PNG  IHDRX cHRMz&u0`:pQ<bKGD pHYsodtIME MeqIDATxw]Wug^Qd˶ 6`!N:!@xI~)%7%@Bh&`lnjVF29gΨ4E$|>cɚ{gk= %,a KX%,a KX%,a KX%,a KX%,a KX%,a KX%, b` ǟzeאfp]<!SJmɤY޲ڿ,%c ~ع9VH.!Ͳz&QynֺTkRR.BLHi٪:l;@(!MԴ=žI,:o&N'Kù\vRmJ雵֫AWic H@" !: Cé||]k-Ha oݜ:y F())u]aG7*JV@J415p=sZH!=!DRʯvɱh~V\}v/GKY$n]"X"}t@ xS76^[bw4dsce)2dU0 CkMa-U5tvLƀ~mlMwfGE/-]7XAƟ`׮g ewxwC4\[~7@O-Q( a*XGƒ{ ՟}$_y3tĐƤatgvێi|K=uVyrŲlLӪuܿzwk$m87k( `múcE)"@rK( z4$D; 2kW=Xb$V[Ru819קR~qloѱDyįݎ*mxw]y5e4K@ЃI0A D@"BDk_)N\8͜9dz"fK0zɿvM /.:2O{ Nb=M=7>??Zuo32 DLD@D| &+֎C #B8ַ`bOb $D#ͮҪtx]%`ES`Ru[=¾!@Od37LJ0!OIR4m]GZRJu$‡c=%~s@6SKy?CeIh:[vR@Lh | (BhAMy=݃  G"'wzn޺~8ԽSh ~T*A:xR[ܹ?X[uKL_=fDȊ؂p0}7=D$Ekq!/t.*2ʼnDbŞ}DijYaȲ(""6HA;:LzxQ‘(SQQ}*PL*fc\s `/d'QXW, e`#kPGZuŞuO{{wm[&NBTiiI0bukcA9<4@SӊH*؎4U/'2U5.(9JuDfrޱtycU%j(:RUbArLֺN)udA':uGQN"-"Is.*+k@ `Ojs@yU/ H:l;@yyTn}_yw!VkRJ4P)~y#)r,D =ě"Q]ci'%HI4ZL0"MJy 8A{ aN<8D"1#IJi >XjX֔#@>-{vN!8tRݻ^)N_╗FJEk]CT՟ YP:_|H1@ CBk]yKYp|og?*dGvzنzӴzjֺNkC~AbZƷ`.H)=!QͷVTT(| u78y֮}|[8-Vjp%2JPk[}ԉaH8Wpqhwr:vWª<}l77_~{s۴V+RCģ%WRZ\AqHifɤL36: #F:p]Bq/z{0CU6ݳEv_^k7'>sq*+kH%a`0ԣisqにtү04gVgW΂iJiS'3w.w}l6MC2uԯ|>JF5`fV5m`Y**Db1FKNttu]4ccsQNnex/87+}xaUW9y>ͯ骵G{䩓Գ3+vU}~jJ.NFRD7<aJDB1#ҳgSb,+CS?/ VG J?|?,2#M9}B)MiE+G`-wo߫V`fio(}S^4e~V4bHOYb"b#E)dda:'?}׮4繏`{7Z"uny-?ǹ;0MKx{:_pÚmFמ:F " .LFQLG)Q8qN q¯¯3wOvxDb\. BKD9_NN &L:4D{mm o^tֽ:q!ƥ}K+<"m78N< ywsard5+вz~mnG)=}lYݧNj'QJS{S :UYS-952?&O-:W}(!6Mk4+>A>j+i|<<|;ر^߉=HE|V#F)Emm#}/"y GII웻Jі94+v뾧xu~5C95~ūH>c@덉pʃ1/4-A2G%7>m;–Y,cyyaln" ?ƻ!ʪ<{~h~i y.zZB̃/,雋SiC/JFMmBH&&FAbϓO^tubbb_hZ{_QZ-sύodFgO(6]TJA˯#`۶ɟ( %$&+V'~hiYy>922 Wp74Zkq+Ovn錄c>8~GqܲcWꂎz@"1A.}T)uiW4="jJ2W7mU/N0gcqܗOO}?9/wìXžΏ0 >֩(V^Rh32!Hj5`;O28؇2#ݕf3 ?sJd8NJ@7O0 b־?lldщ̡&|9C.8RTWwxWy46ah嘦mh٤&l zCy!PY?: CJyв]dm4ǜҐR޻RլhX{FƯanшQI@x' ao(kUUuxW_Ñ줮[w8 FRJ(8˼)_mQ _!RJhm=!cVmm ?sFOnll6Qk}alY}; "baӌ~M0w,Ggw2W:G/k2%R,_=u`WU R.9T"v,<\Ik޽/2110Ӿxc0gyC&Ny޽JҢrV6N ``یeA16"J³+Rj*;BϜkZPJaÍ<Jyw:NP8/D$ 011z֊Ⱳ3ι֘k1V_"h!JPIΣ'ɜ* aEAd:ݺ>y<}Lp&PlRfTb1]o .2EW\ͮ]38؋rTJsǏP@芎sF\> P^+dYJLbJ C-xϐn> ι$nj,;Ǖa FU *择|h ~izť3ᤓ`K'-f tL7JK+vf2)V'-sFuB4i+m+@My=O҈0"|Yxoj,3]:cо3 $#uŘ%Y"y죯LebqtҢVzq¼X)~>4L׶m~[1_k?kxֺQ`\ |ٛY4Ѯr!)N9{56(iNq}O()Em]=F&u?