Three-pass protocol

The Massey- Omura scheme is a cryptosystem which allows two parties without the existence of public keys or shared secret keys exchange messages confidential. It is based on the difficulty of the discrete logarithm.

The Massey- Omura scheme was developed in 1983 by the cryptographer James Massey and Jim Omura.

Requirements

Condition of Massey- Omura scheme is the common knowledge of all participants to a large prime number.

In addition, each participant generated for communication a key with which to be relatively prime, so it is valid.

This is determined the number (for example, by means of the extended Euclidean algorithm ). It is the multiplicative inverse of modulo. Hence:.

Now applies to all messages:

Due to the small set of Fermat.

Expiration

As an example, one participant A is to transmit the confidential message to subscriber B. They have both, in addition, each knows only its own key and or and.

A now forms and sends the resulting number of B.

B exponenziert with the received message and responds.

A is generated, which corresponds according to the little theorem of Fermat and sends it back to B. Thus A has the effect of exponentiation with the " lifted " only known to him. However, the message is still " protected" by the exponentiation or encrypted.

B can now win by exponentiation with the message: .

From all the messages exchanged can not be deduced without knowledge of the key participants.

Safety considerations

The Massay - Omura scheme is secure against passive eavesdropping of messages, that third parties can not be returned close to the original text of the messages exchanged. However, it is vulnerable to a man-in -the -middle attack ( Janus attack). By the assumed severity of computing discrete logarithms is to open up the original text almost impossible elected by a participant T key and using a recorded through message even with existing knowledge.

• Cryptologic method