Chapter 24 – Public Key Cryptography and the RSA Cipher 387

makeRsaKeys.py

7. def main():


8. 
   

   create a public/private keypair with 1024 bit keys

   
   


9. print('Making key files...')


10. makeKeyFiles('al_sweigart', 1024)


11. print('Key files made.')

When makeRsaKeys.py is run, the main() function is called, which will create the key files.
Since the keys might take a while for the computer to generate, we print a message on line 9
before the makeKeyFiles() call so the user knows what the program is doing.

The makeKeyFiles() call on line 1 0 passes the string 'al_sweigart' and the integer
1024. This will generate keys with a size of 1024 bits and store them in files named
al_sweigart_pubkey.txt and al_sweigart_privkey.txt.

The Program’s generateKey() Function

makeRsaKeys.py

13. def generateKey(keySize):


14. 
    

    Creates a public/private key pair with keys that are keySize bits in

    
    


15. 
    

    size. This function may take a while to run.

    
    


16. 
    


17. 
    

    Step 1: Create two prime numbers, p and q. Calculate n = p * q.

    
    


18. print('Generating p prime...')


19. p = rabinMiller.generateLargePrime(keySize)


20. print('Generating q prime...')


21. q = rabinMiller.generateLargePrime(keySize)


22. n = p * q

The first step of creating keys is coming up with two random prime numbers which are called p
and q. The generateLargePrime() function we wrote in the last chapter’s rabinMiller.py
program will return a prime number (as an integer value) of the size determined by the value in
keySize on line 19 and line 21. These integer values are stored in variables named p and q.

On line 2 2 , the number n is calculated by multiplying p and q, and stored in n.

makeRsaKeys.py

24. 
    

    Step 2: Create a number e that is relatively prime to (p-1)*(q-1).

    
    


25. print('Generating e that is relatively prime to (p-1)*(q-1)...')


26. while True:


27. 
    

    Keep trying random numbers for e until one is valid.

    
    


28. e = random.randrange(2 (keySize - 1), 2 (keySize))


29. if cryptomath.gcd(e, (p - 1) * (q - 1)) == 1: