quadratic formula in python for rsa decryption

# then to a big integer which should be encrypted, but here for the sake of # ideally we should convert the plain text to byte array and The following code shows how the encryption / decryption can be done: def rsa_encrypt(plain_text, e, n): Python code for steps 1-5: p, q = 937, 353 # use large primes hereĮ = 5 # choose public key e as a prime, s.t., gcd(φ, e) = 1ĭ = multiplicative_inverse(e, φ) # private key dĦ.Encrypt the message (plaintext) with the receiver's public key ( e) at sender's endħ.Decrypt the ciphertext received at the receiver end with his private key ( d) d*e ≡ 1 (mod φ(n)), using the multiplicative inverse algorithm (extended Euclidean) from here:Ĭompute multiplicative inverse of a modulo n # solution t to a*t ≡ 1 (mod n) The implementation of RSA can be further simplified as follows:ġ.Choose two different large primes, here for the sake of simplicity let's choose p=937, q=353, as done in the exampleģ.Compute Euler Totient φ(n) ≡ (p-1)*(q-1)Ĥ.Choose the public key e as coprime with φ(n), for simplicity, let's choose e=5, which is a primeĥ.Compute the private key d, s.t. In any case, you might want to swap the keys and values in your dictionary: right now your find_key might as well be using a list, as you're simply searching over all the k,v pairs until you find a match. As well, if you want to turn a letter into a number, and you don't really care what number, you could use the 'ord'/'chr' functions, and not even need a dictionary. The following aren't bugs, but suggestions: you should probably use pow(c,d,n) rather than (c**d)%n for large numbers the former will be much faster. You want modInverse(e, phi(n)), not modInverse(e, n) see this worked example.Īfter fixing those, it seems to work for me. (4) You're taking the wrong multiplicative modular inverse. (3) Your alpha should be alpha (otherwise you'll get '96llo, worl5'). (2) You also don't check to see that p != q.

Getting a composite will lead to problems.

Q = random.choice(primes_range(Low, High))Ĭhar_array.append(encrypt_byte(alpha], e, n)) P = random.choice(primes_range(Low, High)) The code: import fractions, sys, random, math I decided to write a simple RSA encryption implementation in Python, but every time I run it it prints the error Inde圎rror: list out of range when it's decrypting and in find_key.

Quadratic formula in python for rsa decryption