$HypWUeB\k]JɩSع9 Zqg4ZĊo oMcjZBU]B\TUd34ݝ~:7ڶSUsB0Z3srx 7`:5xcx !qZA!;%͚7&P H<WL!džOb5kF)xor^aujƍ7 Ǡ8/p^(L>ὴ-B,{ۇWzֺ^k]3\EE@7>lYBȝR.oHnXO/}sB|.i@ɥDB4tcm,@ӣgdtJ!lH$_vN166L__'Z)y&kH;:,Y7=J 9cG) V\hjiE;gya~%ks_nC~Er er)muuMg2;֫R)Md) ,¶ 2-wr#F7<-BBn~_(o=KO㭇[Xv eN_SMgSҐ BS헃D%g_N:/pe -wkG*9yYSZS.9cREL !k}<4_Xs#FmҶ:7R$i,fi!~' # !6/S6y@kZkZcX)%5V4P]VGYq%H1!;e1MV<!ϐHO021Dp= HMs~~a)ަu7G^];git!Frl]H/L$=AeUvZE4P\.,xi {-~p?2b#amXAHq)MWǾI_r`S Hz&|{ +ʖ_= (YS(_g0a03M`I&'9vl?MM+m~}*xT۲(fY*V4x@29s{DaY"toGNTO+xCAO~4Ϳ;p`Ѫ:>Ҵ7K 3}+0 387x\)a"/E>qpWB=1 ¨"MP(\xp߫́A3+J] n[ʼnӼaTbZUWb={~2ooKױӰp(CS\S筐R*JغV&&"FA}J>G֐p1ٸbk7 ŘH$JoN <8s^yk_[;gy-;߉DV{c B yce% aJhDȶ 2IdйIB/^n0tNtџdcKj4϶v~- CBcgqx9= PJ) dMsjpYB] GD4RDWX +h{y`,3ꊕ$`zj*N^TP4L:Iz9~6s) Ga:?y*J~?OrMwP\](21sZUD ?ܟQ5Q%ggW6QdO+\@ ̪X'GxN @'4=ˋ+*VwN ne_|(/BDfj5(Dq<*tNt1х!MV.C0 32b#?n0pzj#!38}޴o1KovCJ`8ŗ_"]] rDUy޲@ Ȗ-;xџ'^Y`zEd?0„ DAL18IS]VGq\4o !swV7ˣι%4FѮ~}6)OgS[~Q vcYbL!wG3 7띸*E Pql8=jT\꘿I(z<[6OrR8ºC~ډ]=rNl[g|v TMTղb-o}OrP^Q]<98S¤!k)G(Vkwyqyr޽Nv`N/e p/~NAOk \I:G6]4+K;j$R:Mi #*[AȚT,ʰ,;N{HZTGMoּy) ]%dHء9Պ䠬|<45,\=[bƟ8QXeB3- &dҩ^{>/86bXmZ]]yޚN[(WAHL$YAgDKp=5GHjU&99v簪C0vygln*P)9^͞}lMuiH!̍#DoRBn9l@ xA/_v=ȺT{7Yt2N"4!YN`ae >Q<XMydEB`VU}u]嫇.%e^ánE87Mu\t`cP=AD/G)sI"@MP;)]%fH9'FNsj1pVhY&9=0pfuJ&gޤx+k:!r˭wkl03׼Ku C &ѓYt{.O.zҏ z}/tf_wEp2gvX)GN#I ݭ߽v/ .& и(ZF{e"=V!{zW`, ]+LGz"(UJp|j( #V4, 8B 0 9OkRrlɱl94)'VH9=9W|>PS['G(*I1==C<5"Pg+x'K5EMd؞Af8lG ?D FtoB[je?{k3zQ vZ;%Ɠ,]E>KZ+T/ EJxOZ1i #T<@ I}q9/t'zi(EMqw`mYkU6;[t4DPeckeM;H}_g pMww}k6#H㶏+b8雡Sxp)&C $@'b,fPߑt$RbJ'vznuS ~8='72_`{q纶|Q)Xk}cPz9p7O:'|G~8wx(a 0QCko|0ASD>Ip=4Q, d|F8RcU"/KM opKle M3#i0c%<7׿p&pZq[TR"BpqauIp$ 8~Ĩ!8Սx\ւdT>>Z40ks7 z2IQ}ItԀ<-%S⍤};zIb$I 5K}Q͙D8UguWE$Jh )cu4N tZl+[]M4k8֦Zeq֮M7uIqG 1==tLtR,ƜSrHYt&QP윯Lg' I,3@P'}'R˪e/%-Auv·ñ\> vDJzlӾNv5:|K/Jb6KI9)Zh*ZAi`?S {aiVDԲuy5W7pWeQJk֤#5&V<̺@/GH?^τZL|IJNvI:'P=Ϛt"¨=cud S Q.Ki0 !cJy;LJR;G{BJy޺[^8fK6)=yʊ+(k|&xQ2`L?Ȓ2@Mf 0C`6-%pKpm')c$׻K5[J*U[/#hH!6acB JA _|uMvDyk y)6OPYjœ50VT K}cǻP[ $:]4MEA.y)|B)cf-A?(e|lɉ#P9V)[9t.EiQPDѠ3ϴ;E:+Օ t ȥ~|_N2,ZJLt4! %ա]u {+=p.GhNcŞQI?Nd'yeh n7zi1DB)1S | S#ًZs2|Ɛy$F SxeX{7Vl.Src3E℃Q>b6G ўYCmtկ~=K0f(=LrAS GN'ɹ9<\!a`)֕y[uՍ[09` 9 +57ts6}b4{oqd+J5fa/,97J#6yν99mRWxJyѡyu_TJc`~W>l^q#Ts#2"nD1%fS)FU w{ܯ R{ ˎ󅃏џDsZSQS;LV;7 Od1&1n$ N /.q3~eNɪ]E#oM~}v֯FڦwyZ=<<>Xo稯lfMFV6p02|*=tV!c~]fa5Y^Q_WN|Vs 0ҘދU97OI'N2'8N֭fgg-}V%y]U4 峧p*91#9U kCac_AFңĪy뚇Y_AiuYyTTYЗ-(!JFLt›17uTozc. S;7A&&<ԋ5y;Ro+:' *eYJkWR[@F %SHWP 72k4 qLd'J "zB6{AC0ƁA6U.'F3:Ȅ(9ΜL;D]m8ڥ9}dU "v!;*13Rg^fJyShyy5auA?