7$$"3[-++++++eF.$!3%olg$)4aF@"Ffer7$$"3P^t&*y%pZw&F.$!33,++++++7Ffer7$F\^s7$$"3hXS:&Hwun&F.$!37z5/7qKn6Ffer7$7$$"3zq:BY0!zl&F.$!3.,+++++g6FferFb^s7$Fh^sFe[s7$Fc]s7$$"35MaZj&zYl&F.$"3c^lS;@ve6Ffer7$7$$"3-p:BY0!zl&F.$"39++++++g6FferF__s7$Fe_s7$$"3%*=E$oD?qr&F.$"3C-8^Jz7#="Ffer7$7$$"3r[t&*y%pZw&F.$"3=+++++++7FferF[`s7$Fa`s7$$"3DU0)z08(zdF.$"3e*=07&)4a?"Ffer7$7$Fh]s$"3mc1O)4aF@"FferFg`s7$7$$"3%G++++++&fF.$!3a5Q_f]Ip7Ffer7$$"3xm;K.<1reF.$!35,+++++S7Ffer7$FfasFg]s7$F]as7$$"3R`4w1<">%eF.$"3_YP'[aB)G7Ffer7$7$$"3*\m@Lqh5(eF.$"3@++++++S7FferF]bs7$Fcbs7$$"3S"[P+fgS!fF.$"3KRLK40D_7Ffer7$7$Fbas$"3a5Q_f]Ip7FferFibs7$7$$"3?.++++++hF.$!3`<nloi\E8Ffer7$$"3Mne"[p(R#3'F.$!3N,+++++?8Ffer7$7$Fics$!3<,+++++?8Ffer7$$"3r0Ipa58TgF.$!39-[e9;I/8Ffer7$7$$"3E"3@Z%*[s(fF.$!39,+++++!G"FferFads7$FgdsFaas7$F_cs7$$"3;Xt\&=Di'fF.$"3dvt'QGtcF"Ffer7$7$$"3rx5sW*[s(fF.$"3D++++++!G"FferF^es7$7$Fees$"32++++++!G"Ffer7$$"3Jid#GfNy-'F.$"33JJ">%QC*H"Ffer7$7$$"3zje"[p(R#3'F.$"36++++++?8FferF]fs7$7$Fdfs$"3G++++++?8Ffer7$$"3W!\bYJ"y*3'F.$"3'p`eF)\sA8Ffer7$7$Fdcs$"3q<nloi\E8FferF\gs7$7$$"3c.+++++]iF.$!3uzM/j^?%Q"Ffer7$$"3aa.q1y+'='F.$!3@,+++++g8Ffer7$F[hs7$Fdcs$!3q<nloi\E8Ffer7$Fbgs7$$"31eo")\k0^hF.$"3d0brY\QY8Ffer7$7$$"3x_.q1y+'='F.$"3]++++++g8FferFehs7$7$F\is$"3K++++++g8Ffer7$$"3*HxR<(yY7iF.$"3^hg`n&3+P"Ffer7$7$Fggs$"3czM/j^?%Q"FferFdis7$7$$"3#R++++++S'F.$!3*3&o]J\oU9Ffer7$$"3oLe#[=uGR'F.$!35,+++++S9Ffer7$7$Fdjs$!3G,+++++S9Ffer7$$"31,ykNc8xjF.$!3>ZF<OG!RV"Ffer7$7$$"3(>7+sdA'*G'F.$!3C,++++++9FferF\[t7$Fb[tFfgs7$7$Fggs$"3uzM/j^?%Q"Ffer7$$"3#pE<J'4utiF.$"3Sj?]w!pOR"Ffer7$7$$"3I>,?xDi*G'F.$"3O+++++++9FferF\\t7$Fb\t7$$"3TLfecQiMjF.$"3s_PCQOV<9Ffer7$7$$"3#>$e#[=uGR'F.$"3d++++++S9FferFh\t7$7$F_]t$"3R++++++S9Ffer7$$"3Y72GFt#eR'F.$"3sW^s7F6T9Ffer7$7$F_js$"3*3&o]J\oU9FferFg]t7$7$$"3E/+++++]lF.$!3r,++]7d,:Ffer7$$"3)o/>g[2T\'F.$!39,+++++!["Ffer7$7$Fg^t$!3J,+++++!["FferF^js7$7$F_js$"3r]o]J\oU9Ffer7$$"3%ytSAqmiX'F.$"3/Q"pga&*\Y"Ffer7$7$$"33X!>g[2T\'F.$"3V++++++!["FferFc_t7$Fi_t7$$"3.!z-45Yp^'F.$"3&4f#4tV"))["Ffer7$7$Fb^t$"3r,++]7d,:FferF_`t7$7$$"3g/++++++nF.$!35)pbkJv7c"Ffer7$$"3G/+9mzo'p'F.$!3@,+++++g:Ffer7$7$F_at$!3R,+++++g:Ffer7$$"31]q]j)3)*o'F.$!3<!)=gjBGd:Ffer7$7$$"379/p2nV&f'F.$!3N,+++++?:FferFgat7$F]btFa^t7$Fe`t7$$"3vV<"o>8ud'F.$"3aON=9)*o7:Ffer7$7$$"3O7/p2nV&f'F.$"3Y++++++?:FferFdbt7$Fjbt7$$"3"4?>lYuvj'F.$"3s9#G*3okO:Ffer7$7$$"3]-+9mzo'p'F.$"3]++++++g:FferF`ct7$Ffct7$$"3O/o%*eJ/)p'F.$"3%Q&3GC=_g:Ffer7$7$Fj`t$"3$zpbkJv7c"FferF\dt7$7$$"3(\++++++&oF.