def testLagrange(n):
"""Tests for each element x of Z*_n if x^phi(n) is 1"""
order = numbthy.eulerphi(n)
result = True
for i in range(1,n):
inverse = (i**order) % n
if inverse != 1:
print('Test failed for ' + str(i) + ': ' + str(inverse))
result = False
return result
def root(a, e, n):
"""Efficiently find the modular root: find x where x^e = a mod n"""
d = multiplicativeInverse(e, numbthy.eulerphi(n))
return (a ** d) % n
if (len(sys.argv) != 5):
print "Usage: {0} p q e m".format(sys.argv[0])
sys.exit(1)
(p,q,e,m) = sys.argv[1:]
#convert to int
p = int(p)
q = int(q)
e = int(e)
m = int(m)
n = p * q
#compute d using extended euclidean algorithm
phi = numbthy.eulerphi(n)
results = []
results = euclid(e,phi)
d = results[1]
if (d < 0):
d = d + phi
print "Plaintext input: {0}".format(m)
#encryption of plaintext m into C
C = m**e % n
print "Encryption Result:{0}".format(C)
#decryption of ciphertext C back into M
M = C**d % n
from numbthy import eulerphi
def are_permutations(n1, n2):
return sorted(str(n1)) == sorted(str(n2))
limit = 10000000
ratio = 100
winning_n = 0
for n in xrange(2, limit):
phi = eulerphi(n)
if are_permutations(n, phi) and float(n) / phi < ratio:
print n, phi
winning_n = n
ratio = float(n) / phi
print winning_n, ratio
# print sorted(str(54321))
import numbthy
max_ratio = 0
max_n = 0
limit = 1000000
for x in range(1, limit):
ratio = float(x) / numbthy.eulerphi(x)
if ratio > max_ratio:
print x, ratio
max_ratio = ratio
max_n = x
print max_ratio, max_n