class ecprng:
# Curve P-256; source: https://safecurves.cr.yp.to/
p = 2**256 - 2**224 + 2**192 + 2**96 - 1
a = p - 3
b = 41058363725152142129326129780047268409114441015993725554835256314039467401291
ec = ecc.CurveFp(p, a, b)
_Px = 115113149114637566422228202471255745041343462839792246702200996638778690567225
_Py = 88701990415124583444630570378020746694390711248186320283617457322869078545663
Point_P = ecc.Point(ec, _Px, _Py)
_Qx = 75498749949015782244392151836890161743686522667385613237212787867797557116642
_Qy = 19586975827802643945708711597046872561784179836880328844627665993398229124361
Point_Q = ecc.Point(ec, _Qx, _Qy)
def __init__(self, seed):
self.seed = seed
if self.seed:
assert len(long_to_bytes(self.seed)) == 32
def update_seed(self, intermediate_state_S_1):
self.seed = (intermediate_state_S_1 * ecprng.Point_P).x()
assert len(long_to_bytes(self.seed)) == 32
def ec_generate(self):
intermediate_state_S_1 = (self.seed * ecprng.Point_P).x()
self.update_seed(intermediate_state_S_1)
r_1 = long_to_bytes(
(intermediate_state_S_1 * ecprng.Point_Q).x())[-30:]
r_2 = long_to_bytes((self.seed * ecprng.Point_Q).x())[-30:][:2]
assert len(r_1 + r_2) == 32
return bytes_to_long(r_1 + r_2)
def baby_step_giant_step(curve, G, H, order):
m = int(math.ceil(gmpy2.sqrt(order)))
L = {}
# Baby steps
for j in range(0, m):
P_tmp = curve.mul(j, G)
L[str(P_tmp)] = j
mG = curve.mul(m, G)
# Giant steps
for i in range(0, m):
P_tmp = curve.mul(i, mG)
if not P_tmp.isInf():
P_tmp = ecc.Point(P_tmp.x, (-P_tmp.y) % curve.p)
P = curve.add(H, P_tmp)
index = str(P)
if index in L:
return (L[index] + i * m) % curve.p
return None
def bits_to_point(p):
(x_size, ) = struct.unpack('!H', p[:2])
if x_size == 0:
return ecc.PointInf()
x = bits_to_int(p[2:x_size + 2])
y = bits_to_int(p[x_size + 4:])
return ecc.Point(x, y)
def dechiffrement_Alice(curve):
'''
Alice reçoit C1 et C2
elle calcule daC1 grâce à sa clé privée
elle calcule l'inverse de daC1
elle déchiffre C2 qui correspond à M
'''
C1, C2 = chiffrement_Bob(curve)
f = open("cle.txt", "r")
cle = int(f.read())
daC1 = ecc.Curve.mul(curve, cle, C1)
daC1_inv = ecc.Point(daC1.x, -daC1.y)
M = ecc.Curve.add(curve, C2, daC1_inv)
return M
def find_next_e(e):
r = long_to_bytes(e)[:-2]
for i in trange(133, 140):
for j in range(256):
x = bytes_to_long(chr(i) + chr(j) + r)
y = find_point(ec, x)
if test_Point(x, y):
R = ecc.Point(ec, x, y)
r_2 = long_to_bytes(
(((R * inverse(d, order)).x()) * Point_Q).x())[-30:][:2]
if long_to_bytes(e)[-2:] == r_2:
print "finally"
return R
return R
blue = '\033[34m'
# New urandom seed for each session (Not really relevant for the challenge)
prng_obj = prng(16793527392756720769,
2358102439659339126076356431940385122127543421625845446663,
False)
p = 2**256 - 2**224 + 2**192 + 2**96 - 1
a = p - 3
b = 41058363725152142129326129780047268409114441015993725554835256314039467401291
ec = ecc.CurveFp(p, a, b)
_Px = 53881495764268889303293517690095107010093794097958309592680107528631746121613
_Py = 69534606358473748292927094386662082099432383517498778127513290350658945146669
Point_P = ecc.Point(ec, _Px, _Py)
iteration = True
counter = 0
