? e=ellinit([0,0,0,Mod(1,11),Mod(2,11)])
%1 = [0, 0, 0, Mod(1, 11), Mod(2, 11), 0, Mod(2, 11), Mod(8, 11), Mod(10, 11), Mod(7, 11), Mod(10, 11), Mod(1, 11), Mod(2, 11), 0, 0, 0, 0, 0, 0]
? for(x=0,10,for(y=0,10,P=[Mod(x,11),Mod(y,11)];if(ellisoncurve(e,P),print(P))))
[Mod(1, 11), Mod(2, 11)]
[Mod(1, 11), Mod(9, 11)]
[Mod(2, 11), Mod(1, 11)]
[Mod(2, 11), Mod(10, 11)]
[Mod(4, 11), Mod(2, 11)]
[Mod(4, 11), Mod(9, 11)]
[Mod(5, 11), Mod(0, 11)]
[Mod(6, 11), Mod(2, 11)]
[Mod(6, 11), Mod(9, 11)]
[Mod(7, 11), Mod(0, 11)]
[Mod(8, 11), Mod(4, 11)]
[Mod(8, 11), Mod(7, 11)]
[Mod(9, 11), Mod(5, 11)]
[Mod(9, 11), Mod(6, 11)]
[Mod(10, 11), Mod(0, 11)]
? P=[Mod(2,11),Mod(10,11)]
%2 = [Mod(2, 11), Mod(10, 11)]
? ellisoncurve(e,P)
%3 = 1
? ellpow(e,P,2)
%4 = [Mod(8, 11), Mod(7, 11)]
? ellpow(e,P,3)
%5 = [Mod(4, 11), Mod(2, 11)]
? elladd(e,P,%4)
%6 = [Mod(4, 11), Mod(2, 11)]
? ellap(e)
%7 = -4
? n=11+1+%
%8 = 8
? n=11+1-%7
%9 = 16
? ellpow(e,P,16)
%10 = [0]
? ellpow(e,P,4)
%11 = [Mod(10, 11), Mod(0, 11)]
? ellpow(e,P,8)
%12 = [0]
? P
%13 = [Mod(2, 11), Mod(10, 11)]
? for(n=1,8,print(ellpow(e,P,n)))
[Mod(2, 11), Mod(10, 11)]
[Mod(8, 11), Mod(7, 11)]
[Mod(4, 11), Mod(2, 11)]
[Mod(10, 11), Mod(0, 11)]
[Mod(4, 11), Mod(9, 11)]
[Mod(8, 11), Mod(4, 11)]
[Mod(2, 11), Mod(1, 11)]
[0]
? Q=[Mod(5,11),Mod(0,11)]
%14 = [Mod(5, 11), Mod(0, 11)]
? elladd(e,P,Q)
%15 = [Mod(9, 11), Mod(6, 11)]
? for(n=1,8,print(elladd(e,ellpow(e,P,n),Q)))
[Mod(9, 11), Mod(6, 11)]
[Mod(1, 11), Mod(2, 11)]
[Mod(6, 11), Mod(2, 11)]
[Mod(7, 11), Mod(0, 11)]
[Mod(6, 11), Mod(9, 11)]
[Mod(1, 11), Mod(9, 11)]
[Mod(9, 11), Mod(5, 11)]
[Mod(5, 11), Mod(0, 11)]
? \rCursos/343L.13/bitcoin.gp
? p=2^256-2^32-2^9-2^8-2^7-2^6-2^4-1
%16 = 115792089237316195423570985008687907853269984665640564039457584007908834671663
? e=ellinit(Mod(1,p)*[0,0,0,0,7])
%17 = [Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(7, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(28, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(115792089237316195423570985008687907853269984665640564039457584007908834665615, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(115792089237316195423570985008687907853269984665640564039457584007908834650495, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), 0, 0, 0, 0, 0, 0]
? g=[Mod(55066263022277343669578718895168534326250603453777594175500187360389116729240,115792089237316195423570985008687907853269984665640564039457584007908834671663),Mod(32670510020758816978083085130507043184471273380659243275938904335757337482424,115792089237316195423570985008687907853269984665640564039457584007908834671663)]
%18 = [Mod(55066263022277343669578718895168534326250603453777594175500187360389116729240, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(32670510020758816978083085130507043184471273380659243275938904335757337482424, 115792089237316195423570985008687907853269984665640564039457584007908834671663)]
? G
%19 = G
? g
%20 = [Mod(55066263022277343669578718895168534326250603453777594175500187360389116729240, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(32670510020758816978083085130507043184471273380659243275938904335757337482424, 115792089237316195423570985008687907853269984665640564039457584007908834671663)]
? e