ɩGHRjo^]׽S)Fm\toy 4WQS@mE#%5ʈfFYDX ~D5Ϡ9tE9So_aU4?Ѽm%&c{n>.KW1Tlb}:j uGi(JgcYj0qn+>) %\!4{LaJso d||u//P_y7iRJ߬nHOy) l+@$($VFIQ9%EeKʈU. ia&FY̒mZ=)+qqoQn >L!qCiDB;Y<%} OgBxB!ØuG)WG9y(Ą{_yesuZmZZey'Wg#C~1Cev@0D $a@˲(.._GimA:uyw֬%;@!JkQVM_Ow:P.s\)ot- ˹"`B,e CRtaEUP<0'}r3[>?G8xU~Nqu;Wm8\RIkբ^5@k+5(By'L&'gBJ3ݶ!/㮻w҅ yqPWUg<e"Qy*167΃sJ\oz]T*UQ<\FԎ`HaNmڜ6DysCask8wP8y9``GJ9lF\G g's Nn͵MLN֪u$| /|7=]O)6s !ĴAKh]q_ap $HH'\1jB^s\|- W1:=6lJBqjY^LsPk""`]w)󭃈,(HC ?䔨Y$Sʣ{4Z+0NvQkhol6C.婧/u]FwiVjZka&%6\F*Ny#8O,22+|Db~d ~Çwc N:FuuCe&oZ(l;@ee-+Wn`44AMK➝2BRՈt7g*1gph9N) *"TF*R(#'88pm=}X]u[i7bEc|\~EMn}P瘊J)K.0i1M6=7'_\kaZ(Th{K*GJyytw"IO-PWJk)..axӝ47"89Cc7ĐBiZx 7m!fy|ϿF9CbȩV 9V-՛^pV̌ɄS#Bv4-@]Vxt-Z, &ֺ*diؠ2^VXbs֔Ìl.jQ]Y[47gj=幽ex)A0ip׳ W2[ᎇhuE^~q흙L} #-b۸oFJ_QP3r6jr+"nfzRJTUqoaۍ /$d8Mx'ݓ= OՃ| )$2mcM*cЙj}f };n YG w0Ia!1Q.oYfr]DyISaP}"dIӗթO67jqR ҊƐƈaɤGG|h;t]䗖oSv|iZqX)oalv;۩meEJ\!8=$4QU4Xo&VEĊ YS^E#d,yX_> ۘ-e\ "Wa6uLĜZi`aD9.% w~mB(02G[6y.773a7 /=o7D)$Z 66 $bY^\CuP. (x'"J60׿Y:Oi;F{w佩b+\Yi`TDWa~|VH)8q/=9!g߆2Y)?ND)%?Ǐ`k/sn:;O299yB=a[Ng 3˲N}vLNy;*?x?~L&=xyӴ~}q{qE*IQ^^ͧvü{Huu=R|>JyUlZV, B~/YF!Y\u_ݼF{_C)LD]m {H 0ihhadd nUkf3oٺCvE\)QJi+֥@tDJkB$1!Đr0XQ|q?d2) Ӣ_}qv-< FŊ߫%roppVBwü~JidY4:}L6M7f٬F "?71<2#?Jyy4뷢<_a7_=Q E=S1И/9{+93֮E{ǂw{))?maÆm(uLE#lïZ  ~d];+]h j?!|$F}*"4(v'8s<ŏUkm7^7no1w2ؗ}TrͿEk>p'8OB7d7R(A 9.*Mi^ͳ; eeUwS+C)uO@ =Sy]` }l8^ZzRXj[^iUɺ$tj))<sbDJfg=Pk_{xaKo1:-uyG0M ԃ\0Lvuy'ȱc2Ji AdyVgVh!{]/&}}ċJ#%d !+87<;qN޼Nفl|1N:8ya  8}k¾+-$4FiZYÔXk*I&'@iI99)HSh4+2G:tGhS^繿 Kتm0 вDk}֚+QT4;sC}rՅE,8CX-e~>G&'9xpW,%Fh,Ry56Y–hW-(v_,? ; qrBk4-V7HQ;ˇ^Gv1JVV%,ik;D_W!))+BoS4QsTM;gt+ndS-~:11Sgv!0qRVh!"Ȋ(̦Yl.]PQWgٳE'`%W1{ndΗBk|Ž7ʒR~,lnoa&:ü$ 3<a[CBݮwt"o\ePJ=Hz"_c^Z.#ˆ*x z̝grY]tdkP*:97YľXyBkD4N.C_[;F9`8& !AMO c `@BA& Ost\-\NX+Xp < !bj3C&QL+*&kAQ=04}cC!9~820G'PC9xa!w&bo_1 Sw"ܱ V )Yl3+ס2KoXOx]"`^WOy :3GO0g;%Yv㐫(R/r (s } u B &FeYZh0y> =2<Ϟc/ -u= c&׭,.0"g"7 6T!vl#sc>{u/Oh Bᾈ)۴74]x7 gMӒ"d]U)}" v4co[ ɡs 5Gg=XR14?5A}D "b{0$L .