run this code python2
# -*- coding: utf-8 -*-
# run python2
# Elliptic curve point operations (Python 2.7)
def OnCurve(x,y): # Check if the point is on the curve
A = (y*y)%P
B = (x*x*x)%P
C = False
if A == (B + 7):
C = True
return C
def legendre_symbol(a,p):
ls = pow(a, (p - 1) / 2, p)
return -1 if ls == p - 1 else ls
def modsqrt(a,p): # Square root A modulo P
if legendre_symbol(a, p) != 1:
return 0
elif a == 0:
return 0
elif p == 2:
return p
elif p % 4 == 3:
return pow(a, (p + 1) / 4, p)
s = p - 1
e = 0
while s % 2 == 0:
s /= 2
e += 1
n = 2
while legendre_symbol(n, p) != -1:
n += 1
x = pow(a, (s + 1) / 2, p)
b = pow(a, s, p)
g = pow(n, s, p)
r = e
while True:
t = b
m = 0
for m in xrange(r):
if t == 1:
break
t = pow(t, 2, p)
if m == 0:
return x
gs = pow(g, 2 ** (r - m - 1), p)
g = (gs * gs) % p
x = (x * gs) % p
b = (b * g) % p
r = m
def modinv(a,n): # Extended Euclidean Algorithm in elliptic curves
lm, hm = 1,0
low, high = a%n,n
while low > 1:
ratio = high/low
nm = hm - lm * ratio
new = high - low * ratio
hm = lm
high = low
lm = nm
low = new
return lm % n
def ECadd(xp,yp,xq,yq): # EC point addition
m = ((yq-yp) * modinv(xq-xp,P))%P
xr = (m*m-xp-xq)%P
yr = (m*(xp-xr)-yp)%P
return (xr,yr)
def ECdouble(xp,yp): # EC point doubling
LamNumer = 3*xp*xp+Acurve
LamDenom = 2*yp
Lam = (LamNumer * modinv(LamDenom,P)) % P
xr = (Lam*Lam-2*xp) % P
yr = (Lam*(xp-xr)-yp) % P
return (xr,yr)
def ECmul(xs,ys,Scalar): # EC point multiplication
if Scalar == 0 or Scalar >= N: raise Exception("Invalid Scalar/Private Key")
ScalarBin = str(bin(Scalar))[2:]
Qx,Qy=xs,ys
for i in range (1,len(ScalarBin)):
Qx,Qy = ECdouble(Qx,Qy)
if ScalarBin[i] == "1":
Qx,Qy = ECadd(Qx,Qy,xs,ys)
return (Qx,Qy)
def ECsub(xp,yp,xq,yq): # EC point subtraction
X = (((yp+yq)*modinv(xq-xp,P))**2-xp-xq)%P
A = (xp + X + xq)%P
B = modsqrt(A,P)
B1 = P - B
Y = yq - (xq - X) * B
X = X % P
Y = Y % P
if not OnCurve(X,Y):
Y = yq - (xq - X) * B1
Y = Y % P
return X,Y
def ECdiv(Qx,Qy,Scalar): # EC point division
A = (N-1)/Scalar
Px,Py = ECmul(Qx,Qy,A)
Py = P-Py
return Px,Py
P = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 - 1
N = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
Gx = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
Acurve = 0
ukx = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 # or your enter publickey x,y
uky = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
#you need add ,sub ,div
fadd = ECadd(ukx,uky,ukx,uky) # 1 + 1 =2
print ('fadd',hex(fadd[0]),hex(fadd[1]))
fsub = ECsub(fadd[0],fadd[1],Gx,Gy) # 2 -1 = 1
print ('fsub',hex(fsub[0]),hex(fsub[1]))
fdub = ECdouble(ukx,uky) # 1 * 2 = 2
print ('fdub',hex(fdub[0]),hex(fdub[1]))
fdiv = ECdiv(fdub[0],fdub[1],2) # 2 / 2 = 1
print ('fdiv',hex(fdiv[0]),hex(fdiv[1]))
output is:
X is incorrect Y output is correct
('fadd', '0xc8333020c4688a754bf3ad462f1e9f1fac80649a463ae4d4c1afd48d20fccffL', '
0xb7c52588d95c3b9aa25b0403f1eef75702e84bb7597aabe663b82f6f04ef2777L')
('fsub', '0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798L', '
0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L')
('fdub', '0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5L', '
0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52aL')
('fdiv', '0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798L', '
0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L')
my output X value incorrect print why? what is mistake this code
Y value is correct print
update please
need correct output:
fadd 1 + 1 = 2
fsub 2 - 1 = 1
fdub 1 * 2 = 2
fdiv 2 / 2 = 1
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