def minus(N,n):
subList = []
for v in N:
if v != n:
subList.append(v)
return subList
def crt(C, N):
Sum = 0
NT = product(N)
for c,n in zip(C,N):
Sum += (c * product(minus(N,n)) * (eea(product(minus(N,n)),n) % n))
# for c,n in zip(C,N):
# if Sum % n != c:
# print "Error CRT"
# print Sum % n, c, n
# exit()
return Sum % NT
P = [11, 17, 41, 53, 27, 47, 31, 37]
m = 55
N = [P[0] * P[3], P[1] * P[4], P[2] * P[5]]
pN = [(P[0] -1) * (P[3] - 1), (P[1] -1) * (P[4] - 1), (P[2] -1) * (P[5] - 1)]
E = [3, 3, 3]
for e,n in zip(E,pN):
print gcd(e,n)
C = [(m ** e) % n for e,n in zip(E,N)]
result = crt(C,N)
print result ** (1/3.0)
Created on Jul 7, 2015
@author: mewolot
'''
from ModMath import eea, gcd
import math
plaintext = 120
p1 = 13
q1 = 23
n1 = p1 * q1
et1 = (p1-1) * (q1-1)
e1 = 7
#GCD must be 1 to work
if gcd(e1,et1) == 1:
print "Good e"
else:
print "Bad e"
d1 = eea(e1,et1) % et1
pub1 = e1,n1
priv1 = d1,n1
c1 = plaintext ** e1 % n1
print c1, n1, d1
p2 = 17
q2 = 11
n2 = p2 * q2
et2 = (p2-1) * (q2-1)
e2 = 7
Created on Jul 7, 2015
@author: mewolot
'''
from ModMath import eea, gcd
import math
plaintext = 120
p1 = 13
q1 = 23
n1 = p1 * q1
et1 = (p1 - 1) * (q1 - 1)
e1 = 7
#GCD must be 1 to work
if gcd(e1, et1) == 1:
print "Good e"
else:
print "Bad e"
d1 = eea(e1, et1) % et1
pub1 = e1, n1
priv1 = d1, n1
c1 = plaintext**e1 % n1
print c1, n1, d1
p2 = 17
q2 = 11
n2 = p2 * q2
et2 = (p2 - 1) * (q2 - 1)
e2 = 7
#GCD must be 1 to work
''' import gensafeprime as prime from ModMath import eea, gcd # p = 7919 # q = 6271 # n = p * q # et = (p-1) * (q-1) # e = 97 # #GCD must be 1 to work # print gcd(e,et) # d = eea(e,et) % et # pub = e,n # priv = d,n # # plaintext = 1337808 # c = plaintext ** e % n # m = c ** d % n # print plaintext, c, plaintext == m # print # print c,n,d # print c ** d % n # print p = 17 q = 11 n = p * q et = (p - 1) * (q - 1) e = 7 print gcd(e, et) print eea(e, et) % et
for v in N:
if v != n:
subList.append(v)
return subList
def crt(C, N):
Sum = 0
NT = product(N)
for c, n in zip(C, N):
Sum += (c * product(minus(N, n)) * (eea(product(minus(N, n)), n) % n))
# for c,n in zip(C,N):
# if Sum % n != c:
# print "Error CRT"
# print Sum % n, c, n
# exit()
return Sum % NT
P = [11, 17, 41, 53, 27, 47, 31, 37]
m = 55
N = [P[0] * P[3], P[1] * P[4], P[2] * P[5]]
pN = [(P[0] - 1) * (P[3] - 1), (P[1] - 1) * (P[4] - 1),
(P[2] - 1) * (P[5] - 1)]
E = [3, 3, 3]
for e, n in zip(E, pN):
print gcd(e, n)
C = [(m**e) % n for e, n in zip(E, N)]
result = crt(C, N)
print result**(1 / 3.0)
''' import gensafeprime as prime from ModMath import eea,gcd # p = 7919 # q = 6271 # n = p * q # et = (p-1) * (q-1) # e = 97 # #GCD must be 1 to work # print gcd(e,et) # d = eea(e,et) % et # pub = e,n # priv = d,n # # plaintext = 1337808 # c = plaintext ** e % n # m = c ** d % n # print plaintext, c, plaintext == m # print # print c,n,d # print c ** d % n # print p = 17 q = 11 n = p * q et = (p-1) * (q-1) e = 7 print gcd(e,et) print eea(e,et) % et
