-
Notifications
You must be signed in to change notification settings - Fork 4
/
rsa.py
98 lines (77 loc) · 2.13 KB
/
rsa.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
import random
'''
Euclid's algorithm for determining the greatest common divisor
Use iteration to make it faster for larger integers
'''
def gcd(a, b):
while b != 0:
a, b = b, a % b
return a
'''
Euclid's extended algorithm for finding the multiplicative inverse of two numbers
'''
def multiplicative_inverse(a, m) :
m0 = m
y = 0
x = 1
if (m == 1) :
return 0
while (a > 1) :
# q is quotient
q = a // m
t = m
# m is remainder now, process
# same as Euclid's algo
m = a % m
a = t
t = y
# Update x and y
y = x - q * y
x = t
# Make x positive
if (x < 0) :
x = x + m0
return x
'''
Tests to see if a number is prime.
'''
def is_prime(num):
if num == 2:
return True
if num < 2 or num % 2 == 0:
return False
for n in range(3, int(num**0.5)+2, 2):
if num % n == 0:
return False
return True
def generate_keypair(p, q):
if not (is_prime(p) and is_prime(q)):
raise ValueError('Both numbers must be prime.')
elif p == q:
raise ValueError('p and q cannot be equal')
#n = pq
n = p * q
#Phi is the totient of n
phi = (p-1) * (q-1)
#Choose an integer e such that e and phi(n) are coprime
e = random.randrange(1, phi)
#Use Euclid's Algorithm to verify that e and phi(n) are comprime
g = gcd(e, phi)
while g != 1:
e = random.randrange(1, phi)
g = gcd(e, phi)
#Use Extended Euclid's Algorithm to generate the private key
d = multiplicative_inverse(e, phi)
#Return public and private keypair
#Public key is (e, n) and private key is (d, n)
return ((e, n), (d, n))
def encrypt(pk, num):
#Unpack the key into it's components
key, n = pk
#Convert each letter in the plaintext to numbers based on the character using a^b mod m
return (num ** key) % n
def decrypt(pk, num):
#Unpack the key into its components
key, n = pk
#Generate the plaintext based on the ciphertext and key using a^b mod m
return (num ** key) % n