def gen_dsa_params():
# FIPS L,N (1024,160), (2048,224), (2048,256), (3072,256)
# choose L, multiple of 64 between 512-1024, 2048, 3072
l = 1024
# n must be less than or equal to length of hash
n = SHA1_BIT_LENGTH
# choose n bit prime q
q = gen_seq_prime(start=pow(2, n) + pow(2, random.randint(8, 16)))
# choose l bit prime p such that p-1 is multiple of q
i = pow(2, l) + pow(2, random.randint(8, 16))
while True:
p = q * i
if is_prime(p + 1):
break
i += 1
p += 1
assert (is_prime(p))
assert ((p - 1) % q == 0)
# chose smallest int g such that g^q = 1 mod p
h = 1
x = (p - 1) / q
while h < p - 1:
g = modexp(h, x, p)
h += 1
if g == 1:
continue
elif modexp(g, q, p) != 1:
continue
else:
break
return (p, q, g)
def miller_rabin_test(n):
# if its even, why bother?
if n % 2 == 0:
return False
if n in [2, 3, 5, 7, 11, 13, 17]:
return True
# n - 1 = 2^s * d
s = 0
d = n - 1
while d % 2 == 0:
d >>= 1
s += 1
# logging.debug("n: {n}".format(n=n))
# logging.debug("d: {d}".format(d=d))
# logging.debug("s: {s}".format(s=s))
a = random.randrange(2, n - 2)
x = modexp(a, d, n)
# needs to be +1, or -1 for first gen
if x in [1, n - 1]:
return True
for i in xrange(s):
x = modexp(x, 2, n)
if x == 1:
return False
# needs to be -1 for rest of tests
elif x == n - 1:
return True
return False
def dsa_verify(pkey, sig, msg):
p, q, g, key = pkey
r, s = sig
if r < 0 or r > q:
return False
if s < 0 or s > q:
return False
w = inverse_modulo(s, q)
h = int(hashlib.sha1(msg).hexdigest(), 16)
u1 = (h * w) % q
u2 = (r * w) % q
# (A*B) Mod C == (A Mod C * B Mod C ) Mod C
part1 = modexp(g, u1, p)
part2 = modexp(key, u2, p)
v = ((part1 * part2) % p) % q
logging.debug("v: {}".format(v))
logging.debug("r: {}".format(r))
return v == r
def fermat_test(n):
# if its even, why bother?
if n <= 3 or n % 2 == 0:
return False
a = random.randint(2, n - 2)
r = modexp(a, n - 1, n)
if r != 1:
return False
return True
def dsa_sign(pkey, msg, fixedk=0):
p, q, g, key = pkey
r = 0
k = 0
s = 0
while s == 0:
if fixedk:
k = fixedk
r = modexp(g, fixedk, p) % q
else:
while r == 0:
k = random.randint(1, q)
r = modexp(g, k, p) % q
h = hashlib.sha1(msg).digest()
h = str2int16(h)
np1 = inverse_modulo(k, q)
np2 = (h + r * key) % q
s = (np1 * np2) % q
return (r, s, k)
def dsa_sign_insecure(pkey, msg):
p, q, g, key = pkey
r = 0
k = 0
s = 0
while s == 0:
while r == 0:
k = random.randint(1, pow(2, 16))
r = modexp(g, k, p) % q
h = hashlib.sha1(msg).digest()
h = str2int16(h)
np1 = inverse_modulo(k, q)
np2 = (h + r * key) % q
s = (np1 * np2) % q
return (r, s, k)
def gen_user_keys(p, q, g):
x = random.randint(0, q)
y = modexp(g, x, p)
priv_key = (p, q, g, x)
pub_key = (p, q, g, y)
return [pub_key, priv_key]
def simple_rsa(m, keypair):
k, n = keypair
return modexp(m, k, n)