def generateKeys(security_level = 1):
prime_size, random_size = 0, 0
if security_level == 1: prime_size, random_size = 160, 864
elif security_level == 2: prime_size, random_size = 224, 1824
elif security_level == 3: prime_size, random_size = 256, 2816
else: return
q = number.getPrime(prime_size)
k = number.getRandomInteger(random_size)
p = k * q + 1
while utils.rm_primality(p) != True:
k = utils.gen_random(random_size)
p = k * q + 1
a = number.getRandomRange(0, p)
g = utils.mod_exp(a, (p - 1) / q, p)
while g == 1:
a = number.getRandomRange(0, p)
g = utils.mod_exp(a, (p - 1) / q, p)
x = number.getRandomRange(1, q - 2)
y = utils.mod_exp(g, x, p)
return p, q, g, x, y
def verifySignature(p, q, g, y, r, s, message):
if r <= 0 or r >= q or s <= 0 or s >= q:
print "Rejected!"
return
H = int(hexlify(CryptoBox.generateHash(message, 1)), 16)
w = utils.inverse(s, q)
u1 = (H * w) % q
u2 = (r * w) % q
v = ((utils.mod_exp(g, u1, p) * utils.mod_exp(y, u2, p)) % p) % q
return True if v == r else False
def verifySignature(p, q, g, y, r, s, message):
if r <= 0 or r >= q or s <= 0 or s >= q:
print "Rejected!"
return
H = int(hexlify(CryptoBox.generateHash(message, 1)), 16)
w = utils.inverse(s, q)
u1 = (H * w) % q
u2 = (r * w) % q
v = ((utils.mod_exp(g, u1, p) * utils.mod_exp(y, u2, p)) % p) % q
return True if v == r else False
def generateSignature(p, q, g, x, message):
H = int(hexlify(CryptoBox.generateHash(message, 1)), 16)
k = number.getRandomRange(1, q)
r = utils.mod_exp(g, k, p) % q
k_inv = utils.inverse(k, q)
s = (k_inv * (H + x * r)) % q
if (r == 0 or s == 0):
# since it is very unlikely to make a recursive call, function will terminate eventually
return generateSignature(p, q, g, x, message)
return r, s
def generateSignature(p, q, g, x, message):
H = int(hexlify(CryptoBox.generateHash(message, 1)), 16)
k = number.getRandomRange(1, q)
r = utils.mod_exp(g, k, p) % q
k_inv = utils.inverse(k, q)
s = (k_inv * (H + x * r)) % q
if (r == 0 or s == 0):
# since it is very unlikely to make a recursive call, function will terminate eventually
return generateSignature(p, q, g, x, message)
return r, s
def RSAEP(N, e, m):
if m < 0 or m > N - 1:
print "Message representative out of range!"
return -1
return utils.mod_exp(m, e, N)
def RSAVP1(N, e, s):
if s < 0 or s > N - 1:
print "Signature representative out of range"
return
return utils.mod_exp(s, e, N)
def RSASP1(N, d, m):
if m < 0 or m > N - 1:
print "Message representative out of range"
return
return utils.mod_exp(m, d, N)
def RSADP(N, d, c):
if c < 0 or c > N - 1:
print "Ciphertext representative out of range"
return
return utils.mod_exp(c, d, N)
def RSAEP(N, e, m):
if m < 0 or m > N - 1:
print "Message representative out of range!"
return -1
return utils.mod_exp(m, e, N)
def RSAVP1(N, e, s):
if s < 0 or s > N - 1:
print "Signature representative out of range"
return
return utils.mod_exp(s, e, N)
def RSASP1(N, d, m):
if m < 0 or m > N - 1:
print "Message representative out of range"
return
return utils.mod_exp(m, d, N)
def RSADP(N, d, c):
if c < 0 or c > N - 1:
print "Ciphertext representative out of range"
return
return utils.mod_exp(c, d, N)
def decrypt(p, q, x, r, t):
k = utils.inverse(utils.mod_exp(r, x, p), p)
message = (t * k) % p
return message
def encrypt(p, q, g, y, message):
k = number.getRandomRange(1, p - 2)
r = utils.mod_exp(g, k, p)
t = (utils.mod_exp(y, k, p) * message) % p
return r, t
