def secp256k1():
"""
create the secp256k1 curve
"""
GFp= FiniteField(2**256 - 2**32 - 977)
ec= EllipticCurve(GFp, 0, 7)
return ECDSA(ec, ec.point( 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798, 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8 ), 2**256 - 432420386565659656852420866394968145599)
def main():
curve = EllipticCurve(EC_A, EC_B, EC_P)
base_point = curve.create_point(EC_POINT_COORD)
diffie = DiffieHellman(base_point)
private_key = random.randint(1, 1000)
public_key = diffie.get_public_key(private_key)
q = random.randint(1, 100)
to_encrypt = base_point * 2
encrypted_points = diffie.encrypt(to_encrypt, public_key, q)
decrypted = diffie.decrypt(encrypted_points, private_key)
print('Base eliptic curve point: ', to_encrypt)
print('Encrypted: ', encrypted_points[0], encrypted_points[1])
print('Decryped: ', decrypted)
if decrypted == to_encrypt:
print('Decrypted successfully')
else:
print('Something went wrong')
from ec import EllipticCurve e = EllipticCurve(-11, 11, 593899) print e(5, 9) - e(1, 1)
from ec import EllipticCurve
e = EllipticCurve(2,3,19)
print e
print '(a)', e(1,5) + e(9,3)
print '(b)', e(9,3) + e(9,3)
print '(c)', e(1,5) - e(9,3)
for i in range(100):
p = i*e(1,5)
if p == e(9,3):
print '(d)', i
break
print '(e)'
for i in range(1,100):
p = i*e(1,5)
print '\t%dP ='%i, p
if p == e('inf'):
break
from ec import EllipticCurve e = EllipticCurve(-10, 21, 557) p = e(2, 3) print '189P =', 189 * p print ' 63P =', 63 * p print ' 27P =', 27 * p
# print("gamma:", gamma_)
# print("m:", m_)
# print("f(x) =", ((x - gamma_)**2 + gamma_ + m_).expand())
# print("f^3(x) = p1(x)*p2(x)")
# p1, p2 = factor(gamma_, m_, d_)
# print("p1(x) =", p1)
# print("p2(x) =", p2)
# print()
# P = P - P0
m_ = -Rational(7, 4)
cs = [16 * m_**2 + 16 * m_, 0, 8 * m_, 0, 2]
alpha_ = 1
coeffs, xtrans, ytrans = transform(*cs, alpha_)
gx, gy = Rational(53, 81), Rational(289, 81)
C = EllipticCurve(*coeffs)
P0 = Point(0, 0, 1, C)
P = P0
while True:
d_ = xtrans.subs(x, P.x).subs(y, P.y)
for gamma_ in gammas_at(m_, d_):
if check_newly(gamma_, m_):
print("gamma:", gamma_)
print("m:", m_)
print("f(x) =", ((x - gamma_)**2 + gamma_ + m_).expand())
print("f^3(x) = p1(x)*p2(x)")
p1, p2 = factor(gamma_, m_, d_)
print("p1(x) =", p1)
print("p2(x) =", p2)
print()
P = P - P0
def aCurve(x, y, b, n):
c = (pow(y, 2, n) - pow(x, 3, n) - b * x) % n
return EllipticCurve(b, c, n)
plt.contour(x.ravel(), y.ravel(),
pow(y, 2) - pow(x, 3) - x * ec.a - ec.b, [0])
plt.grid()
def draw_point(P):
plt.plot([P.x], [P.y], marker='o', color='r')
def draw_sum(P, Q):
R = P + Q
plt.plot([P.x, Q.x], [P.y, Q.y], marker='o', color='r')
if isinstance(R, O):
pass
else:
plt.plot([R.x], [R.y], marker='o', color='r')
if __name__ == '__main__':
ec = EllipticCurve(a=frac(-2), b=frac(4))
p = Point(ec, frac(3), frac(5))
q = Point(ec, frac(-2), frac(0))
print p + q
print q + p
print q + q
print 10 * p
draw(ec)
draw_sum(p, q)
draw_sum(q, q)
plt.show()
from ec import EllipticCurve
p = 593899
e = EllipticCurve(7, 11, p)
for i in range(10):
x = 123450 + i
r = (x**3 + 7 * x + 11) % p
y = pow(r, (p + 1) / 4, p)
if y**2 % p == r:
print e(x, y)