RSA-Encrypt

This program implements the RSA encryption scheme in C++ and allows for encryptng and decrypting integers.

How RSA Encryption Works

Setup

1. Let e = 65537
2. Find two large unique prime numbers p and q
3. Calculate n = pq
4. Calculate ϕ(n) = (p - 1)(q - 1)
5. Make sure that 1 < e < ϕ(n) and e is coprime with ϕ(n)
6. Solve the congruence ed === (mod ϕ(n))
7. Your public key is (e, n) and your private key is (d, n)

Public Key (e, n)

• The public key is used for encrypting a message M
• To do so, we perform the operation C === M^e (mod n)
• C is your ciphertext (encrypted number)

Private Key (d, n)

• The private key is used for decrypted the ciphertext C to retrieve the original message M
• To retrieve M, we calculate M === C^d (mod ϕ(n))
• M is your original message