In cryptography, a `Three-Pass Protocol' facilitates a secure communication of confidential messages, over insecure channels, without the need of any exchange of keys. Each communicating entity is required to generate a pair of keys, related to each other. One of the keys is used for encryption and the other key is used for decryption. Transmission of information between a sender and the intended recipient requires making of three passes. Each pass involves exchange of an encrypted message between the communicating entities. In pass 1, the sender encrypts the plain text with one of its keys and sends the resulting cipher text to the intended recipient. The intended recipient further encrypts the received cipher text with one of its keys and bounces the doubly-encrypted cipher text back to the sender. This cipher text exchanged in pass 2 has double encryption—one applied by the sender and the other applied by the intended recipient.

The sender decrypts the doubly-encrypted cipher text using its second key and removes its part of the encryption. The resulting cipher text now has only one encryption—the one applied by the intended recipient. In pass 3, this singly-encrypted cipher text is sent by the sender to the intended recipient. The intended recipient receives the cipher text and removes the residual encryption using its second key; and successfully recovers the original plain text, meant to be conveyed to the intended recipient in a secure way. In all the three passes, the message is encrypted—having single encryption during passes 1 and 3 and double encryption during pass 2. Thus, the two communicating entities are able to exchange information in a secure way, without any need of exchange of keys.

This paper proposes three new Three-Pass Cryptosystems. All the three schemes draw their strength from the difficulty of computing discrete logarithms (Diffie and Hellman, 1976 and 1979 and ElGamal, 1985). The first two schemes are highly efficient requiring less computation in all the three passes; but are prone to `cipher text only attacks'. The third scheme, though involving extra computation, is highly robust against any "cipher text only attacks".

Three-Pass Cryptosystems Based on Discrete Logarithms, encryption, decryption, extra computation, highly robust, cipher text only attacks, communicating entities, doubly-encrypted, residual encryption, exchange of keys, Extended Euclid's algorithm, Prime numbers, Primitive roots, Galoi's field.