The RSA Public-Key Encryption Algorithm

Definition:The RSA is one of the popular public-key encryption algorithms.

Rivest et al published a method for obtaining digital signatures and public-key cryptosystems in 1978 [1]. In order to use the method, the encryption and decryption keys must be chosen as follows:

• 1. Compute n as the product of two primes p and q: n=p×q. These two primes are very large and randomly selected primes.

• 2. Compute φ(n)=(p−1)(q−1).

• 3. Select e such that e is relatively prime to φ(n).

• 4. Select d such that e×d≡1 mod (φ(n), where stands for modular operation.

• 5. Choose (e, n) as the public key.

• 6. Choose (d, n) as the private key.

In encryption and decryption, receiver’s public key (e _R , n _R ) and private key (d _R , n _R ) are used. Encryption is carried out by using mod n _R , where m is the plaintext and m _c is the ciphertext. Decryption is carried out by using mod n _R .

For authentication, sender’s public key (e _s , n _s ) and private key (d _s , n s) are used. The signature is generated by using mjod n...