Security
A necessary condition for a three-pass algorithm to be secure is that an attacker cannot determine any information about the message m from the three transmitted messages E(s,m), E(r,E(s,m)) and E(r,m).
For the encryption functions used in the Shamir algorithm and the Massey-Omura algorithm described above, the security relies on the difficulty of computing discrete logarithms in a finite field. If an attacker could compute discrete logarithms in GF(p) for the Shamir method or GF(2n) for the Massey-Omura method then the protocol could be broken. The key s could be computed from the messages mr and mrs. When s is known, it is easy to compute the decryption exponent t. Then the attacker could compute m by raising the intercepted message ms to the t power. K. Sakurai and H. Shizuya show that under certain assumptions breaking Massey-Omura cryptosystem is equivalent to the Diffie-Hellman assumption.
Read more about this topic: Three-pass Protocol
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