\4y{_fe:kVS\\O]c^W52LSBDM! C3Dhr̦RtArx4&agaN3Cf<Ԉp4~ B'"1@.b_/xQ} _߃҉/gٓ2Qkqp0շpZ2fԫYz< 4L.Cyυι1t@鎫Fe sYfsF}^ V}N<_`p)alٶ "(XEAVZ<)2},:Ir*#m_YӼ R%a||EƼIJ,,+f"96r/}0jE/)s)cjW#w'Sʯ5<66lj$a~3Kʛy 2:cZ:Yh))+a߭K::N,Q F'qB]={.]h85C9cr=}*rk?vwV렵ٸW Rs%}rNAkDv|uFLBkWY YkX מ|)1!$#3%y?pF<@<Rr0}: }\J [5FRxY<9"SQdE(Q*Qʻ)q1E0B_O24[U'],lOb ]~WjHޏTQ5Syu wq)xnw8~)c 쫬gٲߠ H% k5dƝk> kEj,0% b"vi2Wس_CuK)K{n|>t{P1򨾜j>'kEkƗBg*H%'_aY6Bn!TL&ɌOb{c`'d^{t\i^[uɐ[}q0lM˕G:‚4kb祔c^:?bpg… +37stH:0}en6x˟%/<]BL&* 5&fK9Mq)/iyqtA%kUe[ڛKN]Ě^,"`/ s[EQQm?|XJ߅92m]G.E΃ח U*Cn.j_)Tѧj̿30ڇ!A0=͜ar I3$C^-9#|pk!)?7.x9 @OO;WƝZBFU keZ75F6Tc6"ZȚs2y/1 ʵ:u4xa`C>6Rb/Yм)^=+~uRd`/|_8xbB0?Ft||Z\##|K 0>>zxv8۴吅q 8ĥ)"6>~\8:qM}#͚'ĉ#p\׶ l#bA?)|g g9|8jP(cr,BwV (WliVxxᡁ@0Okn;ɥh$_ckCgriv}>=wGzβ KkBɛ[˪ !J)h&k2%07δt}!d<9;I&0wV/ v 0<H}L&8ob%Hi|޶o&h1L|u֦y~󛱢8fٲUsւ)0oiFx2}X[zVYr_;N(w]_4B@OanC?gĦx>мgx>ΛToZoOMp>40>V Oy V9iq!4 LN,ˢu{jsz]|"R޻&'ƚ{53ўFu(<٪9:΋]B;)B>1::8;~)Yt|0(pw2N%&X,URBK)3\zz&}ax4;ǟ(tLNg{N|Ǽ\G#C9g$^\}p?556]/RP.90 k,U8/u776s ʪ_01چ|\N 0VV*3H鴃J7iI!wG_^ypl}r*jɤSR 5QN@ iZ#1ٰy;_\3\BQQ x:WJv츟ٯ$"@6 S#qe딇(/P( Dy~TOϻ<4:-+F`0||;Xl-"uw$Цi󼕝mKʩorz"mϺ$F:~E'ҐvD\y?Rr8_He@ e~O,T.(ފR*cY^m|cVR[8 JҡSm!ΆԨb)RHG{?MpqrmN>߶Y)\p,d#xۆWY*,l6]v0h15M˙MS8+EdI='LBJIH7_9{Caз*Lq,dt >+~ّeʏ?xԕ4bBAŚjﵫ!'\Ը$WNvKO}ӽmSşذqsOy?\[,d@'73'j%kOe`1.g2"e =YIzS2|zŐƄa\U,dP;jhhhaxǶ?КZ՚.q SE+XrbOu%\GتX(H,N^~]JyEZQKceTQ]VGYqnah;y$cQahT&QPZ*iZ8UQQM.qo/T\7X"u?Mttl2Xq(IoW{R^ ux*SYJ! 4S.Jy~ BROS[V|žKNɛP(L6V^|cR7i7nZW1Fd@ Ara{詑|(T*dN]Ko?s=@ |_EvF]׍kR)eBJc" MUUbY6`~V޴dJKß&~'d3i WWWWWW
Current Directory: /opt/cpanel/ea-openssl11/share/doc/openssl/html/man3
Viewing File: /opt/cpanel/ea-openssl11/share/doc/openssl/html/man3/EC_GROUP_new.html
<?xml version="1.0" ?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>EC_GROUP_new</title> <meta http-equiv="content-type" content="text/html; charset=utf-8" /> <link rev="made" href="mailto:root@localhost" /> </head> <body style="background-color: white"> <ul id="index"> <li><a href="#NAME">NAME</a></li> <li><a href="#SYNOPSIS">SYNOPSIS</a></li> <li><a href="#DESCRIPTION">DESCRIPTION</a></li> <li><a href="#RETURN-VALUES">RETURN VALUES</a></li> <li><a href="#SEE-ALSO">SEE ALSO</a></li> <li><a href="#COPYRIGHT">COPYRIGHT</a></li> </ul> <h1 