%21 = [Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(7, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(28, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(115792089237316195423570985008687907853269984665640564039457584007908834665615, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(115792089237316195423570985008687907853269984665640564039457584007908834650495, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(0, 115792089237316195423570985008687907853269984665640564039457584007908834671663), 0, 0, 0, 0, 0, 0]
? p
%22 = 115792089237316195423570985008687907853269984665640564039457584007908834671663
? ellisoncurve(e,g)
%23 = 1
? ellpow(e,g,8382388928339297327372781982771828)
%24 = [Mod(9363958337619339877455955832502193911636772919858359641909537275401830838135, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(80038749046395693117708054566330572904936611978587840902722944932012599664696, 115792089237316195423570985008687907853269984665640564039457584007908834671663)]
? ellap(e)
%25 = 432420386565659656852420866390673177327
? n=p+1-%
%26 = 115792089237316195423570985008687907852837564279074904382605163141518161494337
? ellpow(e,g,n)
%27 = [0]
? isprime(n)
%28 = 1
? g
%29 = [Mod(55066263022277343669578718895168534326250603453777594175500187360389116729240, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(32670510020758816978083085130507043184471273380659243275938904335757337482424, 115792089237316195423570985008687907853269984665640564039457584007908834671663)]
? issquare(Mod(1,p)^3+Mod(7,p),&y)
%30 = 1
? y
%31 = Mod(29896722852569046015560700294576055776214335159245303116488692907525646231534, 115792089237316195423570985008687907853269984665640564039457584007908834671663)
? h=[Mod(1,p),y]
%32 = [Mod(1, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(29896722852569046015560700294576055776214335159245303116488692907525646231534, 115792089237316195423570985008687907853269984665640564039457584007908834671663)]
? ellisoncurve(e,h)
%33 = 1
? for(x=1,20,ifissquare(Mod(x,p)^3+Mod(7,p)),print(x))
  ***   too many arguments: ...are(Mod(x,p)^3+Mod(7,p)),print(x))
  ***                                                   ^---------
? for(x=1,20,if(issquare(Mod(x,p)^3+Mod(7,p)),print(x)))
1
2
3
4
6
8
12
13
14
16
20
? issquare(Mod(2,p)^3+Mod(7,p),&y)
%34 = 1
? k=[Mod(2,p),y]
%35 = [Mod(2, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(46580984542418694471253469931035885126779956971428003686700937153791839982430, 115792089237316195423570985008687907853269984665640564039457584007908834671663)]
? ellisoncurve(e,k)
%36 = 1
? elladd(e,h,k)
%37 = [Mod(6229588549486259819305920621984993562998356423740097654874267457020397458585, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(36292416413292293100184136570770513527529562975075548635839627194334289071908, 115792089237316195423570985008687907853269984665640564039457584007908834671663)]
? g
%38 = [Mod(55066263022277343669578718895168534326250603453777594175500187360389116729240, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(32670510020758816978083085130507043184471273380659243275938904335757337482424, 115792089237316195423570985008687907853269984665640564039457584007908834671663)]
? ellpow(e,g,-1)
%39 = [Mod(55066263022277343669578718895168534326250603453777594175500187360389116729240, 115792089237316195423570985008687907853269984665640564039457584007908834671663), Mod(83121579216557378445487899878180864668798711284981320763518679672151497189239, 115792089237316195423570985008687907853269984665640564039457584007908834671663)]
? \q