Asymmetric Cryptosystems

Throughout the history of cryptography, hundreds of cryptosystems have been developed. The earliest ones, as well as many later ones, relied on the complete secrecy in transferring keys between the sender and recipient. These kinds of systems, called secret key cryptosystem, have just a single key which is used for both encryption and decryption; therefore, these systems are more frequently known as symmetric cryptosystems. In contrast to a symmetric cryptosystem, an asymmetric cryptosystem is associated with a pair of keys; therefore, not everything related to the cryptosystem needs to be kept secret. This kind of a cryptosystem is also called public-key cryptosystem. A public key cryptosystem consists of a public key, which is used for encryption, and a private key, used for decryption. Therefore, anybody can encrypt plaintext since the encryption key is available to everyone, but only the holders of the private key corresponding to the public key used for encryption can decrypt the ciphertext [2]. The first asymmetric cryptosystems appeared in 1970s to address the problem of key management in symmetric cryptography. In 1976, Whitfield Diffie and Martin Hellman published a key management scheme that was the predecessor to the first public-key cryptosystems; it later became known as the DiffieHellman Key Exchange Protocol. Later, several asymmetric cryptosystems were developed, including ElGamal, Rabin, and RSA cryptosystems ([2], [1]).