├── README.md
└── main.py


/README.md:
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1 | # RSA-Implementation-in-Python
2 | This is a simple but slow implementation of the RSA Algorithm in Python.
3 | I made this for Studying purposes in my 2nd Semester.
4 | 


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/main.py:
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 1 | '''
 2 | Created on 07.09.2016
 3 | 
 4 | @author: Marius
 5 | '''
 6 | 
 7 | import random
 8 | max_PrimLength = 1000000000000
 9 | 
10 | '''
11 | calculates the modular inverse from e and phi
12 | '''
13 | def egcd(a, b):
14 |     if a == 0:
15 |         return (b, 0, 1)
16 |     else:
17 |         g, y, x = egcd(b % a, a)
18 |         return (g, x - (b // a) * y, y)
19 | 
20 | '''
21 | calculates the gcd of two ints
22 | '''
23 | def gcd(a, b):
24 |     while b != 0:
25 |         a, b = b, a % b
26 |     return a
27 | 
28 | '''
29 | checks if a number is a prime
30 | '''
31 | def is_prime(num):
32 |     if num == 2:
33 |         return True
34 |     if num < 2 or num % 2 == 0:
35 |         return False
36 |     for n in range(3, int(num**0.5)+2, 2):
37 |         if num % n == 0:
38 |             return False
39 |     return True
40 | 
41 | def generateRandomPrim():
42 |     while(1):
43 |         ranPrime = random.randint(0,max_PrimLength)
44 |         if is_prime(ranPrime):
45 |             return ranPrime
46 | 
47 | def generate_keyPairs():
48 |     p = generateRandomPrim()
49 |     q = generateRandomPrim()
50 |     
51 |     n = p*q
52 |     print("n ",n)
53 |     '''phi(n) = phi(p)*phi(q)'''
54 |     phi = (p-1) * (q-1) 
55 |     print("phi ",phi)
56 |     
57 |     '''choose e coprime to n and 1 > e > phi'''    
58 |     e = random.randint(1, phi)
59 |     g = gcd(e,phi)
60 |     while g != 1:
61 |         e = random.randint(1, phi)
62 |         g = gcd(e, phi)
63 |         
64 |     print("e=",e," ","phi=",phi)
65 |     '''d[1] = modular inverse of e and phi'''
66 |     d = egcd(e, phi)[1]
67 |     
68 |     '''make sure d is positive'''
69 |     d = d % phi
70 |     if(d < 0):
71 |         d += phi
72 |         
73 |     return ((e,n),(d,n))
74 |         
75 | def decrypt(ctext,private_key):
76 |     try:
77 |         key,n = private_key
78 |         text = [chr(pow(char,key,n)) for char in ctext]
79 |         return "".join(text)
80 |     except TypeError as e:
81 |         print(e)
82 | 
83 | def encrypt(text,public_key):
84 |     key,n = public_key
85 |     ctext = [pow(ord(char),key,n) for char in text]
86 |     return ctext
87 | 
88 | if __name__ == '__main__':
89 |     public_key,private_key = generate_keyPairs() 
90 |     print("Public: ",public_key)
91 |     print("Private: ",private_key)
92 |     
93 |     ctext = encrypt("Hello World",public_key)
94 |     print("encrypted  =",ctext)
95 |     plaintext = decrypt(ctext, private_key)
96 |     print("decrypted =",plaintext)
97 |   


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