Massey-Omura scheme
The Massey-Omura scheme is a cryptosystem that allows two parties to exchange messages in confidence without the existence of public keys or shared secret keys . It is based on the difficulty of the discrete logarithm .
The Massey-Omura scheme was developed in 1983 by cryptologists James Massey and Jim Omura .
requirements
A prerequisite for the Massey-Omura scheme is the common knowledge of all participants about a large prime number .
In addition, each subscriber generated for the communication a key with which relatively prime to is, so we have: .
The number is determined for this (e.g. using the extended Euclidean algorithm ) . It is the multiplicative inverse of modulo . Thus: .
Now applies to all messages :
based on Fermat's Little Theorem , da
procedure
As an example, subscriber A should transmit the confidential message to subscriber B. You have both , in addition, each only knows his own key and or and .
A now forms and sends the resulting number to B.
B raises the received message to the power and replies .
A generated , which after the small Fermat's theorem corresponds and sends this back to B. Thus, A has the effect of exponentiation with the known only to him to "canceled." However, the message is still encrypted by the exponentiation .
B can now by exponentiation with the message win: .
It is not possible to infer from all exchanged messages without knowing the key of the participants .
Safety considerations
The Massey-Omura scheme is secure against passive eavesdropping on messages; H. Third parties cannot infer the original text from the messages exchanged. Furthermore, due to the assumed severity of the calculation of discrete logarithms , it is almost impossible, even with existing knowledge of the original text , to open up the key selected by a subscriber T and with the aid of a recorded message .
However, the method is susceptible to a man-in-the-middle attack (Janus attack) by proceeding similarly to a man-in-the-middle attack on the Diffie-Hellman method .