while iteration == True and counter < 10:
print colors.blue + "Choose one between authentication protocols listed below:" + colors.reset
print colors.orange + "[1] Asynchronous SchnorrID" + colors.reset
print colors.orange + "[2] Synchronous SchnorrID" + colors.reset
choice = int(raw_input("Enter your choice: "))
print ""
if choice == 1:
print "Here are the coordinates of the base point P: ", _Px, _Py
_Qx, _Qy = map(
int,
return R
return R
st = lambda x: str(x).strip('L')
if __name__ == "__main__":
p = 2**256 - 2**224 + 2**192 + 2**96 - 1
a = p - 3
b = 41058363725152142129326129780047268409114441015993725554835256314039467401291
ec = ecc.CurveFp(p, a, b)
_Px = 115113149114637566422228202471255745041343462839792246702200996638778690567225
_Py = 88701990415124583444630570378020746694390711248186320283617457322869078545663
Point_P = ecc.Point(ec, _Px, _Py)
_Qx = 75498749949015782244392151836890161743686522667385613237212787867797557116642
_Qy = 19586975827802643945708711597046872561784179836880328844627665993398229124361
Point_Q = ecc.Point(ec, _Qx, _Qy)
d = 1735
x = 53881495764268889303293517690095107010093794097958309592680107528631746121613
y = 69534606358473748292927094386662082099432383517498778127513290350658945146669
P = ecc.Point(ec, x, y)
Q = 123 * P
order = 115792089210356248762697446949407573529996955224135760342422259061068512044369
#io = process('./encrypt.py')
io = remote('34.74.30.191', 3333)
(gcd, x0, x1) = xgcd(ni, tmp)
x += x_prime * x1 * tmp
return x % N
# (A, B, N)
A = 0
B = 0
N = 0
X = 0
Y = 0
curve = ecc.Curve(A, B, N)
G = ecc.Point(X, Y)
sent = [
0x00, 0x30, 0x00, 0x16, 0x0d, 0x6c, 0x24, 0xb0, 0x5a, 0xf7, 0xff, 0x4f,
0xa6, 0x28, 0xeb, 0xce, 0xfd, 0x43, 0xdd, 0xad, 0x1a, 0x57, 0xac, 0xb9,
0xa4, 0x65, 0x00, 0x16, 0x0a, 0x00, 0x63, 0x5f, 0x98, 0x88, 0x1c, 0x47,
0x07, 0x50, 0x48, 0x3e, 0xa0, 0x59, 0x77, 0xc1, 0x93, 0x28, 0x9a, 0xeb,
0x50, 0x64
]
H = bits_to_point("".join(map(chr, sent)).encode())
x = pohlig_hellman(curve, G, H)
print("x = %s" % x)
import os.path
import sys
import ecc
sys.path.append(os.path.join(os.path.dirname(__file__), '..'))
''' Création de la courbe elliptiques '''
A = 109454571331697278617670725030735128145969349647868738157201323556196022393856
B = 107744541122042688792155207242782455150382764043089114141096634497567301547839
''' Ordre du point P '''
l = 109454571331697278617670725030735128146004546811402412653072203207726079563233
''' Ordre de la courbe '''
N = 109454571331697278617670725030735128145969349647868738157201323556196022393859
'''n pour la multiplication '''
n = 2
''' Point de la courbe elliptique '''
P = ecc.Point(
82638672503301278923015998535776227331280144783487139112686874194432446389503,
43992510890276411535679659957604584722077886330284298232193264058442323471611
)
Q = ecc.Point(
100597391921786027039183722380481804805320476080319934670061678997404767442782,
80123073214026054915454326239165515159448240266403681526048086449062769463365
)
'''Point M du message'''
M = ecc.Point(
100597391921786027039183722380481804805320476080319934670061678997404767442782,
80123073214026054915454326239165515159448240266403681526048086449062769463365
)