$!3"e2uSKb8i"Ffer7$$"3g<qPF0#ez'F.$!3U,++++++;Ffer7$F[et7$Fj`t$!3$zpbkJv7c"Ffer7$Fbdt7$$"34)*ymK(Gxv'F.$"3)>c)Grcg%e"Ffer7$7$$"3#\,xt_?ez'F.$"3O+++++++;FferFeet7$F[ft7$$"3^3]vtQo<oF.$"3vK`mLwh3;Ffer7$7$Fgdt$"3"e2uSKb8i"FferFaft7$7$$"3K0++++++qF.$!3+\w6%HNAo"Ffer7$$"3+wWacHK%*pF.$!39,+++++!o"Ffer7$F`gt7$$"3(3Gj5XPK)pF.$!3=3-&p)*Hbn"Ffer7$7$$"3wnJ&>4C^*oF.$!3G,+++++S;FferFfgt7$F\htFfdt7$Fgft7$$"3*G$yn`XUxoF.$"3x7fo&y'oK;Ffer7$7$$"3+mJ&>4C^*oF.$"3@++++++S;FferFcht7$Fiht7$$"3.;$y$f@(o$pF.$"3Y]C$34Mol"Ffer7$7$$"3MtWacHK%*pF.$"32++++++!o"FferF_it7$Feit7$$"3amV$)*G:m*pF.$"3*R]x$*e-4o"Ffer7$7$F\gt$"3O\w6%HNAo"FferF[jt7$7$$"3p0+++++]rF.$!3eZ.JHE_V<Ffer7$$"3oE$z'>9g"4(F.$!3*4++++++s"Ffer7$7$$"3yD$z'>9g"4(F.F][uF[gt7$Fajt7$$"3uou4VJibqF.$"3Zw1%=;n^q"Ffer7$7$$"37B$z'>9g"4(F.$"3$*************><FferFd[u7$Fj[u7$$"3'e'*RAMj[6(F.$"3LxESv(p$H<Ffer7$7$Ffjt$"3BZ.JHE_V<FferF`\u7$7$$"3/1++++++tF.$!3O67z37a0=Ffer7$$"3yc>Cx@C'G(F.$!3s+++++++=Ffer7$F_]u7$$"3$pa4k&p'4E(F.$!3_yeP)="f*y"Ffer7$7$$"3eK)))\37"*=(F.$!3&3++++++w"FferFe]u7$7$$"3pJ)))\37"*=(F.F^^u7$$"3![++++++:(F.$!3BZ.JHE_V<Ffer7$Ff\u7$$"3KAYJ<8&R<(F.$"3BN%\?)Hh`<Ffer7$7$$"3"*H)))\37"*=(F.$"3z************f<FferFj^u7$F`_u7$$"3O!3_*4YpKsF.$"3&)zF,/"[zx"Ffer7$7$$"3*e&>Cx@C'G(F.$"#=F[hrFf_u7$7$$"3+b>Cx@C'G(F.$"3k*************z"Ffer7$$"3a'R**HbA<H(F.$"31i,?>t?-=Ffer7$7$F[]u$"3O67z37a0=FferFg`u7$7$$"3R1+++++]uF.$!3%3EK!zt/o=Ffer7$$"3["R&R%R&)=Q(F.$!3d++++++S=Ffer7$FfauFj\u7$F]au7$$"3Ni7\YI7]tF.$"3%z**oU&QjE=Ffer7$7$$"3r*Q&R%R&)=Q(F.$"3]************R=FferF]bu7$Fcbu7$$"3uK(zhle'3uF.$"3gs?NeV-^=Ffer7$7$Fbau$"3%3EK!zt/o=FferFibu7$7$$"3w1++++++wF.$!3kh>td_<J>Ffer7$$"3J\:"Q3!)Gd(F.$!3G++++++?>Ffer7$Fhcu7$$"3W\#oQeUf_(F.$!3X)>)pb8D+>Ffer7$7$$"3emZ"pE5yZ(F.$!3V++++++!)=FferF^du7$FdduFaau7$F_cu7$$"35X3Q/?;nuF.$"3DU%)\lMUv=Ffer7$7$$"3#Rw9pE5yZ(F.$"3O************z=FferF[eu7$7$$"3"[w9pE5yZ(F.Fdeu7$$"3%Hc\;F6__(F.$"3c]M*3mV***=Ffer7$7$$"3lY:"Q3!)Gd(F.$"3A************>>FferFjeu7$F`fu7$$"33;$*=n^`$e(F.$"3I]G3A1RC>Ffer7$7$Fdcu$"3kh>td_<J>FferFffu7$7$$"362+++++]xF.$!3s!zyy.5\*>Ffer7$$"3:D#)oF:3nwF.$!39++++++g>Ffer7$FeguFccu7$F\gu7$$"3`heT@KRTwF.$"3;QCi2='*[>Ffer7$7$$"3f@#)oF:3nwF.$"33************f>FferF\hu7$7$Fchu$"3s)***********f>Ffer7$$"3!QD(p"GN#*p(F.$"3jmS@es`t>Ffer7$7$Fagu$"33"zyy.5\*>FferF[iu7$7$$"3gsstDUghxF.$Fb`oF[hr7$Fagu$!33"zyy.5\*>Ffer7$Faiu7$$"3iut1nn@dxF.$"3/M?yGb2)*>Ffer7$7$$"3%*pstDUghxF.$"3#*)*************>FferF]ju-I'COLOURGF%6&I$RGBGF("""F[hrF[hr-I+AXESLABELSGF%6$I"xGF(I"yGF(

