Experiment 4
Aim: - Implementing RSA Algorithm
Theory: - The RSA algorithm is named after those who invented it in 1978: Ron
Rivest, Adi Shamir, and Leonard Adleman.
The RSA algorithm is an asymmetric cryptography algorithm; this means that it
uses a public key and a private key (i.e two different, mathematically linked keys).
As their names suggest, a public key is shared publicly, while a private key is
secret and must not be shared with anyone.
How it works:
The RSA algorithm ensures that the keys, in the above illustration, are as secure
as possible. The following steps highlight how it works:
1. Generating the keys
i. Select two large prime numbers, xx and yy. The prime numbers need to be
large so that they will be difficult for someone to figure out.
ii. Calculate n = xn=x x yy.
iii. Calculate the totient function; \phi(n) = (x-1)(y-1)ϕ(n)=(x−1)(y−1).
iv. Select an integer ee, such that ee is co-prime to \phi(n)ϕ(n) and 1 < e < \
phi(n)1<e<ϕ(n). The pair of numbers (n,e)(n,e) makes up the public key.
v. Calculate dd such that e.d = 1e.d=1 modmod \phi(n)ϕ(n).
d can be found using the extended euclidean algorithm. The pair (n,d)(n,d) makes
up the private key.
2. Encryption
Given a plaintext PP, represented as a number, the ciphertext CC is calculated as:
