Working key pair generation, encryption and decryption
TODO: - Clean up - Split into methods - Save a key pair in a file (interactivly)?
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rsa.py
38
rsa.py
@ -5,14 +5,48 @@
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import math
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import os
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import decimal
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def main():
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#Prime of size 32 bit random
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print(getPrime(32))
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#Primes of size 32 bit random
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#resulting in a 64-bit key mod
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p = getPrime(32)
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print("p: ", p)
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q = getPrime(32)
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print("q: ", q)
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n = p*q
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print("n: ", n)
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print("%d bit key" % n.bit_length())
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#lamda(n) = LCM(p-1, q-1)
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#Since LCM(a,b) = ab/GCD(a,b)
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#gcd = math.gcd(p-1, q-1)
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#print("GCD: ", gcd)
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#lcm = abs((p-1) * (q-1)) / gcd
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#print("LCM: ", lcm)
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phi = (p-1)*(q-1)
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print("phi: ", phi)
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#e exponant should be 1 < e < lamda(n) and GCD(e, lamda(n)) = 1 (coprime)
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# recommended value is 65,537
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e = 65537
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d = pow(e,-1,phi)
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print("d: ", d)
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print("--------------")
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print("public key (%d, %d)" % (n,e) )
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msg_text = "Hello"
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msg_number_form = int.from_bytes(msg_text.encode(),"little")
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print("Message: %s or %d" % (msg_text, msg_number_form))
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msg_encrypted_number_form = pow(msg_number_form, e, n)
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print("Encrypted msg: ", msg_encrypted_number_form)
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msg_decrypted_number_form = pow(msg_encrypted_number_form, d, n)
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print("Decrypted msg: ", msg_decrypted_number_form)
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def getPrime(bits):
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while True:
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#Byte order "little" or "big" does not matter here since we want a random number from os.urandom()
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x = int.from_bytes(os.urandom(int(bits/8)),"little")
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if isPrime(x):
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return x
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