id="NAME">NAME</h1> <p>EC_GROUP_get_ecparameters, EC_GROUP_get_ecpkparameters, EC_GROUP_new, EC_GROUP_new_from_ecparameters, EC_GROUP_new_from_ecpkparameters, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_new_curve_GFp, EC_GROUP_new_curve_GF2m, EC_GROUP_new_by_curve_name, EC_GROUP_set_curve, EC_GROUP_get_curve, EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m, EC_get_builtin_curves - Functions for creating and destroying EC_GROUP objects</p> <h1 id="SYNOPSIS">SYNOPSIS</h1> <pre><code> #include &lt;openssl/ec.h&gt; EC_GROUP *EC_GROUP_new(const EC_METHOD *meth); EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params) EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params) void EC_GROUP_free(EC_GROUP *group); void EC_GROUP_clear_free(EC_GROUP *group); EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); EC_GROUP *EC_GROUP_new_by_curve_name(int nid); int EC_GROUP_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); int EC_GROUP_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); ECPARAMETERS *EC_GROUP_get_ecparameters(const EC_GROUP *group, ECPARAMETERS *params) ECPKPARAMETERS *EC_GROUP_get_ecpkparameters(const EC_GROUP *group, ECPKPARAMETERS *params) size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);</code></pre> <h1 id="DESCRIPTION">DESCRIPTION</h1> <p>Within the library there are two forms of elliptic curve that are of interest. The first form is those defined over the prime field Fp. The elements of Fp are the integers 0 to p-1, where p is a prime number. This gives us a revised elliptic curve equation as follows:</p> <p>y^2 mod p = x^3 +ax + b mod p</p> <p>The second form is those defined over a binary field F2^m where the elements of the field are integers of length at most m bits. For this form the elliptic curve equation is modified to:</p> <p>y^2 + xy = x^3 + ax^2 + b (where b != 0)</p> <p>Operations in a binary field are performed relative to an <b>irreducible polynomial</b>. All such curves with OpenSSL use a trinomial or a pentanomial for this parameter.