Cryptograph - Public Key Algorithm

In traditional method of encryption and decryption of a particular plain text (data to be encrypted), a key was used to encrypt the data and the data was transmitted to the person who was intended receiver of the information. But the major flaw of their technique was that the method used to encrypt the data was not strong enough, and the key that was used to encrypt the message was also needed to transfer so that the intended receiver of the message to decrypt it can use it at the other end. In such scenario, if an intruder could steal the key, then the method that was used to encrypt the message was useless.

Distribution of key had always been a problem, as there were chances of intruder getting the key by any chance. In 1976, two researchers at Stanford University, Diffie and Hellman formed a method that would help solving the problem with the key distribution. Diffie and Hellman proposed a cryptosystem in which the encryption key and the decryption key were different. The important point was that, the decryption key could not be derived from the encryption key. According to their method, the encryption algorithm (E) and the decryption algorithm (D), had to meet the following three requirements:

1) D(E(P)) = P
2) It is exceedingly difficult to deduce D from E.
3) E cannot be broken by chosen plain text attack.

According to the first requirement, if we apply decryption algorithm (D) to the encrypted data/message E(P), we get the original message, P, back. As per second requirement, it should be nearly impossible to deduce decryption algorithm (D) from encryption algorithm (E). And as per third requirement, it may happen that intruder try to figure out the encryption algorithm with the help of plaintext, but the encryption algorithm (E) should be made in such a way that it cannot be broken easily by using anticipation.

Suppose two persons A and B wish to communicate with each other over the Internet, but at the same time they do not wish their message to be read by any other person. A will device his/her own encryption algorithm, a decryption algorithm, an encryption key (Ea) and a decryption key (Da). A makes the encryption algorithm public along with encryption key, but will keep the decryption key (Db) private.

Similarly, B will device his/her encryption algorithm, decryption algorithm, Public Key i.e. encryption key (Eb) and a decryption key (Db). B will also make his/her encryption algorithm and encryption key (Eb) public keeping decryption key (Db) private. Now if A&B are on net and are willing to send message to each other, then A will take a plain text P and will encrypt it (Eb(P)) using the encryption algorithm (Eb) and encryption/public key (Eb) provided by B. A then will send this message to B and B will use his/her decryption key (Db) to retrieve plain text i.e. Db(Eb(P)) = P. Same way B will use A's public key (Ea) and encryption algorithm to send a message to A. This way A and B will encrypt the data and will send it to the other person, as it is exceedingly hard to anticipate decryption key (D) from the encryption key (E), which is made public, no one else except for A and B will be able to retrieve the message. Thus A and B will be able to communicate successfully with each other.