def primality_test(n,
certainty=50000
): #returns true if n is prime, if composite returns false
if not isinstance(n, int):
raise ValueError("n cannot be anything but an int you gave: " +
str(type(n)))
elif n < 1:
raise ValueError("n cannot be less than 0")
elif n == 1:
return True
elif n % 2 == 0:
return False
else:
for i in range(0, certainty):
a = random.randint(2, n - 1)
if eea(a, n).get("gcd") != 1: return False
k = 1
q = (n - 1) / 2
while q % 2 == 0:
k = k + 1
q = q / 2
a = fast_power(a, q, n)
if a == 1: continue
while k > 1:
if a == -1: break
a = (a * a) % n
k = k - 1
if a == -1: continue
return True
def set_e(self, e):
if self.q is None or self.p is None:
raise ValueError("(self.) p and q cannot be None")
if eea(e, (self.p-1)*(self.q-1)).get("gcd") == 1:
self.e = e
else:
raise ValueError("Invalid e value, gcd of input e and (p-1)*(q-1) must be 1")
def pollard(N):
a = 2
p = None
for j in range(2, 1000):
a = fast_power(a, j, N)
d = eea(a-1, N).get("gcd")
if d > 1 and d < N:
p = d
break
return p
def test_eea_2(self):
x = 63451367846845
y = 52352467468873425
self.assertEqual(eea(x, y), {
"gcd": 5,
"a": 4310308599955094,
"x": x,
"b": -5224108618601,
"y": y
})
def gen_e(self, p = None, q = None):
if (p is not None):
self.p = p
if (q is not None):
self.q = q
e = 0
while (e != 0 and eea(e, (self.p-1)*(self.q-1)).get("gcd") != 1):
e = random.randint(3, (p-1)*(q-1))
self.e = e
return e
def decrypt(self, c, p = None, q = None, e = None):
if q is not None and p is not None:
self.q = q
self.p = p
self. N = self.p * self.q
if e is not None:
self.e = e
self.c = c
if None in [self.N, self.p, self.q, self.e, self.c]:
raise ValueError("c, e, p, q, or N is None")
g = eea(self.p - 1, self.q-1).get("gcd")
self.d = int(mod_inv(self.e % ((self.p-1)*(self.q-1)/g), (self.p-1)*(self.q-1)/g))
self.m = fast_power(self.c, self.d, self.N)
return self.m
def mod_inv(a, m): # Where a*b = 1 mod(m)
inv = None
if m <= 0: # Error and Base Case Handling
raise ValueError("m cannot be 0 or less")
elif a > m:
raise ValueError("a cannot be larger than m")
elif a == 0:
return 0
else:
eea_res = eea(a, m)
inv = eea_res.get("a")
if eea_res["gcd"] != 1:
if eea_res["gcd"] != m:
raise ValueError("a divides m, there is no modular inverse for a:" + str(a)+" with modulo m: "+str(m))
inv = (inv % m)
return inv
def test_eea_1(self):
print("\n\nRunning test for src module: eea")
x = 3
y = 21
self.assertEqual(eea(x, y), {"gcd": 3, "a": 1, "x": x, "b": 0, "y": y})