# # Doubling on an elliptic "curve" modulo n, where gcd(n,6)=1. # P is the point to double and a, b are the parameters. # The return value is the double of the point P or # a divisor d of n. # elldou:=proc(P,a,b,n) local l,d; if P[3]=0 then return P fi; if P[2]=0 then return [0,1,0] fi; d:=igcdex(2*P[2],n,'l'); if 1<d and d<n then return d fi; l:=(3*P[1]^2+a)*l mod n; l^2-2*P[1] mod n; [%,l*(P[1]-%)-P[2] mod n,1]; end;

Zio2JkkiUEc2IkkiYUdGJUkiYkdGJUkibkdGJTYkSSJsR0YlSSJkR0YlRiVGJUMpQCQvJkYkNiMiIiQiIiFPRiRAJC8mRiQ2IyIiI0YyTzclRjIiIiJGMj5GKy1JJ2lnY2RleEdGJTYlLCQqJkY4RjtGNkY7RjtGKC5GKkAkMzJGO0YrMkYrRihPRis+RiotSSRtb2RHRiU2JComLCYqJkYxRjspJkYkNiNGO0Y4RjtGO0YmRjtGO0YqRjtGKC1GSjYkLCYqJClGKkY4RjtGOyomRjhGO0ZQRjshIiJGKDclSSIlR0YlLUZKNiQsJiomRipGOywmRlBGO0ZaRlhGO0Y7RjZGWEYoRjtGJUYlRiU=

# # Addition on an elliptic "curve" modulo n, where gcd(n,6)=1. # P and Q are the points to add and a,b are the parameters. # The return value is the sum of the points or a divisor d of n. # elladd:=proc(P,Q,a,b,n) local l,d; if P[3]=0 then return Q fi; if Q[3]=0 then return P fi; if P=Q then return elldou(P,a,b,n) fi; if P[1]=Q[1] then return [0,1,0] fi; d:=igcdex(P[1]-Q[1],n,'l'); if 1<d and d<n then return d fi; l:=(P[2]-Q[2])*l mod n; l^2-P[1]-Q[1] mod n; [%,l*(P[1]-%)-P[2] mod n,1]; end;

Zio2J0kiUEc2IkkiUUdGJUkiYUdGJUkiYkdGJUkibkdGJTYkSSJsR0YlSSJkR0YlRiVGJUMrQCQvJkYkNiMiIiQiIiFPRiZAJC8mRiZGMUYzT0YkQCQvRiRGJk8tSSdlbGxkb3VHRiU2JkYkRidGKEYpQCQvJkYkNiMiIiImRiZGQk83JUYzRkNGMz5GLC1JJ2lnY2RleEdGJTYlLCZGQUZDRkQhIiJGKS5GK0AkMzJGQ0YsMkYsRilPRiw+RistSSRtb2RHRiU2JComLCYmRiQ2IyIiI0ZDJkYmRlpGTEZDRitGQ0YpLUZVNiQsKCokKUYrRmVuRkNGQ0ZBRkxGREZMRik3JUkiJUdGJS1GVTYkLCYqJkYrRkMsJkZBRkNGXW9GTEZDRkNGWUZMRilGQ0YlRiVGJQ==

n:= 97; P:=[59,92,1]; a:=13; b:=4;

IiMoKg==

NyUiI2YiIyMqIiIi

IiM4

IiIl

elldou(P,a,b,n); elldou(%,a,b,n); elldou(%,a,b,n);

NyUiIyEpIiNnIiIi

NyUiI3giI2YiIiI=

NyUiI24iI0giIiI=

elladd(P,P,a,b,n); elladd(%,P,a,b,n); elladd(%,P,a,b,n); elladd(%,P,a,b,n);

NyUiIyEpIiNnIiIi

NyUiI24iI28iIiI=

NyUiI3giI2YiIiI=

NyUiIyIqIiMnKiIiIg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn