We would now have to choose a number d (for ‘decryption’), such that d*e (mod 𝜙) = 1. (i) 1 ' + str (e ) ) #Display the public key print ( ' Public Key -> (' + str (public_exponent ) + ', ' + str (RSA_modulus ) + ')' ) Public-Key exponent, e -> 3 The number e must obey the following two properties. We will now have to select a number e (for ‘encryption’) that will be our public-key exponent.

Totient = (prime1 - 1 ) * (prime2 - 1 ) print ( ' Euler's totient -> ' + str (totient ) ) Euler's totient -> 59800 #Calculate and display the Euler’s totient. We will now have to calculate the Euler’s totient φ = (p-1)(q-1). Thank You!!! You have chosen the desired key size to be of 16 bits. Please do not go for more than a 24 bit key because Python is too slow for larger numbers. Print ( ' RSA Modulus r -> ' + str (RSA_modulus ) ) Prime2 = randprime ( 3, 2 **key_size / 2 ) #Display the two prime numbers print ( ' 1st Prime Number -> ' + str (prime1 ) ) print ( ' 2nd Prime Number -> ' + str (prime2 ) ) #Calculate and display the RSA modulus r Prime1 = randprime ( 3, 2 **key_size / 2 ) Return lastremainder, lastx * ( - 1 if aa 2 **key_size : Lastremainder, (quotient, remainder ) = remainder, divmod (lastremainder, remainder ) X, lastx, y, lasty = 0, 1, 1, 0 while remainder : Lastremainder, remainder = abs (aa ), abs (bb ) #The following two functions will return a value of d when you pass it the parameters public-key exponent and totient.

#Importing the greatest common divisor method from math from math import gcd #Importing the SymPy library from sympy import randprime Our code should have the logic to ensure that the RSA modulus r is less than 2^KeySize. Therefore, we need to check in our code that the RSA modulus r is not too large for the desired key size. For example, if we want to use a 8-bit key, the RSA modulus r cannot exceed 2^8 = 256. IMPORTANT NOTE: - Talking about the key size (in bits), it is the RSA modulus r that is constrained. And, as we know, the RSA modulus r is used later on in the encryption and decryption processes. r = p* q (remember that the fundamental basis of the RSA Asymmetric Encryption Process is the fact that it is extremely easy to compute the RSA modulus r = p*q, but very difficult to reverse). Once we have the two (different) prime numbers, we should calculate the RSA modulus r. We need to ensure that the two prime numbers generated are different. SymPy has a method called randprime() that can generate a random prime between two numbers. We are going to use the SymPy built-in Python module. The very first step is to generate two prime numbers, p and q. Implementing the RSA Asymmetric Encryption Process in Python The code has been broken down into three distinct tasks - Key Generation, Encryption and Decryption. This technical article walks the reader through the Python code that can be used to implement the RSA Asymmetric Encryption Process.

How to decrypt rsa python