def main():
p, q = find_p_q() #1
print 'Moving on..'
n = p * q # 2
et = euler(p, q) # 3
e = (2**16) + 1 # 4
d = mulinv(e, et) #5
#6 NA
"""
Test values
"""
m1 = 8049
encm1 = rypto.mod_exp(m1, e, n)
decm1 = rypto.mod_exp(encm1, d, n)
print 'Checking m1 is decrypted correctly'
print m1, decm1, m1 == decm1
m2 = 'Hi this is short'
m2encoded = int(m2.encode("hex"), 16)
encm2 = rypto.mod_exp(m2encoded, e, n)
decm2 = rypto.mod_exp(encm2, d, n)
hexad = rypto.standard(hex(decm2))
decm2b = hexad[:-1].decode("hex")
print 'Checking m2 is decrypted correctly'
print m2, decm2b, m2 == decm2b
def main():
N = 402394248802762560784459411647796431108620322919897426002417858465984510150839043308712123310510922610690378085519407742502585978563438101321191019034005392771936629869360205383247721026151449660543966528254014636648532640397857580791648563954248342700568953634713286153354659774351731627683020456167612375777
e1 = 3
e2 = 0x10001
c1 = 4020137574131575546540268502595841326627069047574502831387774931737219358054228401772587980633053000
c2 = 170356929377044754324767086491413709789303946387160918939626824506821140429868670769571821346366209258416985269309515948776691067548265629489478628756185802183547222688698309731374342109385922509501909728895585636684978295199882599818258590851085977232207148101448845575681189389906429149193460620083999406237
g, x, y = rypto.egcd(e1, e2) #Euclidean algorightm
i = rypto.mulinv(c2, N) #multiplicative inverse of C2 because y is -1
test = (rypto.mod_exp(c1, x, N) *
rypto.mod_exp(i, -y, N)) % N #plain = (c1^a) * (i^-b) %N
answer = rypto.standard(hex(test)).decode("hex")
print answer
def diffie(p, g):
a = int((os.urandom(256).encode("hex")), 16) % p
b = int((os.urandom(256).encode("hex")), 16) % p
A = rypto.mod_exp(g, a, p)
B = rypto.mod_exp(g, b, p)
s1 = rypto.mod_exp(A, b, p)
s2 = rypto.mod_exp(B, a, p)
if s1 == s2:
print 'Keys are the same'
return s1
else:
print 'Key exchange failed'
exit()
def main():
session = setup() #Setup mutual variables
a = int((os.urandom(256).encode("hex")),16) % session.n #Secret value A (For client)
A = rypto.mod_exp(session.g,a,session.n)
i = session.i #username (will soon send)
#client_recv = None
"""
Server stores the password using the steps:
1. Generate salt as a random integer
2. Generate string xH = SHA256(salt|password)
3. Convert xH to integer x
4. Generate v = g^x mod N
5. Save everything but x, xH
"""
session.store() #Simulating server storing values to db
"""
Client -> Server:
"""
#session.client_send(i, A) #Simulating sending username and public A for auth
session.client_send(i, 0) #Hacker sends 1
"""
Server -> Client:
"""
user_recv = session.response() #Simulating receiving salt and public B from server
client_recv = {'s': user_recv[0], 'B':user_recv[1] } #Storing previous line into something easier to understand
"""
Server, Client:
"""
session.calc_u() #Server calculating u
"""
Server:
1. Generate S = (A*v^u)^b mod N
2. Generate K = SHA256(S)
"""
session.generate_k()
"""
Validate
"""
print 'Hacker trying Key 0....'
hacker_k = rypto.sha256(str(0))
user_try = rypto.sha256(hacker_k+str((client_recv['s'])))
session.validate(user_try)
def main():
session = setup() #Setup mutual variables
a = int((os.urandom(256).encode("hex")),16) % session.n #Secret value A (For client)
A = rypto.mod_exp(session.g,a,session.n)
i = session.i #username (will soon send)
#client_recv = None
"""
Server stores the password using the steps:
1. Generate salt as a random integer
2. Generate string xH = SHA256(salt|password)
3. Convert xH to integer x
4. Generate v = g^x mod N
5. Save everything but x, xH
"""
session.store() #Simulating server storing values to db
"""
Client -> Server:
"""
session.client_send(i, A) #Simulating sending username and public A for auth
"""
Server -> Client:
"""
user_recv = session.response() #Simulating receiving salt and public B from server
client_recv = {'s': user_recv[0], 'B':user_recv[1] } #Storing previous line into something easier to understand
"""
Server, Client:
"""
uH = rypto.sha256(str(A) + str(client_recv['B']))#Client calculating u
client_u = int(uH,16) #Client calculating u
session.calc_u() #Server calculating u
"""
Client:
1. Generate string xH = SHA256(salt|password)
2. Convert xH to integer x
3. Generate S = (B-k*g^x)^(a+u*x) mod N
4. Generate K = SHA256(S)
"""
xH = rypto.sha256(str(client_recv['s'])+session.p)
client_x = int(xH,16)
client_S = rypto.mod_exp((client_recv['B']-session.k*(rypto.mod_exp(session.g,client_x,session.n))),(a+client_u*client_x),session.n)
client_K = rypto.sha256(str(client_S))
#print client_K
"""
Server:
1. Generate S = (A*v^u)^b mod N
2. Generate K = SHA256(S)
"""
session.generate_k()
#print session.server_K
"""
Validate
"""
user_try = rypto.sha256(client_K+str(client_recv['s']))
session.validate(user_try)