def rabin_miller(n, target=128):
"""returns True if prob(`n` is composite) <= 2**(-`target`)"""
###############
## Start your code here
def calculate_t(n):
t = 0
n = n-1
while n%2 == 0:
n = n/2
t = t+1
return t
if n%2 == 0:
return False
t = calculate_t(n)
s = (n-1)/2**t
tried = set()
n_tests = target / 2 + 1
for i in range(n_tests):
while True:
a = radrange(1,n)
if a not in tried:
tried.add(a)
break
if mod_exp(a,s,n) == 1:
continue
found = False
for j in range(0,t):
if mod_exp(a,2**j*s,n) == n-1:
found = True
break
if not found:
return False
return True
def rabin_miller(n, target=128):
"""
returns True if prob(`n` is prime) <= 2**(-`target`)
"""
###############
## Start your code here
def calculate_t(n):
n = n - 1
t = 0
while n % 2 == 0:
n = n / 2
t += 1
return t
if n % 2 == 0:
return False
t = calculate_t(n)
s = (n - 1) / (2 ** t)
n_tests = target / 2 # 2 ** ((-1/2) * n_test) = 2 ** (-target)
tried = set()
if n_tests > n:
raise Exception("n is too small")
for i in range(n_tests):
while True:
a = randrange(1, n)
if a not in tried:
break
tried.add(a)
# there are two tests in Rabin-Miller
# here is the first one
if mod_exp(a, s, n) == 1:
continue
# and here is the second
found = False
for j in range(0, t):
if mod_exp(a, 2**j*s, n) == (n - 1):
found = True
break
if not found:
# we failed them both, lets leave
return False
# if we made it here, all the tests have passed
return True
