HeshamTB
1993551a59
TODO: - Clean up - Split into methods - Save a key pair in a file (interactivly)?
79 lines
2.1 KiB
Python
Executable File
79 lines
2.1 KiB
Python
Executable File
#!/usr/bin/python3
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#program to generate rsa key pair using methods in EE-305
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# Hesham Banafa
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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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#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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def isPrime(number):
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if number == 2:
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return True
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#if 2 devides number then num is not prime. pg.21
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if number % 2 == 0 or number == 1:
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return False
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#largest integer less than or equal square root of number (K)
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rootOfNum = math.sqrt(number)
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K = math.floor(rootOfNum)
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#Take odd D such that 1 < D <= K
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#If D devides number then number is not prime. otherwise prime.
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for D in range(2, K):
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if D % 2 == 0:
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pass
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else:
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if number % D == 0 or number % 5 == 0:
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return False
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return True
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if __name__ == "__main__":
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main() |