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def I(s):
val = 0
for i in range(len(s)):
digit = ord(s[len(s) - i - 1])
val <<= 8
val |= digit
return val
def Sn(i, length):
s = ''
while i != 0:
digit = i & 0xff
i >>= 8;
s += chr(digit)
return s
def egcd(a, b):
if a == 0:
return (b, 0, 1)
else:
g, y, x = egcd(b % a, a)
return (g, x - (b // a) * y, y)
def modinv(a, p):
a %= p
g, x, y = egcd(a, p)
if g != 1:
raise Exception('No inverse exists for %d mod %d' % (a, p))
else:
return x % p
def add(a, b, p):
if a == -1:
return b
if b == -1:
return a
x1, y1 = a
x2, y2 = b
x3 = ((x1*x2 - x1*y2 - x2*y1 + 2*y1*y2)*modinv(x1 + x2 - y1 - y2 - 1, p)) % p
y3 = ((y1*y2)*modinv(x1 + x2 - y1 - y2 - 1, p)) % p
return (x3, y3)
def double(a, p):
return add(a, a, p)
def mul(m, g, p):
r = -1
while m != 0:
if m & 1:
r = add(r, g, p)
m >>= 1
g = double(g, p)
return r
def encrypt(message, key):
return message ^ key
# Modulus
p = 606341371901192354470259703076328716992246317693812238045286463
# g is the generator point.
g = (160057538006753370699321703048317480466874572114764155861735009, 255466303302648575056527135374882065819706963269525464635673824)
# Alice's public key A:
A = (460868776123995205521652669050817772789692922946697572502806062, 263320455545743566732526866838203345604600592515673506653173727)
# Bob's public key B:
B = (270400597838364567126384881699673470955074338456296574231734133, 526337866156590745463188427547342121612334530789375115287956485)
if __name__ == "__main__":
# from secret_data import aliceSecret, bobSecret, flag
aliceSecret = 6621005115841589341021728146593578127178145692816888878
bobSecret = 3717310807101673722781843653766732925831732205102857032
assert A == mul(aliceSecret, g, p)
assert B == mul(bobSecret, g, p)
cipher = 137737300119926924583874978524079282469973134128061924568175107915062758827931077214500356470551826348226759580545095568667325
aliceMS = mul(aliceSecret, B, p)
bobMS = mul(bobSecret, A, p)
assert aliceMS == bobMS
masterSecret = aliceMS[0]*aliceMS[1]
length = 31 # len(flag)
encrypted_message = encrypt(cipher, masterSecret)
print "length = %d, encrypted_message = %d" % (length, encrypted_message)
print (Sn(encrypted_message, 31))
# length = 31, encrypted_message = 137737300119926924583874978524079282469973134128061924568175107915062758827931077214500356470551826348226759580545095568667325
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