OpenSSL_basic.sagews

import hashlib
bitmask = (2^(30*8) - 1);

#internal state
s_i = None;

def Dual_EC_DRBG(P, Q, h_adin=0, s_0=None):

    global s_i;

    if(s_0 == None):
        s_0 = int(floor((2^16-1)*random()));

    if(s_i == None):
        s_i = s_0;

    t_i = s_i ^^ h_adin;
    s_i = (t_i*P)[0].lift();
    r_i = (s_i*Q)[0].lift();
    r_i = r_i & bitmask;

    return r_i;

def Random_Generator(P, Q, byte, h_adin=0):

    result = 0;
    req = (byte/30).ceil();

    for i in range(req):
        if(i == 0):
            result = (result << (30*8)) | Dual_EC_DRBG(P, Q, h_adin)
        else:
            result = (result << (30*8)) | Dual_EC_DRBG(P, Q)

    result = result >> ((30*req - byte)*8)

    return result;

#Curve P-256
p = 115792089210356248762697446949407573530086143415290314195533631308867097853951;
n = 115792089210356248762697446949407573529996955224135760342422259061068512044369;
b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b;
Px = 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296;
Py = 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5;
Qx = 0xc97445f45cdef9f0d3e05e1e585fc297235b82b5be8ff3efca67c59852018192;
Qy = 0xb28ef557ba31dfcbdd21ac46e2a91e3c304f44cb87058ada2cb815151e610046;

# y^2 = x^3 - 3*x + b (mod p)
curve = EllipticCurve(GF(p), [0, 0, 0, -3, b]);
print curve;

P = curve(Px, Py);
Q = curve(Qx, Qy);
print "P = ", P;
print "Q = ", Q;

#%time r = Random_Generator(P, Q, 32);
#print "r = ", hex(r);

#Public Key

pubkey = 0x04773c9f67094f7134bb3e652d9a8058b6136831e974b114687e41c01a1f688af5dcc0a3176689b9345169ca2efbea17ef8dc9a9b00977d8e6f4a2e685fdac8b0c;
h = hashlib.sha256();
h.update(str(pubkey));
z = int(h.hexdigest(), 16);

#Cx = (pubkey >> (32*8)) & (2^(32*8) - 1);
#print hex(Cx);
#Cy = pubkey & (2^(32*8) - 1);
#print hex(Cy)
#Cx = 0x362a25787ff78da06f709ba9617786f66db9acefebbd165c41aaec258cb8514b;
#Cy = 0xa56b419c7a5d477360229126224965b01745d71d94191086ea5a08254ad727f5;
#C = curve(Cx,Cy);C
#pk = sk*C;
k = 0x1B6B0CB15C1D2C2C872AE47E87994382A6396E3E8DFDE380FF7BA837374626A7;
R = k*P;
r = R[0].lift();
print hex(r);

d = 0x8af8aba2bd307f3e1dd9394752a7ab2b385a5f009632d60cfc9a46c8543f5518;
r = 0x304502207daadbbd56373c24bcea3c2f86291ab9b4ef9628fc7cd213292522ff6dbea2ff;
s = 0x022100af0eb58e3c3cebc15e7238e9d8ce64206e7f5090e13c6b33750eda03542beac0;
#s = Mod(k_1*(z + r*d), n);
dA = Mod((s*k - z)/r, n);
print hex(int(dA));

Elliptic Curve defined by y^2 = x^3 + 115792089210356248762697446949407573530086143415290314195533631308867097853948*x + 41058363725152142129326129780047268409114441015993725554835256314039467401291 over Finite Field of size 115792089210356248762697446949407573530086143415290314195533631308867097853951 P = (48439561293906451759052585252797914202762949526041747995844080717082404635286 : 36134250956749795798585127919587881956611106672985015071877198253568414405109 : 1) Q = (91120319633256209954638481795610364441930342474826146651283703640232629993874 : 80764272623998874743522585409326200078679332703816718187804498579075161456710 : 1) 6623cb19a9a51ba9fbb7991dd05a8f05ac264703732bb24d6bc5f47217bac669 0x874fbed3f4b8ab7c08a170c3d581d3db9f45ad7a0c5932ca22178da72f66ed63L