Cipher security is becoming an important step when transmitting important information through networks. The algorithms of cryptography play major roles in providing security and avoiding hacker attacks. In this work two hybrid cryptosystems have been proposed, that combine a modification of the symmetric cryptosystem Playfair cipher called the modified Playfair cipher and two modifications of the asymmetric cryptosystem RSA called the square of RSA technique and the square RSA with Chinese remainder theorem technique. The proposed hybrid cryptosystems have two layers of encryption and decryption. In the first layer the plaintext is encrypted using modified Playfair to get the cipher text, this cipher text will be encrypted using squared RSA to get the final cipher text. This algorithm achieved higher security to data but suffers from a long computational time. So Chinese remainder theorem has been used in the second hybrid cryptosystem to obtain less encryption and decryption time. The simulation results indicated that using the modified Playfair with the proposed square RSA has improved security. Moreover, using the Chinese remainder theorem achieved less encryption and decryption time in comparison to our first proposed and the standard algorithms.
