Masey-Omura scheme

The Masey-Omura scheme is a scheme that enables encryption without shared keys (based on the discrete logarithm problem).

Principals share some (public) prime $p$ . Principals $u \in {A, B}$ chooses (private) $e_{u}, d_{i} \in Z$ such that $e_{u} d_{u} mod (p - 1) = 1$ So $(p - 1) ∣ (e_{u} d_{u} - 1)$ . So there is a $k$ where $e_{u} d_{u} = k (p - 1) + 1$ . Hence, by Euler’s theorem, for all $m \in {1, \dots, p - 1}$ :

m^{e_{u} d_{u}} mod p = m^{k (p - 1)} m mod p = m mod p = m

Steps go as follows:

$A \to B : m^{e_{A}} mod p$
$B \to A : m^{e_{A} e_{B}} mod p$
$A \to B : m^{e_{A} e_{B} d_{A}} mod p (= m^{e_{B}})$
$m^{e_{A} e_{B} d_{A} d_{B}} mod p (= m)$

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Masey-Omura scheme

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