Inputs:

1. Two prime numbers: p and q

2. The message to be encrypted (this is an integer): m

Required features:

1. An independent method that could be used to compute gcd of two numbers using the Euclidean algorithm: gcd(a,b) = gcd(b,rem(a,b))

2.Ability to find the values of two integers s and t such that gcd(a,b) = sa+tb . This should be implemented as an independent method. This method is the Pulverizer or the Extended Euclidean algorithm.

3. Compute the public and private keys. You need to think about an intelligent way to utilize the routines that you have developed in Step 1 and Step 2

4. Perform encryption and decryption.

5. The application should print the encrypted message on the output screen and should also verify that decryption actually reproduce the original message.

6. Your application should NOT be using any built in libraries.

7. Use the (%) operator to compute the remainder

8.You may compute rem(a^x ,b) using successive squaring. For example, all the congruences below hold modulo 17

Need help with this C++ program please dont use java. Thanks for the help.

The RSA Cryptosystem Beforehand The receiver creates a public key and a secret key as follows 1. Generate two distinct primes, p and Since they can be used to generate the secret key, they must be kept hidden 2. Let n 3 pa 3. Select an integer e such that grd(e,(p-100g -1) 31.The public key is the pair (e, n) .This should be distributed widely. 4. Compute d such that de 10mod (p-1)(q-1)). This can be done using the Pulverizer. The secret key is the pair(d,n).This should be kept hidden! Encoding: Given a messagem, the sender first checks that grd( m, n The sender then encrypts message m to produce m' using the public key m rem (m ,n Decoding: The receiver decrypts message m' back to message m using the secret key m rem mn ,n Develop an application that will implement the RSA cryptosystem