The modular exponentiation should be performed modular version of repeated squaring method.This is considered helpful if you consider client's low power devices. This helps to reduce the number of multiplications. Message = 'hello this is my encrypted message'ĭecrypted_message = rsa.decrypt(encrypted_message) Return (cls.prime_factor, cls.public_key, cls.private_key) X = (cls.public_key * cls.private_key - 1) % totient # calculate the private key based on public key and totient when (public_key * private_key - 1) % totient = 0 # and the prime_factor as suggested in the article) # (Note above link has an error that the gcd of public_key and totient must be 1, not public_key # of the public_keys could have been selected # calculate the possible public keys where gcd(public_key, totient) = 1, then select the 5th one (this is abritary, any ''' methods for calculating keys, encrypt and decrypt ascii gcd(a, b): so for example (2, 191) will do as well as (11, 17)
prime factor must sufficiently large to accommodate the ascii numbers, let's say > 150 prime numbers must be > 1 and not equal How is this solved in practice? and how is this all working with really large primes?Ĭomments, suggestions welcome. One observation is that with large prime numbers encryption goes relatively fast starting with ascii code numbers that are relatively small less than 200 or so, but the decryption goes much slower as the encrypted numbers are magnitudes larger. Fascinating what you can do in a few lines of code and how Python can handle to powering of large numbers. To calculate the keys I used the explanation in this link: rsa public private key encryption explained. Inspired by a Numberphile video I made a little program that shows the principles of RSA encryption and decryption.
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