</p> <p>A new curve can be constructed by calling EC_GROUP_new(), using the implementation provided by <b>meth</b> (see <a href="../man3/EC_GFp_simple_method.html">EC_GFp_simple_method(3)</a>). It is then necessary to call EC_GROUP_set_curve() to set the curve parameters. EC_GROUP_new_from_ecparameters() will create a group from the specified <b>params</b> and EC_GROUP_new_from_ecpkparameters() will create a group from the specific PK <b>params</b>.</p> <p>EC_GROUP_set_curve() sets the curve parameters <b>p</b>, <b>a</b> and <b>b</b>. For a curve over Fp <b>p</b> is the prime for the field. For a curve over F2^m <b>p</b> represents the irreducible polynomial - each bit represents a term in the polynomial. Therefore, there will either be three or five bits set dependent on whether the polynomial is a trinomial or a pentanomial. In either case, <b>a</b> and <b>b</b> represents the coefficients a and b from the relevant equation introduced above.</p> <p>EC_group_get_curve() obtains the previously set curve parameters.</p> <p>EC_GROUP_set_curve_GFp() and EC_GROUP_set_curve_GF2m() are synonyms for EC_GROUP_set_curve(). They are defined for backwards compatibility only and should not be used.</p> <p>EC_GROUP_get_curve_GFp() and EC_GROUP_get_curve_GF2m() are synonyms for EC_GROUP_get_curve(). They are defined for backwards compatibility only and should not be used.</p> <p>The functions EC_GROUP_new_curve_GFp() and EC_GROUP_new_curve_GF2m() are shortcuts for calling EC_GROUP_new() and then the EC_GROUP_set_curve() function. An appropriate default implementation method will be used.</p> <p>Whilst the library can be used to create any curve using the functions described above, there are also a number of predefined curves that are available. In order to obtain a list of all of the predefined curves, call the function EC_get_builtin_curves(). The parameter <b>r</b> should be an array of EC_builtin_curve structures of size <b>nitems</b>. The function will populate the <b>r</b> array with information about the builtin curves. If <b>nitems</b> is less than the total number of curves available, then the first <b>nitems</b> curves will be returned. Otherwise the total number of curves will be provided. The return value is the total number of curves