Variable d is kept as the private key exponent. Recall that we defined this function earlier.

Calculate d, which is the multiplicative inverse of e and phi.

We derive the random integer e such that, e and phi are coprime.

Recall that coprime refers to two or more positive integers having no positive integer factors in common aside from 1.

This is the function that counts how many integers below a given integer are coprime to it. We calculate phi which is the totient function of n, specifically the Euler’s totient function.Also, as you can see from the return value of the generate_keypair() function, it is disclosed as part of the public key. Value n is the modulus of both the public and private key and is also used as the key length. The product of p and q is calculated as n.These numbers have to be prime and are kept secret.

The function accepts two random prime integers p and q.

Here’s a rough outline of how this is done: It is the core component of the RSA algorithm.

The generate_keypair() function does just that: generate our public and private keys.

The Multiplicative Inverse is defined as a number which when multiplied by the original number gives the product as 1.

The multplicative_inverse() function is used to calculate the Multiplicative Inverse which is part of our private key.

This function simply takes two integers a and b and returns the GCD. This is the largest positive integer that would divide both numbers without leaving a fraction. Recall that the GCD in Math is short for Greatest Common Divisor and is also called the Highest Common Factor or HCF.

We define our function gcd() which will take two integers: a and b.

First we import our modules: random and sympy.

Let’s explain what is happening here, step by step: Advertisements Let’s write some code: import randomĬipher = Messages or data can be encrypted by anyone using the public key, but can only be decrypted by someone who knows the specific prime numbers.įollowing is a simple implementation of the RSA algorithm. The prime numbers are usually kept secret.

Someone using RSA encryption would have to create and publish a public key based on two large prime numbers. Recall that a key is basically a string of characters used within an encryption algorithm. In this system of encryption there are two keys: a public key and a private key. AES encryption, alternatively, is a block cipher. The term RSA is an acronym for Rivest– Shamir– Adleman, which are the surnames of its creators. RSA is a public/private key based system of cryptography developed in the 1970s. Let’s do an RSA Algorithm Encrypt/Decrypt Example with Python.

Decrypt rsa with private key python