def is_valid_point(self, x, y):
x = mfi(x, self.mod)
y = mfi(y, self.mod)
if x == 0 and y == 1:
return True
l = y**2
r = x**3 + x*self.a4 + self.a6
return l == r
def get_point(self, n):
x = mfi(n, self.mod)
while x != 0:
t = (x ** 3) + (self.a4 * x) + self.a6
if t == 0:
return [(x, mfi(0, self.mod))]
elif self.is_quadratic_residue(t):
vals = t.modsqrt()
points = []
for k in vals:
points.append((x,k))
return points
x += 1
return []
def double(self, x1, y1):
x1 = mfi(x1, self.mod)
y1 = mfi(y1, self.mod)
if (y1 == 1 and x1 == 0):
return 0,1
if (y1 + y1) == 0:
return 0,1
mi = self.modinv(y1 * 2)
a4 = mfi(self.a4, self.mod)
ld = (x1*x1*3 + a4) * mi
x3 = ld * ld - x1 - x1
y3 = ld * (x1 - x3) - y1
return x3, y3
def get_points_list(self):
points = [(0,1)]
x = mfi(1, self.mod)
while x != 0:
p = self.get_point(x)
points += p
x = p[0][0] + 1
return points
def next_b(self, b, xi):
x = xi[0]
b = mfi(b, self.order)
if x >= 0 and x <= self.curve.mod / 3:
return b + 1
elif x > self.curve.mod / 3 and x <= (self.curve.mod * 2) / 3:
return b * 2
else:
return b
def next_a(self, a, xi):
x = xi[0]
a = mfi(a, self.order)
if x >= 0 and x <= self.curve.mod / 3:
return a
elif x > self.curve.mod / 3 and x <= (self.curve.mod * 2) / 3:
return a * 2
else:
return a + 1
def solve(self, p, q):
global itercount
next_x = self.next_x
next_a = self.next_a
next_b = self.next_b
global tests
tests += 1
xi = (0, 1)
a = mfi(0, self.order)
b = mfi(0, self.order)
x2i = (0, 1)
a2 = mfi(0, self.order)
b2 = mfi(0, self.order)
while True:
old_xi = xi
xi = next_x(xi, p, q)
a = next_a(a, old_xi)
b = next_b(b, old_xi)
old_x2i = x2i
x2i = next_x(next_x(x2i, p, q), p, q)
a2 = next_a(next_a(a2, old_x2i), next_x(old_x2i, p, q))
b2 = next_b(next_b(b2, old_x2i), next_x(old_x2i, p, q))
itercount += 1
if xi == x2i:
print a, b, a2, b2
r = mfi(b - b2, self.order).modinv()
p = mfi(a2 - a, self.order)
print "iterations", itercount
return p * r
def add(self, x1, y1, x2, y2):
ld = 0
x1 = mfi(x1, self.mod)
y1 = mfi(y1, self.mod)
x2 = mfi(x2, self.mod)
y2 = mfi(y2, self.mod)
if (y1 == 1 and x1 == 0):
return x2, y2
elif (x2 == 0 and y2 == 1):
return x1,y1
if x1 == x2:
if y1 == y2:
return self.double(x1,y1)
else:
return (0,1)
else:
ld = (y2 - y1) * (x2-x1).modinv()
x3 = ld * ld - x2 - x1
y3 = ld * (x1 - x3) - y1
return x3, y3
def __init__(self, a4, a6, mod):
self.a4 = mfi(a4, mod)
self.a6 = mfi(a6, mod)
self.mod = mod
def modinv(self, n):
n = mfi(n, self.mod)
return n.modinv()
def negate(self, x,y):
x = mfi(x, self.mod)
y = mfi(y, self.mod)
return x, y + x