available (whether that number has been populated in <b>r</b> or not). Passing a NULL <b>r</b>, or setting <b>nitems</b> to 0 will do nothing other than return the total number of curves available. The EC_builtin_curve structure is defined as follows:</p> <pre><code> typedef struct { int nid; const char *comment; } EC_builtin_curve;</code></pre> <p>Each EC_builtin_curve item has a unique integer id (<b>nid</b>), and a human readable comment string describing the curve.</p> <p>In order to construct a builtin curve use the function EC_GROUP_new_by_curve_name() and provide the <b>nid</b> of the curve to be constructed.</p> <p>EC_GROUP_free() frees the memory associated with the EC_GROUP. If <b>group</b> is NULL nothing is done.</p> <p>EC_GROUP_clear_free() destroys any sensitive data held within the EC_GROUP and then frees its memory. If <b>group</b> is NULL nothing is done.</p> <h1 id="RETURN-VALUES">RETURN VALUES</h1> <p>All EC_GROUP_new* functions return a pointer to the newly constructed group, or NULL on error.</p> <p>EC_get_builtin_curves() returns the number of builtin curves that are available.</p> <p>EC_GROUP_set_curve_GFp(), EC_GROUP_get_curve_GFp(), EC_GROUP_set_curve_GF2m(), EC_GROUP_get_curve_GF2m() return 1 on success or 0 on error.</p> <h1 id="SEE-ALSO">SEE ALSO</h1> <p><a href="../man7/crypto.html">crypto(7)</a>, <a href="../man3/EC_GROUP_copy.html">EC_GROUP_copy(3)</a>, <a href="../man3/EC_POINT_new.html">EC_POINT_new(3)</a>, <a href="../man3/EC_POINT_add.html">EC_POINT_add(3)</a>, <a href="../man3/EC_KEY_new.html">EC_KEY_new(3)</a>, <a href="../man3/EC_GFp_simple_method.html">EC_GFp_simple_method(3)</a>, <a href="../man3/d2i_ECPKParameters.html">d2i_ECPKParameters(3)</a></p> <h1 id="COPYRIGHT">COPYRIGHT</h1> <p>Copyright 2013-2020 The OpenSSL Project Authors. All Rights Reserved.</p> <p>Licensed under the OpenSSL license (the &quot;License&quot;). You may not use this file except in compliance with the License. You can obtain a copy in the file LICENSE in the source distribution or at <a href="https://www.openssl.org/source/license.html">https://www.openssl.org/source/license.html</a>.</p> </body> </html>